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LIBRARY OF USEFUL KNOWLEDGE.
ON THE
VALUE OF ANNUITIES
REVERSIONARY PAYMENTS,
NUMEROUS TABLES.
BY
DAVID JONES,
ACTUARY TO THE UNIVERSAL LIFE ASSURANCE OFFICE.
UNDER THE SUPERINTENDENCB OF THE SOCIETY FOR THE
DIFFUSION OF USEFUL KNOWLEDGE.
VOLUME!^
LONDON:
BALDWIN AND CRADOCK, PATERNOSTER-RGW.
1843.
Digitized by VjOOQ IC
GENERAL
COMMITTEE.
CftMnNM—TlM llffht Hon. LORD BIOUOHAM. P.ILS., Mcntar of Hm If •tioMd
IiMttUitc of Pruioe.
ne»-Cft«{nnM.—TlM Bight H«i. KARL SPENCER.
WjUlrt^Riq^ff. t. Hid 1, A.«.
t: WBL Bf «Ml«ftt B^ . . P a , rtd
Jahn C«pallf, M^tl.
The nifttt Pli*f , I he ULi1in|i of
Sir llt'orr L% li tlv^hE', PFl.R.
The fit. Vim. lionl I.lvn'i1jia.
Samuel t9»i-kv..«lb. Klf|
TlV tUjEhl Krr. il» BiJiop of
nwrlimm, |1,T>.
T P. ini«, E«i|.tA,M..P St.AA.
John eillDUm, M Jl.. P.H.S.
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Jnlia l<\<rti^. M II- l-.R i?.
Sir 1= L= l.;Ml.l«nttl* lUn , t'.R.
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Riftlii t|i?n. I^nl WTOllnlcT^
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J. A.Yiktev^E*].
LOCAL COMMITTEES.
>ltt<m. SttifardMr^^Vfy. J. P.
JoBCt.
^iu|<<aM-R««. E. irUIIUM.
K«T. W. Johnton.
Bonutapf* IteiKniR. E«4|.
William Gribble. Em).
BtthuU—Ja*. L. Drummoad,
Birn^iifftam — Pmil Moon
JnmM, Ewi., 7V*«.
1nt. VKllliuut. Em|.
Briflol— J. N. Sander*,
PjG.8., Ckatrmtm.
li«q.
J. RamoldB, Rcq., TVcoj.
J. B. 'teatlin. Era., ¥.l..9.,S«t.
CMcBlto— Ja«M» Vouag, Baq.
C. H. Cameron. F.«n.
Camibridgt—nvf. {.raanrd; J«-
nyns. M.A..P.L.S.
Rev. John Lodge, M.A.
R«e. Pror^kSedgwiclu M.A.,
' P.R.5. A n.s.
CMlerftnry— John Brent, Esq.,
Alderman.
TPiiliam Mnttcn. Eeq.
CorMW*— Thomas Bancs,M.D.,
P.R.S.B.
CmrmflinwM— R. A. Poole, Eaq.
tniliam RoberU, Em.
CImUr—Umrj PoUe, Em.
€Mckttl*r-C. C. Dcndj. Rwi.
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PlaUi retridct.
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Edward 8iruM, Eeq.. MT.P.
Dmmpmrt «nd Siotuham*
John Colo, Eaq.
John Norman, Eeq.
Lt.-CnL C. Hamilton Smilb,
P.R.S.
Dmham-^Very Rrr. the Dean.
Mintergii-J. 8. Traill, H D.
JBfnwfa-^M. Wedgwood, Km.
Bj*«er-J. T]rrrdl.lBM|.
John MiUbrd, E»n. (Coavtr.)
^ O/amorgoiulUr*— W. Williomt,
AlesNuder If c6 rigor, E«<v
Jamec Coaner, Beq.
A. J. D. D'Urter, Etq.
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UiUhmm, SnJTJk, Per. Profeei.
Hentlow, II.A., P.US. and
0.8.
Hull—JmM. Bowden. Em.
L«de->f. MarUall, Eaq.
I.«iM*— J. W. Woollgar, S*q.
Reory Browne. Em.
LiMrpotrf Local AuoeuUim—
J. MuUeacus, Em.
B«f Wn. ShirphM. LL.D.
Waidffone— Clemeni T. Smjrtb,
John Caae. Eeq.
MoncAcster Local AmockMam—
O. W. Wood, Bm|., II J».,
Chairman..
Sir Benj. HeywDod, Bart.,
Sir O. Pbilipi, Bart.. M.P.
T. N. WinaUalejr, Esq., Horn.
See.
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Em-, P.A.8., CMnirmnn.
W. Snow Harrlii, Fm., P.R.S.
R. Moore. M.D., P.L.S.. He.
mtary.
Q. Wigtitwirk. Vmi.
/Vaafeign - Rt. Hon. Sk H.
Brrdge*. Bart.
A.W. lUria, M.D.
ffipen— Rcr. H. P. Hamilton,
M.A.,F.R.S.andG.S.
Rev. P. Ewart. M.A.
RM/Me— KcT. the Warden.
Huropbre ITS Jnnm, Eaq.
Rydff, >«/« of n'tgU— Sir Rd.
Simeon, Bart.
SMaUrv- Rev. J. Barfltt.
SWWd-J. H.Abraham.Eaq.
Slwftnm Mallet—
a. p. Bnrrougha, Eaq.
SAmrafrary— R. A.8lancr, Eeq.
BaiUk nclkfrUm—
J.Nieholett»,E«i.
Stockport-H. MaraUnd, Em|..
f\rmimer.
Henrj Coppocfc, Eaq. Sm.
Sydn<Y. ^^«w Somtk Watto^
wmiam M. Manning. Eeq.
Mn««*-MaUhew Moggrldge.
Eaq.
IWiflaeA^-Rer. W. Erana.
John Ruadle, Eaq.. M.P.
TVwe— H. Sewftll Stokes, Eaq.
TMnWiilgff ll'aUa— Dr. Yeata.
Vltoaaier — Robert Blnrton.
Kaq.
Fir g ma, U. 8. — ProfeiMr
lucker.
freri-eiCfr — Chartee Hastinga,
M.D.
C. H. Ilebb. Eaq.
rFrcxJbtai— Tbomita Edgworth,
Eaq.
Major Sir WillUm Lloyd.
rarnMmk-C. P.. Rumbold.
Eaq.
Dawaon Tamer, Eaq.
rer*.Rev. J. Kenriek. M.A.
John Phniipe, £«q., P.K.S. ,
F.a.8.
THOMAS C0ATB8, Eeq., 8««re<ory, 4t, Bedford Square.
Digitized by VjOOQiC
PREFACE.
The nmnerouB transactloTis wLicK take place connected with the sale of
Annnitiea and RevetBions, render a knowledge of the principles on which
their values are calculated extremely desirable.
This treatise is intended to give the student an opportunity of acquire
ing a knowledge by no means superficial of the method of calculating
Annuities and Reversions, whether dependent on a fixed number of
yean, or the uncertain tenure of human life.
The First Part, which refers to Annuities and Reversions not dependent
on life, contains algebraical solutions of the different caBes, with the rules
in words and with examples for illustration. The Algebraical Fonnulse,
and practical examples and illustrations, are afterwards given separately
at the end.
The Second Part contains the method of finding the values of An-
nuities and Reversions dependent on the existence of one or more lives,
with A brief account at the end of the difierent Insurance Offices in
London. To avoid misconception on the part of the public, or the
charge of partiality on the part of any of the offices noticed, it must be
observed that the accounts are mere abstracts of the prospectuses issued
by the offices, and the length or brevity of the notices is by tio means
to be considered as a standard of recommendation ; for it will be found,
on inquiry, that the established offices of respectability in general afford
all the solid advantages ofiered by those recently established.
A variety of Tables will be found at the end of the First and Second
Parts.
In the part which treats of Life Contingencies resort has been had
to Mr. Griffith Davies's Method of constructing Tables of the Values
of Annuities, published by him in a small tract in 1825, and a variety
of formulae have been deduced therefrom of considerable utility in
working numerous cases connected with Life Annuities and Assurances.
The advantage of this method is the use which is made of the ele-
ments emploved in the calculation, and which are given under the
Digitiied^yV^UUVlVC
IV PREFACE.
designation of Columns D, N, M, S, and R, for single lives, and
Columns D and N for two joint lives for the Carlisle rate of mortality.
Similar tables are given for single and joint lives by the Northampton
rate of mortality at 3 per cent interest
It affords the Author great pleasure to acknowledge here the liberality
of Messrs. Davies and MHn6 in giving permlssiob to use their respective
works to assist in the objects of this publication. From Mr. Milne's
work have been taken the values of Annuities by the Carlisle table for
single lives, and at 5 and 6 per cent for joint lives. Mr. Davies*s work
has furnished the rates of premiums for two lives by the Northampton,
the values of policies by the same mortality, &c.
The values for two joint lives by the Carlisle 3 per cent were kindly
furnished by Mr. Ansell, Actuary to the Atlas Office, and for two joint
lives by the Northampton 3 per cent by Mr. Ingall, Actuary to the
Imperial. For the D and N columns by the Northampton 3 pei cent,
the author has to express his thanks to Mr. Keys, Secretary to the
Guardian Assurance Office.
It may be here remarked, that all the tables which have been con-
structed for this work have been done independently by two separate
computers, and the results afterwards carefully compared. The tables
for joint lives by the Carlisle rate of mortality at 3 J, 4j, 5, and 6, per
cent have the values interpolated for those ages where Uie difference is not
some multiple of 5. The difficulty of guarding against every source of
error in such a multiplicity of operations has always been felt by the
author, but he trusts that the care which has been bestowed on the
tables has been such as to render them entitled to confidence.
For valuable assistance in the construction of the various tables com-
puted expressly for this work, the Author is indebted to his brother,
Mr. Jenkin Jones, Actuary to the National Mercantile Assurance Office,
and to Mr. David Jones, at present engaged in the service of the Poor
Law Commission.
Those who are not intimately acquainted with Algebra will find it
convenient to possess the Treatise on Arithmetic and Algebra published
by the Society, and frequently referred to in the present work.
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TABLE OF CONTENTS,
PART I.
Page
Simple Interest
Art
4. To find the simple interest and anount of a sum in any nuiul)er
of years 1
6. To find what principal will amount to a given sum at a fixed
rate of interest in a certain number of years ... 2
7. To find in what numher of years the original principal will
amount to a given sum at a fixed rate of interest . . 2
8. To find at what rate of interest in a given number of years the
original principal will amount to a certain sum • • « 3
Diicouni:
11. To find the present value of a sum due at the end of a certain
time at a given rate of interest 3
12. To find the discount « • • ^ 4
Annuities at Simple Interest :
14. To find the amount of an annuity forborne a given number of
years at a fixed rate of simple interest . . • .5
15. To find what annuity will amount to a stated sum in a given
number of years at a fixed rate of interest v.. ... 6
16. To find what number of years an annuity with the simple
interest thereon must be forborne to amount to a certain sum, 7
17. To find at what rate of siinple interest an annuity will amount to
a given sum in a certain number of years • • • . 8
18. To find the present value of an annuity to continue ^ given
number of years at a certain rate of interest • t • 9
Amount of Sums at Compound Interest :
19. To find the amount of a sum put out at compound interest for a
certain number of years 10
.21. To find what principal will amount to a certain sum in a given
number of years .«•••••• 13
Digitized by VLjUUV IC
VI coimfiifTs.
Art. P*ge
22. To find in what number of years a principal put out at com*
pound interest will amount to a given sum • . .13
23. To find at wliat rate of interest the original principal will amount
to a given sum in a certain time 14
IVhen Interest is eonverUhle more than once a Year :
24. To find the amoMW* 11
29- To find tho />n>?cipa^ , 18
30. To find the number of years 19
31. To find the number of intervals • . . . .19
32. To find the rate of interest . • /- • • • .20
Present Value qf Sums at Compound Interest :
35. To find the present value • 23
36. To find the sum due 24
37. To find the numbeiT of years ...••. 25
38. To find the rate of interest « 25
Ty?^en the Interest is convertible more than once a Year :
39. To find the present value 26
41. To find the sum due ........ 27
42. To find the number of years 28
43. To find the rate of interest 28
Amount of 4nntdties at . Compound Interest : .
45. To find the amount 30
46. To find the annuity 32
47. To find the number of years 33
48. To find the rate of interest 35
Present Values of Annuities at Compound Interest :
50. To find the present value 38
52. To find the annuity 40
53. To find the number of years 40
54. To find the rate of interest 41
55. To find the present value when the interest is convertible more
• than once a year • • • 43
Perpetuities :'
56. To find the present value of a perpetuity • . • .44
57. To find the annuity • .' 45
58. To find the rate of interest ••••••• 45
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OONTBlfTS. ¥U
Art. Page
Deferred Anrndtiei :
59. To find the present value of a deferred annuity to continue a
limited number of years 46
60. To find the annuity 46
61. To find the number of years the annuity continues • . 47
62. To find the number of yean the annuity is deferred \ • 48
63. To find the rate of interest « • 48
Deferred Perpetuities :
64. To find the present value ••••.*. 60
65. To find the annuity 50
66. To find the number of years deferred « • . . .51
;67. Tofindtherateofintere^ ••••»•• 51
Renewal of Leasee :
68. To determine the fine which should be paid to renew any number
of years lapsed in the term of a lease • • « .53
77--88. Recapitulation of formuln • • . • . • 57—60
89 — 101. Practical rules and examples •••.•• 61
TABLES.
No.
I. The decimal parts of a pound corresponding to any number of
shillings, pence, and farthings • • . • « 66
II. The decimal parts of a year corresponding to any number of
days 71
III., The amount of £l in any number of years at compound
interest 73
IV. The present value at compound interest of £1 due at the end
of any number of years •«.«•• 79
V. The amount of £1 per annum in any number of years • . 85
VI. The present value of £l per annum for any number of years
not exceeding 100 •...«». 91
VII. The annuity which £l will purchase fbr any number of years
not exceeding 100 97
VIII. Logarithm of the present value of £l due at the end of any
, number of years 103
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VllI CaWTEKTO.
PAB.T II.
Art. ■ Page
Probabilities and Single Premium /or Endoiement :
103. To find the probability of « given life sunrivtng a certain
number of years • • • • • . .109
104. To find the probability of a given life failing within a certain
number of yeara 110
105. To find tbc present value of a sum to be received at the end
of a«ertaia oumbcor ofyean^ presided a given Kfe be then
in existence Ill
106. To find the present value of a sum to be received at the end
of a certain number of years, provided two given lives
jointly survive that period • . • « • .111
1 08. To find the probability of a life failing within a given number
of years •,# 112
109. To find the probability of the jeint existence of two or more
. lives failing within a given number of years • • •112
1 10. To find the probability of any number of lives all dying within
a given number of years 112
111. lb find the probability that one or more of a certain number
of lives shall survive a given period • • • » 112
Construction of Annuity Tables:
112. To find the present value of an annuity on a single life • 113
1 13« The mode of constructing tables of annuities on single lives . 114
] 16. Description of the columns marked D» N, M, S, and R .116
1 1 7. Mode of obtaining Barrett's formula • . • • .117
118. Former mode of forming tables of annuities • • .118
120. To find the annuity which a sum of money will purchase • 119
Construction qf Table qf Eocpectations :
122.* To find the expectation of life • . • • • •120
123. Mode of forming ntabte.of the expeotation . . .121
124. The formula for the expeetation of life «fler a oei4ain number
of years • • • . • • " • • .121
126, To find the expectation of life for a limited number of years 122
Annuity for Two Joint Lives :
1 28. To find the value of an annuity , on two joint lives , • 1 23
Deferred and Temporary Annuities :
133. To find the value of a deferred annuity on a single life .125
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CONTENTS. IX
Art. Pane
137. To 0nd the value of a temporary annuity on a single life » 126
140. To find t]xe annual premium to secure a deferred annuity » 122
Single and Annual Premium for Endowments :
142. To findihe single and annual premium for an endowment • 137
Annuities on Two or Three Lives :
144. To find the value of an annuity on the longest of three lives 133
146. To find by approximation the value of an annuity on three
joint lives •••••••• 133
146. To find the value of an annuity on the longest of two lives . 133
148. To find the value of a deferred annuity on the longest of three
iives • » . 134
149. To flndl the value of a deferred annuity on the longest of two
lives ••••••.•• 136
15 K To find the vdue of a temporary annuity on any numher of
lives « ••••••••• 136
152. To find the value of a deferred temporary annuity • .136
154. 1V> find the annual premium for the same • • • .137
156. To find the value of an annuity payahle so long as two out of
three lives shall he jointly in existence • • • • 138
Survivorehip Annuities :
159. To find the value of an annuity on one life after the decease
of another • • • .^ • • » .139
159. To find the annual premium for the same • • • .139
161. To find the value of an annuity payable during the joint lives
of A and B, and also during t years after the death of B,
provided A shall live so long • • • . .140
162. To find the value of an annuity on a life A, after the failure
of the joint existence of two other lives, P and Q . •141
163. To find the value of an annuity on a life A, after the death of
the survivor of two others, P and Q . . . * . 141
164. To find the value of an annuity on the joint lives of A and B,
after the death of P • • 141
165. To find the value of an annuity on the survivor of two lives,
A and B, after the death of P • * • • . 141
1 78. To find the probability that on« in particular, of two joint
UveSi A and B» shail die before die other • • - • 151
ASSURANCES.
For Life :
187. To find the value of an assurance on the last v survivors of
any numher of lives « • » • « . •154
188. Expression for the single premium on one life « • .155
189. To find the value of an assurance on one life by Davies's
method «. •. • • • • • V .155
Digitized by VjOOQ iC
X eONTBNTS.
Art Vuf^
191. To find the annttal premium for an assurance • • .156
192.- Mode of oonstruetingoolnmnM
1 95. To find the annual premium payablo for a limited number of
years •«•••«••• 161
Deferred and Temporary Assurances :
197. To find the single premium for a temporary assurance . 163
198. To find the same by Davies's method . « 4 •164
200. To find the annual premium for a temporary assurance « 164
205. To find the present value of a deferred assurance • . 1 70
206. To find the annual premium 1 70
207.* To find the single and annual premium for a doicrrcd aasur-
ance, by Davies*s Tables 170
Survivorship Assurances :
213. To find the present value of an assurance on one life against
another • • • * • 172
216. To find the value of a sum payable on the failure of one life,
provided another shall have failed previously • • .174
219. . Fonnula by Davies's method for one life against another • 1 75
224. Formula for one life against another fbr t years • • .176
230. To find the single premium for the assurance of £l payable
on the death of A, provided he die before 6, or wi^in t
years after the death of B • • . • » .184
235. On successive Uves • • • • • • • .186
Loans secured hy Assurance :
244. To find the annuity to be required on a single life Sot a
certain amount of purchase-money, so as to allow the
purchaser a given rate of interest beside the premium
necessary to secure his capital by a life assurance • .189
Valuation of Policies :
252. To find the value of a policy • • • • » .191
Increasing and Decreasing Scale qf Premiums :
257. To find the annual premium that should be required during
the first / years, supposing the annual premium to increase
or decrease a certain sum every t years, and at the end of
V intervals of / years eaeh the premium to cantinMe con-
stant during the remainder of li^ • • « • .194
26 1.^ To 0nd the value of a policy payable by iaereasing <v decreas-
ing premiums •••••••• 195
Increasing and Decreasing Annuities :
262. To find the value of an increasing annuity certain » .196
264. To find the value of an increasing life annuity • * .198
265. To find the value of a decreasing life annuity • . 198
♦ • • •
Increasing and Decreasing Assurances :
266. To find the single and annual premium for an increasing life
aasuraace .- • •* •' •* «- • . .202
Digitiz'ed by VjOOQIC
CONTBMTS JU
Art. Pago
Assurance qf Sums wi inReium qf Premiums :
267. . To find the anaifal premiuai to teoiNr^ a mm «t iha end of n
years, abould the life exiftt 90 long* or Uie vatum of all the
premiums in case of death before that time • • .206
268. To find the annual premium to secure an annuity of £l to be
entered upon at the expiration of n years^ the premiums to
be returned i^ casQ the ^aid life should fail during the n
years • . ,206
269. To find the annual premium for the assurance of a gi^en sum,
and a return of all the premiums • • • . •207
Recapitulation of FbrmiUeB 209
Practical Rules and Exampiee • « • • • 221
TABLES.
Mo.
L Table of rates of mortaUty at Northampton, Carlisle, the
Bqiiitftble Aaauttnoo Oilloe (Daf i«»}i asd according to
the observations of Des Parcieux • • . . 235
II. Oomfarfttive view of the expectation of life at diffomtit
places ••«#««•., 236
III. . Tables from the. experience of the Amieable Corporation • 238
IV. The logarithm and Us arithmetical complement of the
number who complete each year of age, according to Dt,
Price's table of mortality for Northampton • . . 240
V. Proportion that die in each year by the Northampton table
of mortality, also the propoitioA that surriye, and its re-
ciprocal « • . • 241
VI. A preparatory table for finding the values of annuities, &c.
. by the Northampton table of mortality (3 per cent) . 242
VII. The value of an annuity on a single life according to the
Northampton table of mortality . # . . .244
VIII. . Value of an annuity on two joint lives (Northampton 3 per
cent) • • • d . • • • . 246
IX. Value oi a reversion of £1 on a single life (Northampton
rate of mortality) - 288
X. Logaritbin andata aritfametioal complement of the number
vliich completes each year of ag«, according to the Car-
lisle table (^ oaortality • • « . • . . 290
XI. Preparatory table for finding the values of annuities^ assu-
ranees, &e* (Carlisle 3 per cenl) . . .291
XII. ,Ditta (Carlisle 3i per eent) • . «. . . • . • 293
XIII. Ditto (4 per cent) 295
XIV. Ditto (4i per cent) 297
XV. .Ditto (5- per cent) .299
XVI. Ditto (6 per cent) 301
XVII. .Ditto (7.per cent) 303
XVIII. Ditto (8,9,andl0peroent) 305
Digitized by
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No.
XIX.
XXI.
XXII,
XXIIL
XXIV.
XXV.
XXVI.
XXVII.
XXVIIL
XXIX.
XXX.
XXXI.
XXXII.
XXXIII.
XXXIV.
XXXV.
XXXVI.
XXXVII.
XXXVIII.
XXXIX.
XL.
XLI.
CONTENTS.
pAge
Values of annuities on single lives according to the
Carlisle table of mortality 311
Value of £i per annum during the joint continuance of
two liws (Carlisle 3 per cent) .... 315
The present value of £l to be received at the end of
tbe year in vhich an assigned life may fail (Carlisle
rate of mortality) 538
Present value of £l per annum during llie joint con-
tinuance of two lives (Chestef) . . , .542
Showing out of the number entering upon any year
the proportion which die in that year or survive it,
according to the Carlisle rate of mortality ; . .550
The logarithm and its arithmetical complement' of the '
fraction which measures the probability that a life of
an assigned age will survive one year, according to
the Carlisle table of mortality . , . .551
Showing the probabilities of survivorship between every
two lives, whereof the difference of age is either ten
years or any muHiple of ten, according to the Car-
lisle table of mortality 552
Pi^acatory tables >for flnding the values of atmuities
ontwojointlivBsiCwlialeSpercentJ ... 559
Ditto (Carlisle 3j per cent) • .... 609
Ditto (Carlisle 4 per cent) ^59
Ditto (Carlisle 4^ per cent) 709
Ditto (Carlisle 5 per cent) 759
Ditto (Carlisle 6 per cent) 809
Ditto (Northampton 3 per cent) .... 859
Annual premium for assurance of £l00 for 1, 4, 7, or 10
years, and for the whole period of life (Northamplou
3 per cent) 9,^
Annual premium for 1, 5, 7, 10, 15, or 20 payments to
secure £100 at the extinction of a single life (North-
ampton 3 per cent) ^ . q^^
Single and annual premium for assurance of £ 100, pay-
able on the failure of the joint existence of two lives
(Northampton 3 per cent) . . . . .917
Single and annual premium for assurance of £100 on
the death of the last survivor of two lives (North-
ampton 3 per cent) 922
Single and annual premium to secure £ 100 on the
death of A, provided he dies before B (Nortliampton
3 per cent) ^27
Value of £100 policy, charged at the Northampton
rate, on a single life at the end of any number of
years (Northampton 3 per cent) • . . .937
Carlisle rate of mortality and curtate expectotion for
two joint lives •....., 945
Experience of the Amicable Society from April 5*, 1808
to April 5, 1841 ; ,pg(,
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C0KXBN7S.
Xlll
No. Page
XLII. Experience of the Equitable • • « « ^ • 1082
XLIII. Rate of mortality deduced from tbe ej^perience of the
Equitable • • . * • . • .. 1083
XLIV. Expectations of life deduced from experience of the
Equitable ♦ « • , « . .1084
XLV. Tabu of d^rdera of vbicb persons assured by the
Equitable have died from Jan. 1, 1801, to Dec. 31 »
, 1832 .1085
XLVI. Value of an annuity on three joint lives of equal ages
(Carlisle 5 per cent) • • • • « ». ,'1086
XLVIT. Value, of an annuity on threa joint lives, Carlisle 3 per
cent (dijQference of ages 25 and 5) • • . 1087
XL VIII. Value, of an annuity on three joint lives equal ages
(Northampton 3 per cent) • • , • • 1088
Short Account of the London Assurance Offices . 1089
Collection of Legal Decisions connected with Life As-
surances, with remarks . • • « •4161
LIST OP TABLSS IN PART IL ARRANGED ACCORDINtJ TO THE
SUBJECTS.
Rates ofMoriaUty :
L Northampton, Carlisle, Equitable (Davies), and Des Par*
cieux ••♦«.•••« .235
IIL Amicable . . '. 238
XLI. Ditto (extended) 1080
XLIL Equitable (Morgan) . . • * * « 1082
Tables qfihe Expec{aii6n of Life :
IL Chester (males and females), Northampton, Carlisle,
Equitable (Davies), Sweden (General), Des Parcieux,
Government (males and females) .... 236
XIJ. Amicable . • . \ . . . ,1080
XLIV. Equitable (Morgan) 1084
SINGLE LIVES.
Columns p, N, M, S, H*
VI. Northampton
XI.
XIL
XIIL
XIV.
XV.
XVI.
XVIL
XVIII.
CarliOe
Ci^-lisle
3 percent
242
3
. 291
3* -• . .
. 293
4
. 295
4* . ^
. '297
d •••.•• .
» 299
6
301
7 per cent Columns D, N, S« i
» 3^3
8 .. ». . .
. 305
:9 . <» . •. 4 4
, 303
10 ,. «. • <
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by Vj
. 30d
oogle
Xir OOlfTSlTTS.
No. Pagv
Values ofAnHuitiei : *
VII. Northampton 3, 4» 5, 6, 7, 8 per cent . • • 244
XIX. Carlule 3» 3^, 4, 4, 6, C, 7, 8, 9, 10 per oeut » • 311
Logarithm and ArUhmetkal Complement of the number (^Living :
IV. Northampton .240
X. Oarlisie , . • 290
Proportion that die in each year^ also tJw proportion thai survive, and its
rfdprqcal:
V. Norlhampion 241
XXIV. CarlUle 550
XXV. •• Logarithm of lame • • • . 290,551
Values qf Reversions :
IX. Northampton 3, 4, 5, and 6 per eent • « • 288
XXIL Carlisle 3, 3}, 4, 4i 5. 6, 7» 8 per cent • . • 538
XXXIV. Annual premium for assurance of £100 for 1, 4, 7, or
10 years, and for the whole period of life (Northamp-
ton 3 per cent) 915
XXXV. Annual premium for ]> 5, 7, 10, 15, or 20 payments io
secure £ 100 at the extinction of a single life (North-
ampton 3 per cent) .••••• 916
XXXIX. Valueo/£\00 policy after any number of years (NoHh-
arapton 3 per cent) • ' 937
XLIV. Disorders of which lives assured at the Equitable have died 1 084
.
TWO
JOINT LIVBS.
XXXIII. Columns D and N
Northampton
3 per cent
. 859
XXVII.
Carlisle
3
• 559
XXVIIL
3* ..
609
XXIX.
4
. 659
XXX.
44 ..
. 709
XXXI.
5
. 759
XXXII.
;.
c
. 833
Values of Annuities :
VIII. Northampton 3 per cent
• •
. 246
XXI. Carlisle
3
. 315
34
. 463
4
. 352
4*
• &00
5
380
6
. 42G
XXIII. Chester 3 and 5 per
cent.
542
Single and Annual Premiums for Assurance :
XXXVI. Two joint lives (Northampton. 3 per cent) . . . 9 1 7
Last smrrivor of two lives (Ditto) • • . • 922
XXXVUI. On death of A provided he dies before B (Di(le) ' • 927
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CONTENTS. XV
No. Page
Probability of Survivorship :
XXYI. Probabilities of survirorship between every two lives
whereof fhe difference of age is either ten years or
any multiple of ten (Carlisle table of mortality) « 559
XL. Carlisle rate of mortality and curtate expectation • 945
THREE LIVES.
XLVI. Value of an annuity at 5 per cent equal ages (Carlisle) 1086
XLVII. Ditto Difference of age 25 and 5 years 1087
XLVIIT. * Ditto at 3 per cent equal ages (Northampton) 1088
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BXPLANATION OP THE CONSTRUCTION AND USE OF THE
TABLES IN PART I.
Bt means of Table I., the decimal parts of a pound, corresponding to
any number of shillings, pence, and farthings, may be found by inspec-
tion.
Table II. shows the decimal parts of a year corresponding to any
number of days, by means of which, when the rate for a whole year is
given, the proportionate part for any number of days is easily found.
Example, A borrows a sum, for the loan of which he is to pay
simple interest at the rate of £74 6 10 per annum, but wishing at the
expiration of 27 days to repay the amount, it is required to know what
sum he must pay for interest?
By Table I., £74 6 10=:74. 34166
which multiplied by the number i
opposite 27 days in Table II., [.0739726
• • • J
VIZ.
gives 5.499=£5 10, the interest required.
Table III. shows the amount of £l in any number of years, and is
constructed by multiplying the amount of £l in one year by itself,
which gives the amount of £l in two years; this again multiplied by
the amount of £l in one year, gives the amount at the end of three
years ; and so on for any number of years.
At 4 per cent the amount of £l in one year is 1 .04
this multiplied by • . . • 1.04
gives 1.0816 =
the amount of £l at the end of two years.
1.0816x1.04=1 .124864=the amount of ^1 at the end of three
years.
Again, 1. 124864 X 1.04=1. 16985856=:the amount of £l at the
end of four years.
By means of this table the amount of any sum in a given number of
years may be fotrnd by multiplying the amount of £l in the given time,
by the sum of which the amount is required.
Example. To find the amount of £56 in 18 years at 3^ per cent
compound interest, we look in the table under 3J pei cent opposite to
18 years, and there find 1.85748920, which, multiplied by 56, gives
104.018=£l04 0 4, the amount required. Digitized by kjuuvIc
b "^
xviii EXPLANATION OF TABLES IN PART I.
Table IV. is constructed by dividing unity by tbe corresponding num-
ber in Table III : thus, to find the number corresponding to the present
value of £l to be received at the end of 16 years at 5 per cent com-
pound interest, we find in Table III., under column 5 per cent opposite
to 16 years, 2. 18281459 ; then ^ ,g287459 ^ .45811152, the present
value given in Table IV.
By the assistance of this table we may find the present value of any
sum by multiplying the present value of £l by the sum, the present
value of which is required.
Example. To find the present value of £120 to be received at the
end of 9 years, allowing 5 per cent compound interest, we find under
5 per cent opposite to 9 years
.64460892
which multiplied by 120
gives 77.353 =£11 1 1, the present value required.
Table V. is constructed by subtracting unity from the corresponding
number in Table III, and then dividing by the annual interest of £l.
Example. The amount of f I per annum in 15 years at 5 per cent
compound interest is thus found: opposite to 15 years in Table III.,
under column 5 per cent, we fiud 2.01802818, which diminished by
unity gives 1.01892818; this divided by .06 gives 21.518564, which
is the number found in Table V.
This table enables us to fin4 tbe amount of any annuity by multiply
ing the amount in the table by the annuity of which it iy re(}uired to
find the amount.
Example, A has to pay B £30 per annum for 9 lease for 20 yeftrs,
but proposes iu lieu thereof to pay him a fixed suya at tbe expiration of
that term ; what sum should be received so as to allow hm 5 per cent
interest ?
In Table V., opposite to 20 years in column 5 per cent we have
33.065954 '
which multiplied by 30
gives 991.919=£991 19 1 the pum to be received.
Table VI. is constructed by subtracting the number in Table IV, from
unity, and dividing by the annual interest of .^1.
In Table IV., under 5 per cent opposite to 1 1 years we find .58461929,
which subtracted from unity leaves .41532071; this divide by .05,
gives 8.306414, the present value of £l per anijum for 11 yeaw at
5 per cent.
To find the present value of any annuity we muUiply the value given
in the table corresponding to the sum and rate by the annuity of which
t'ne present value is required.
Example, The present value of an annuity of £bO for 18 y^rs at
Digitized by VjUU VIC
EXPLANATION OF TABLES IN PART I. xix
4 per cent is found by extracting from the column headed 4 per cent,
opposite to 8 years, the number
12.65929
which multiplied by 50
gives 632 .^5s= £63*2 19 4, the value required.
Table VII. is constructed l^y dividing unity by the corresponding
number in Table VI. ; thus, in Table VI. at 5 per cent for ten years,
the present value of £l per annum is 1.721735, and =
.129505, the annuity at the same rate, and for a similar term which £1
may purchase.
Multiplying the number in this table by any given sum, we find the
annuity which that sum will purchase.
Example. Under column 3 per cent opposite to 20 years, we have
.067215
which muUiplied by 500
* will give 33.608=£33 12 2, the annuity which may
be purchased for £500 for 20 years at 3 per cent.
Table VI I L shows the logarithm corresponding to the number in
Table IV., the utility of which will be sufficiently obvious to those who
are acquainted with the nature and use of logarithms.
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/; 2
XX.
KXPLANATION OF THE CONSTRUCTION AND USR OF THE
TABLES IN PART II.'
Thb principal tables in this work bein^ deduced from the Carlisle
and Northampton Tables of Mortality, the following extracts are from the
works of Dr. Price and Mr. Milne, explaining the materials from which
they were formed.
(Northampton Table, Dr. Price, *Jth edition, pp. 95 and 10.5.)
In this town, containing four parishes, namely, All- Saints', St.
Giles\ St. Sepulchre's, and St. Peter's, an account lias been kept, ever
since the year 1'741, of the number of males and females that have been
christened and buried (Dissenters included) in the whole town. And
in the parish of All-Saints, containing the greatest part of the town, an
account has been kept, ever since 1135, of the ages at which all have
died there.
In 1746, an account was taken of the number of houses and in-
habitants in the town ; the number of houses was found to be 1083, and
the number of inhabitants 5136. In the parishes of All-Saints and St.
Giles, the number of male and female heads of families, servants, lodgers,
and children were particularly distingnished-— the Heads of families were
701 males and 846 females ; Children, males, 624, females, 759; Ser-
vants, males, 203, females, 280. In St. Peter's, males, 99 ; females, 129.
In St. Sepulchre's, adults, 689 ; children, 477. In the last parish sexes
were not distinguished.
The christenings and burials in the whole town for forty years, from
1741 to 1780, have been as follows : —
Christened jJ^^^Ylca' S} ^^^^' Annual medium 1 58.
»"^^^ -{Females S} '^^^^- Annual medium 189*.
In the parish of AU-Sainta, from 1735 to 1780, or 46 years, —
Christened {pe^^ij,* ^g} ^^^' ■*°''""^ medium 91|.
Buried . {p/^*ales* 2312} '^^^- ^^^^"^ medium 102.
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EXPLANATION OF TABLES IN PART 11.
sii
Of these died,
Under 2
years of age
1529
Between
2 and 5
362
5
„ 10
201
10
99 20
189
20
„ 30
313
30
n 40
329
40
„ 50
365
50
„ 60
384
60
„ W
318
99
W
., 80
. 358
99
80
>, 90
199
99
90
„ 100
22
Total
. 4689
From this account it appears that at Northampton, though more males
are bom than females, and nearly the same number die, yet the
number of living females is greater than the number of males, in the
proportion of 2301 to 1170, or 39 to 30. This cannot be accounted for
without supposing that males are more short-lived than females. One
obvious reason of this fact is, that males are more subject to untimely
deaths, by accidents of various kinds, and also, in general, more addicted
to the excesses and irregularities which shorten life. But this is by
no means the only reason ; for it should be observed at Northampton
the number of female children was, in 1146, greater than the number of
male children, in the proportion of 159 to 624. The greater mortality
of males, therefore, takes place among children,
CARLISLE TABLE.
On the Cailisle Table of Mottality, Milne, article 704.
The following four tables, marked A, B, C, and D, have been deduced
from a quarto tract, published at Carlisle in 1191, entitled, "An Abridg-
ment of Observations on the Bills of Mortality in Carlisle, from the
year 1119 to the year 1187 inclusive,'* and also " ACatalogue of Cum-
berland Animals ; by John Hey&h.am, M. D.''
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xxn
EXPLANATION 0¥ TABLES IN PA&T II.
TABLE A.
Exhibiting the Popdlfltion of the Parishes of St Mary and St. Guthbert, Carlisle,
in 1780 and 1787.
Between the
Agetof
In the ye
tbeCi
Suburbs.
ar 1780 In
tyand
Villages.
Total in bo
i
Jan. 1780.
th Parishcj
a
Dec. 1787.
^ Increase
'during these
8 Years.
0 & 5
859
, 170
1029
1164
135
5 .. 10
731
177
908
1026
118
10 .. 15
587
128
715
808
93
15 .. 20
543
132
675
763
88
20 .. 30
1030
298
1328
1501
173
30 .. 40
733
144
877
991
114
40 .. 50
729
129
858
970
112
5d .. 60
498
do
588
665
77
60 ,. 70
375
63
438
494
56
7d i. 80
164
27
191
216
25
80 .. 90
44
14
58
66
8
90 .. 100
5
5
10
11
1
100 .. 105
1
I
•2
2
• •
Total
6299
2817
1378
674
7677
3491
8677
3864
1000
373
Males
Females
3482
704
4186
4813
627
TABLE B.
1780.
Husbands.
Wives.
Widowers.
Widows.
TotAl.
Within the walls
Suburbs . • •
Villages • • .
Total . .
531
488
188
1207
569
522
191
1282
46
45
17
108
248
160
68
476
1394
1215
464
3073
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BXPtANATION OF TABLES IN PART II.
xxia
TABLE C.
Showing iKd Number of Deaths that toot place in each interval ot Age in the same
Two Parishes during Nine Years^ beginning with 1779, and ending with 1787.
Males.
Both
Males
Females
tinder 1 montK
&Fein.
76
135
59
between 1 ft 2
22
39
17
2 3
10
22
12
3 6
36
72
36
6 9
28
51
23
9 12
38
71
33
tinder 1 year
210
390
180
Between 1 & 2
69
173
84
2 3
63
128
65
3 4
31
70
39
4 5
24
51
27
5 10
42
89
47
10 15
16
34
18
15 20
U
44
20
499
979
480
1
4
1
1
1
1
4
•3
Between 20 &30
20
S
\7
• •
37
96
59
i
55
S3
35
2
22
30 40
lo
35
1
46
89
43
6
30
7
40 50
6
40
3
49
118
69
11
44
14
50 60
8
37
5
50
■ 103
53
16
35
2
60 70
3
64
16
83
173
90
45
35
10
70 80
8
41
17
66
152
86
52
23
11
80 90
5
14
23
42
98
56
49
4
i
90 100
2
4
2
8
28
20
15
2
3
100 105
Totals
62
1
253
67
1
4
3
3
••
• •
85
881
1840
959
199
195
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XXIV
BXPLANATION OF TABLK III PAHT It.
TABLE D.
Register of the Baptifms and Burials in the Parithei of St. Mary and St. Cuthbert,
Carlisle, from Dr. Heysham's Obserrationi.
Baptisms.
Burials.
_ExceMof
Year.
Di..
'
-
IwpCipiiis.
Malet
Females
Total.
wnten.
Malet.
FemalM.
TolaL
1779
102
109
211
•
133
125
253
—47
1780
132
120
252
•
108
117
225
2t
17W
136
130
266
•
103
101
204
62
1782
118
139
257
38
84
122
206
51
1783
139
123
262
35
85
96
181
8L
1784
121
153
274
36
73
85
158
116
1785
148
119
267
28
94
IK)
204
63
178B
123
103
226
43
100
105
205
61
1787
Total
1788
145
122
257
51
101
98
199
68
1164
1118
2282
231
881
959
1840
442
75
144
118
262
44
81
106
187
1789
131
109
240
53
107
106
213
27
1790
107
118
226
49
105
130
235
—10
1791
129
127
256
67
171
173
344
—88
1792
148
137
285
54
109
117
226
59
1793
141
139
280
48
107
109
216
64
1794
145
134
279
39
129
lao
259
20
1796
144
122
266
30
131
157
288
— 2J
1796
147
149
296
39
141
132
273
23
,|
■"I
1
Is
o
1797
• • i
•^279
3
2
284
1
1798
192
1
2
195
1799
170
1
5
176
1
1800
316
0
2
318
1
1801
228
1
7
230
•
1802
243
1
1
245
1803
236
1
4
241
1804
279
2
6
287
1805
205
0
3
208
1800
285
5
8
298
*
1807
386
8
«
B4&^
1808
312
4
5
321
1809
• •
• •
• •
374
1810
• «
• •
••
303
•
Ti
)tal
7912
* The baptisms of Dissenters are iocluded in the other columns^ but were not
obtained separately for the first three years,
t After 1 796 the sexes of the dead are not distinguished, /^ ^ ^ ^T^
Digitized by VjOOQIc
BXPLANATION OF TABLB9 IN PART II.
xxw
TABLB B.
Regsier of tha MBTriaf>^8, Baptisms, and Burials, in the same Two Parishes, from
the Population Abstracts of 1801 aad.lSU.
Baptibus.
Burials
Yw!
Mar-
rUge..
Malei.
Fbm4es
TotaL
Males.
Pemdet
Total.
1780
37
107
102
209
108
115
223
1781
70
115
110
225
102
95
197
1782
66
97
1133
220
85
120
205
1783
56
116
106
222
82
95
177
1784
68
104
126
230
73
81
154
1785
97
132
101
233
93
102
195
178S
70
100
85
185
104
107
211
1787
57
114
94
208
99
97
196
1788
71
118
96
214
80
100
180
1789
75
106
78
184
107
103
210
1790
80
69
93
182
99
127
226
1791
82
101
85
186
166
169
335
1792
95
121
107
228
104
111
215
1793
95
113
115
228
104
109
213
1794
66
118
120
238
123
131
254
1795
85
135
102
237
129
151
280
1796
82
78
129
207
140
133
273
1797
81
151
144
295
120
156
276
1798
85
125
118
243
92
100
192
1799
78
119
137
256
79
91
170
1800
82
124
108
232
154
164
318
1801
85
141
128
269
109
119
228
1802
138
153
135
283
111
132
243
1803
133
182
i;«6
358
105
119
224
1804
161
175
i;2
347
138
139
277
1805
108
164
136
320
104
100
204
1806
116
171
135
326
147
137
284
1807
135
208
204
412
158
178
336
1808
137
180
173
353
146
155
301
1809
91
217
192
409
155
210
365
1810
146
199
179
378
147
148
295
Total
2768
4173
3949
8122
3563
3894
7457
Table C. is printed in the form Mrhich appeared best adapted to con-
vey the intended information : the forms of the others are some of them
exiictly, and the rest very nearly^ those in which Dr. Heysham gave
thetn.
The numbers of the annual burials, in Table D, from 179*1 to 1810,
both years indusive, the same gentleman has been so kind as to furnish
me with, for the purpose of this work, after examining all the registers
Digitized by ^^UUV IC
nvi
EXPLANATION OF TABLES IN PART IL
with the greatest attention, assisted by the clergyman also, for the three
following years : —
1811
1812
1813
Number of Bunals.
Males.
Females.
Both.
127
160
188
132
178
189
259
338
377
Table £. is added from the returns to Parliament, under the Popula-
tion Act, partly because it contains the marriages, which Dr. Heysham
has not given, and, partly, to prove the accuracy of that gentleman's
observations, tt may also be of use in showing (as fair as two parishes
only can furnish the means Of doing so) what dependence is to be placed
upon the accuracy of the returns of Grovernment.
By these two Tables (D and E) it will be found that, in the l7 years
ending with 1796, there were
According to
Dr. Heysham . .
Baptisms.
burials.
Males.
Females.
Both.
Males.
Females.
Both.
3823
2298
2162
4460
1829
1994
Govt, rettims # .
1864
1772
3636
1798
1946
3744
Omissions in latter
434
390
824
31
48
79
And in 31 years, ending with 1810, the total number of burials in
these two parishes was^ according to
Dr. Heysham 7654
The Returns to Parliament • . . 7437
Amount of deficiencies on the latter 197
From the baptisms of Dissenters, which are given Separately in Dr.
Heysham's Table (D) for 15 years, ending with 1796, it appears that
the defects ill the number of baptisms returned to Government have
arisen principally from the omission of these.
The Doctor has also favoured me with separate statements of the
burials in the township or chapelry of Wreay, and those of the Quakers,
for 12 years, ending with 1808, by which it will be seen that these two
form part of the omissions in the returns of Parliament.
Digitized by LjOOQ iC
xxvli
USE AND CONSTRUCTION OF TABLES.
Table I. shows out of a certain number bom how many live to attain
each year of age, and forms the basis of every description of calculation
connected with the subject of life Contingencies.
Table II. shows the expectation of life deduced from the various rates
of mortality, or, in other words, the average number of years that one
individual taken with another may expect to enjoy at the different ages
of existence.
Table III. is similar in description to Table I.
In Table V. the first column shows the proportion to unity that die
at each year of ftge, and is formed by dividing the number ih Table I.,
in the column of decrenleilts, by the number at the same age in the
column of the number of living : the second column is found by sub-
tracting from unity the quantity in the first column ; and the third cblumn
is obtained by dividing unity by the number in the second column, or
by dividing the number in the column of living, at any given age, by
the number in the same column at the next older age. At the age of
20, s= .014030 the number in the first column, I— .014030=
• 985070 the number in the second column, and -r—— or 77^=
1 .01432, the number in the third column.
In Table VI. the number at any age in column D is found by mul-
tiplying the present value of £l due at the end of as many years as the
age by the number of persons, according to the table, living at that age.
In Table IV., Part I., at 3 per cent, the present value of £l, due at
the end of 30 years, id .411986*16; and by Table I., Part II., the
number living at the age of 30, by the Northampton table of mortality,
is 4385 : the product of the two is the number in the table in column D,
viz., 1806.562.
Column N is formed by taking the number in column D, at the oldest
age in the table, and adding to it the number of the oldest age but one,
then to this sum adding the number at the oldest age but two, and so
on throughout the table.
.0585 = No. in column N at age 95 and D at 96.
.2413= ,. D ,, 95
.2998 =r ,, N ,, 94
.5591= ,, D ,, 91
.8589 = ,, N ,, 93
Column S is formed from column N, in a manner similar to that in
which column N is formed f^om colanlu D. ^ r
Digitized by VjOOQ iC
USE AND CONSTRUCTION OF TABLES.
.0585 No. in colttmn S at age 95
.2998 ,, N ,, 94
.3583 ,, S ,, 94
.8589 ,, N ,, 93
1.211 ,, S ,, 93
The construction of columns M and R are somewhat too intricate to
he explained verbally ; an example for the Carlisle 4 per cent is given
in Art. 192.
Tahle VII. shows the number of years* purchase which should be
given for an annuity according to the Northampton table of mortality
at the various rates per cent ; the values given in the table being mul-
tiplied by any annuity will show the value of that annuity.
Example. The value of an annuity of £40, during the existence of
a life aged 45, at 4 per cent, is thus found : opposite to age 45, under
column 4 per cent, is 12.2835, which multiplied by 40, gives 491. 340,
the value required.
The values in this table are obtained by means of D and N columns,
such as are given in Table VI., the number in column N being divided
by the number in column D to find the value of the annuity. As an
example, — the value of £l per annum, at 3 per cent, on a life aged
29, is found by dividing 323*76.615, the number in column N at that
age, by 1892.585, the number in column D, which gives 17.1070
the value of the annuity. \
Table VIII. shows* in a similar manner, the value of an annuity
payable until the failure of the joint existence of two lives, and is con-
structed in a similar manner from columns D and N in Table XXXIII.
Table IX. shows the present value, according to the Northampton
table, of ^1 to be received at the end of the year in which the existence
of a life shall fail : thus, at 5 per cent, at the age of 40, the present
value of a reversion of £l is .38871, this, multiplied by 100, gives
38.871, the value of ^100 to be secured at the end of the year in
which a life aged 40 shall fail.
The Table is constructed by subtracting the present value of «^1 due
at the end of one year from unity, and multiplying the difference by the
value of the annuity given in Table VII., increased by unity, and sub-
tracting the result thus obtained from unity : thus, to find the value at
5 per cent on a life aged 40, we find in Table IV., Part I., the present
value of £l due at the end of one year, at 5 percent, is .952381, which,
taken from unity, leaves .047619, and the value of the annuity in Table
VII., at the age of 40, under column 5 per cent, increased by unity, is
12.837: then, .047619 X 1 2. 837 =.61 129, which, Uken from unity,
leaves .38871, the value in the Table.
Tables XI. to XVII I. are simUar to Table VI.
Digitized by VjOOQ iC
USE AND CONSTRUCTION OF TABLKS. xxix
Table XIX. is similar to Table VII.
Table XXI. is similar to Table YIIL
Table XXII. is similar to Table IX.
Table XXIII. is similar to Table YIII.
Table XXIV. is constructed from the Carlisle in a similar manner to
Table V. from the Northampton.
Table XXYI. is formed from Table XL. in the following manner :—
to the number in column D at the ages of A and B add the number in
column N at ages one year younger than A, and the age of B ; from the
sum subtract the number in column N at the age of A and one year
younger than A> and divide the difference by double the number in
column D, at the age of A and B.
Example. To find the probability of a life aged 10, dying before
a life aged 60 :
To the number at the ages of 10 and 60 in column D, viz., 23533780
Add the number in column N at ages 9 and 60, viz., . 308095139
331629519
From the sum subtract the number in column N, ages 10
and 59 327354967
leaves 4274552
which, divided by 47067560, gives .0909, the required probability.
Column D in Table XXVII. is found by multiplying the number in
column D at the older age in Table XI. by the number of living at the
younger age : thus, to find the number in column D at the ages of 10
and 15, we multiply 4043.730^ the number in column D at age 15, by
6460, the number living at the age of 15 according to the Carlisle mor«
tality in Table I., which gives 26122497.6, the number in column D
at the ages of 10 and 15, under difierence of age 5 years.
Column N is formed from column D in precisely the same manner
as in Table VI.
Tables XXVIII. to XXXIII. are formed in a similar manner.
Tables XXXVI. to XXXVIII. show the single and annual pre-
miums for different assurances on two lives, the construction being
somewhat too intricate to be explained here.
Table XXXIX. shows the value of a policy of £100 according to
the Northampton 'rate of mortality af^er it has been in force any num-
ber of years, the original premium being assumed to have been charged
according to the same table of mortality and rate of interest; it is
constructed in the following manner : divide the value of the annuity
increased by unity at the age when the policy is valued by the value of
the annuity increased by unity at the age when the assurance was
effected, subtract the quotient from unity, and multiply by 100. Or,
To the annual premium for assuring £1 at the age when the policy
was taken out, add .029126, and add the same quantity to the annual
Digitized by VjUUVIC
XXX USE AND CONSTRUCTION OF TABLES.
premium for assurance of .f 1 at the age when the policy is valued ;
divide the former sum by the latter, subtract the quotient from unity,
and multiply by 100.
By this last method a policy may be valued from the published rates
of an office when the rate of interest used is 3 per cent.
To find the value of a policy taken out on a life aged 80, after havipg
been in existence 6 years: by Table VIE. the value of the annuity at
age 80 is 16.921*7, and at age 86 it is 15.7288.
16.1288
1779217 '^•^^^^^'
1 - .93344 = .06656, which multiplied by 100 gives 6.656, the value
required.
By Table IX. the annual premium at age 30 is . 026672, ^nd at age
36 it is .030651, then .026672+ .029126= .055798, and
0^t>1QR
.030651 +.029126= .059777, and l^^^- . 93344, w befo^
.U5y I 77
Digitized by VjOOQ IC
.1G^ '"''
ON THE
VALUE OF ANNUITIES,
SIMPLE INTEREST
1. Is the sum paid for the use of the principal only^ during the
whole term of the loan, and varies (when the rate is the same) with the
time, and the value of the loan ; thus, the interest of ^£100 for one year,
at 4 per cent per annum, is £4 ; the interest of the same sum for two
years, ib £8; the interest of twice the sum (^^200) for one year is £8^
and for two years £16.
2. The sum of principal and interest in any given time is called the
amount ; thus, in one year, the amount of £\Q0 at 4 per cent is £lQO
+ 4 = £IM.
3. To ohtain general rules for the solution of cases in Simple Interest,
let us make
i :s the amount,
p =: the principal,
n s= the numher of years,
% == the interest of £l for one yeai expressed in decimal
parts of a pound.
4. To find {$) the amount.
Multiplying i the interest of £l for one year hy p, we obtain ip the
interest of £p for the same period; this multiplied again by n, gives
tnp, the intereat oi £p for n years.
/• ^ = p 4- inp =: p (1 + in) := the amount
The following is the rule expressed in words : ** Multiply the interest
of £l for one year by the number of years, add one to the product, and
multiply the sum by the principal."
5. Example. A agrees to lend B the sum of j£531 12 6 for 5 years,
at an annual interest of 4 per cent ; what sum must B pay at_ the cxpif-
ration of that period for pnncipal and mterest r o
3 ON THE VALUB OF ANNtJITIES.
Here p = »537.625, i = .04 n = 5
•04 531.625
5 1.2
m = .2 645.1500 = «f645 3 0
1.
1 + in = 1.2
6. To find (p) the principal —
(by Art. 4.) * = p (1 + in)
dividing each side of this equation by 1 + in
P "" 1 + m
Rule. Multiply the interest of .£1 for one year by the number of
years, add one to the product, and divide the amount by the sum.
Example, B returns A .£645 3 0 principal and interest, for the
loan of a sum for 5 years at 4 per cent ; what was the sum advanced ?
^ = 645.15 n= 5 t = .04
•04
5
inxs .2
1.
1 + ffits 1.2) 645.15
, * , = 531.625 r= ^531 12 6
1 + f n
1. To find (n) the number of years,
(by Art 4) * = p + inp
iAritkmetic and Alg,^ 109) by transposition, inp ^ s — p
$ — p
dividing each side by ip, n =: — r— ^.
Bude. Multiply the interest of £1 for one year by the principal^
and divide the difference between the principal and the amount^ by the
product.
Example, In how many years will £531 12 6 amount to £645 3 0
at 4 per cent simple interest ?
p a 931.625 i = 645. 15 i = .04
531.625 645.15
.04 537.625
ip = 21 . 50500) 101 . 525(5 years
101 525
* The decimal parts of a pound corresponding to any number of shillings and
peace may be fo.md by te&mng to Table 1. ^.^^^^^ ^^ ^uuv^ic
DISGOUKT. 3
8. To find (0 the rate of interest,
(by Art 7) inp ::z s — p
dividing each side by wp, i = -.
Rule. Divide the di£ference between the principal and amounty by
the product of the principal and number of yeaxa, which will give the
interest of £l ; this result, multiplied by 100, will produce the rate
per cent.
Example. At what rate per cent, simple interest^ will £537 12 6
amount to £645 3 in 5 years ?
p = 537.625 s = 645.15 n = 5
5 537.625
2688.125 ) 107.525 ( .04
107,525 100
. . . . 4 per cent.
9. When the time is any number of years and days, or of days alone,
the quantity n contains a fraction, the decimal corresponding to which
may be found by Table 2 ; if it were required to find the amount of
£300 in 3 years and 73 days at 5 per cent, we find by the Table the
decimal of a year corresponding to 73 days = .2.
n £= 3.2 p = 300 i = .05
3.2
.05
in = . 160
1.
1 + m = 1.16
300
p (1 + in) = £348 Answer.
In many works on this subject, tables of the interest of £l for any
number of days are given : it is not thought necessary to insert them
here, on account of the great facility with which they may be computed
by the aid of Table 2 : as an example, let it be required to find the
interest of £l for 20 days at 5 per cent per annum ; opposite 20 days
in the Table is .05479452, this multiplied by .05 will give .002739726
the interest of £l for the required time.
DISCOUNT,
10. Is an allowance made for the payment of a sum of money before
it becomes due.
The present value is the sum to be paid after deducting the discount.
Call d = the discount,
p :=z the present value,
s =: the sum due,
n = the number of years,
i = the interest of £l for one year.
11. To find (p) the present value— Digitized byGoOQlc
B 2 ^
4 ON THE VALUE OF ANNUITIES.
When money due at the expiration of a certain period is discharged
by the payment of an immediate sum, the party making it ought not
to pay the whole sum, but that portion of it only, which put out at
interest, will amount at the expiration of the period to the sum due ;
for instance, £lOO paid down when interest is 5 per cent, is equivalent
to the payment of £ 105 at the expiration of a year.
Finding the present value is therefore precisely the same case as
that solved in Art. 6, and as p the present value in this case corresponds
with p the principal in the former, s the sum due with s the amount,
the notation for the time and rate being the same, we have by Art. 6,
P =
I + in
(Art. 4.) « = p (1 + in)
(Artl.) ^='-^-
ip
The rules given in Articles 5, 6, 1, and 8, apply equally here, if we
substitute the words present value, and sum due, for principal and
amount.
12. To find (d) the discount—
This is found by taking the di£ference between the present value and
the sum due.
d = «— j9 = t— ■■ . '
^ 1 + t»
Example. What discount should be allowed for the present pay-
ment of a bill of £325, due at the end of 3 months, interest 5 per cent ?
8 = 325
n
iV
= .25
.05
.0125
i- .05
=: in
in
=
1
325
325 (320.988=
.^0315
+
1.0125)
1+i/t
2125 4.012=
20250
:£4 0 3
discount
1000
911
.89
81
8
The above is the true mode of finding the discount, but in the mer-
cantile world it is customary to take for the discount the interest of the
sum for the time that elapses till it becomes due, by which mode more
than the true discount is obtained.
The formula for finding the interest by Art. 4, is tn*, and therefore
the discount received above the true discount is ^ '^i '^ed by v^uu^ic
ins —
SIMPLE INTEREST.
ins i* n* s
1 + t« I + in
In the example given above, 4.0625 = £4 1 3 is the sum that a
banker would receive for discounting the same bill at the above rate of
interest.
ON ANNUITIES AT SIMPLE INTEREST.
13. An anntUiy is a periodical income arising from lauds, houses,
money lent, pensions, &c.
When the possession of an annuity is not to be entered upon until
the expiration of a certain period, it is called a reversionary or deferred
annuity ; when the time of possession is not deferred, the annuity is
sometimes called immediate^ but in general it is simply termed an
annuity.
At the time of acquiring the title to an annuity the party is said to
enter on possession ; one of the equal intervals at which the annuity is
payable, is always supposed to elapse between the time of entering on
possession and the first payment of the annuity.
14. The amount of an annuity in a given time is the sum of all the
payments with their interest from the time of becoming due, until the
expiration of the term.
Make s = the amount of the annuity,
a = the annuity,
n = the number of years,
i = the interest of £l for one year;
then if the annuity be £l per annum forborne n years, the last or
n th payment being received at the time it falls due, there is no interest
on it, the amount therefore is £l only ; the last payment but one, on
which one year's interest is due, amounts to 1 + ^ ; the last but two, on
which two years* interest is due, amounts to 1 + 2 i ; the last but three
to 1 + 3 i; and so on till we come to the first payment, which being
payable at the end of the first year, has (n — 1) year's interest due
theieon, and amounts to 1 + (n — 1) i ; the following series is there-
fore the amount of an annuity of £l in n years :
l + (l + i) + 0 + 2i) + (1 + 30 + (1 + 4*0 +
+ {1 + (n-3)i} + {l + (n-2)i}+ {1 + (n - l)i.}
This series, in which the difference between each term and the next
succeeding is the same throughout, is termed an Arithmetical progres-
sion, for the summation of which, a general formula with its investiga-
tion is given in Art. 143 of the " Treatise on Arithmetic and Algebra"
published by the Society. The formula there is
«(2a + (m — 1) b} Cr^n,n]o
^ — • — .i : — i i 1, Digitized by VjOOQIC
6 ON THB VALUE OF ANNUTTIKS.
s denoting the sum of the series, n the number of terms, a the first term,
and b the common difference ; applying this to the above series we have
n terms in both, a = 1, 6 = t ; the sum therefore is expressed bj the
formula
n (2 + (n - 1) 0 , n (« — 1) t
2 = ** + 2 '
and this multiplied by a gives
s =: a (n •\ ^-^ 0 = the amount of an annuity of £a in
n years.
Rule, Multiply the number of years by the number of years less
one, and by the interest of £l for one year ; to the half of this product
add the number of years, and multiply the sum by^the annuity.
Example, What is the amount of an annuity of £325 forborne 12
years, at 3]^ per cent simple interest?
n = 12 a = 325 t = .035
tt— 1 £= ^ll
n (n — 1) = 132
• = JD35
660
396
2)4.620
Vl(^Jhl^ 2.310
n =12
n + !L^!LZLl>li =14.310
a = 325
11550
28620
42930
a(n + ^'^^ —^=4650.150 = ^£4650 15 0 the amount.
15. To find (a) the annuity, the amount, &c. being given,
(ArtH.) .==a(« + 2i^^.t)
multiply each side of the equation by 2, then
2* = a (2n + nCn-- 1). i)
dividing each side by 2 n + n (n — 1) . t vire have
28
a =
2n + n In — 1)*'
Rule, Multiply the number of years by the number of years less
one, and by the interest of £l for one year; to this product add twice
SIMPLfi IHTB&SST. 7
the number of yean, and lijr the sum divide Iwieii the amount of the
anniiity.
Example. What annuity forborne 12 years will amount to
J?4650 15 0 at 3]^ per cent iimple interett?
9 = 4650. 75 n = 12 i = .035
n— 1 = H
n.(n-l)= 132
i = .035
660
396
nin-
- 1) t= 4.620
2n = 24
4650.75
2
fi (n-
-l)i=: 28.62)
9301.50
8586
7155
5724
14310
14310
16. To find (n) the number of yeara, the rest being given,
(Art. 15.) 2* = a (2 n + n (n — 1) 0
divide each side by a, we have
— s=2n + n(n — l)i=iii»+2n — m = i»« + n(2— 0
a
J. .J. V . , 2 — t 2»
dividing by I, »■ + — : — »=:—:,
% (XL
/2 — A«
adding ( J to each side to complete the square (iln(Amettc and
Algebra, 206).
8i— + (2-0«
a
4^
extracting the square root of each side :
Irj transporitioii,
^8»-i-+ (2-0*. -(2-t)
2t
Digitized by VjOOQ IC
8 ON THE VALUE OF ANNUITIES.
Rule, Divide the amount by the annuity y and multiply the quotient
by 8 times the interest of £l for one year ; add to this the square of the
difference between 2» and the interest of i£l for a year, and extract the
square root of the sum ; f rt)m this result subtract the difference between
2 and the interest of £l for a year^ and divide by twice the interest of
£l for one year.
Example, How many years must an annuity of £325 be -forborne
to amount at 3]^ per cent simple interest to £4650 15 0?
a = 325 i sz .035 a = 4650.75
8
Sis .280
325)4650.15 ( 14.31 = —
325 .28 = Si
1400 11448
1300 2862
1001 .4.0068 = 81---
975 ^
.325
325
2. .035
.035 2
1.965 = 2-1 ,01=2*
1.965
9825
11190
11685
1965
(2 -0» = 3.861225
8 t—s= 4.0068
a
8 -1 + (2 - 0* 1.868025(2.805 = x/si-^ + (2 - lY
a ^ a /
1.965= 2 - i
48)386 . 07) . 840= \/8 i — + (2-iY— (2 - 1)
384 12 years
5605) 28025
28025
11. To find (0 the rate of interest.
(Art. 16.) — = 2n + n (n- 1) »
Digitized by LjOOQ IC
SIUPLB INTEREST. 9
ArUh, and Alg^ 109. By transposition
«(«-l)£=|! -2n = 2(-i-n)
dividing each side by n (n — 1)
* "" n (n - 1)
' Rule. Divide the amount by the annuity^ subtract the number of
years from the quotient, and multiply the difference by 2; then divide
by the product of the number of years, multiplied by the number less
one.
Example. At what rate per cent sunple interest will an annuity of
£325 amount in 12 years to £4650 15 0?
t = 4650.75 a = 325 n = 12
325)4650.75 ( 14.31 = — 12 = n
325 12. 11 =5 n — 1
1400 i-n=2.31
n(»- 1) =132 4.62(.035xl00
1300 2
396=3.5 peretDt.
1007 4,62 = 2 ^-i
975-
\ 660
- " j 660
• • •
325
325
18. If we wish to obtain the present value of an annuity, it can be
done by finding the present value of each payment separately, and the
sum of these several values will be the present value of the annuity.
If we suppose the annuity to be £l per annum for n years, the ex-
pression for the present value will be by Art. 6,
1111
: + r-r^- + 7-T-T-. +
1 -t- i 1 + 2i 1 + 3i ' 1 + 4i
1
1 + (n - 2) i 1 + (n — l)i I + in
For the summation of this series no general formula has yet been dis-
covered, and when the annuity whose present value is to be found, is for
a long term of years, the computation becomes tedious ; it may, how-
ever, in most cases, be considerably abridged ^by the assistance of Bar-
low's Mathematical Tables, in which are given the reciprocals of all
numbers from 1 to 10,000; for instance, if it were Jf^^lJ^^^^^^P^ft?
10 ON THB VALUB OF AUNUITIES.
present value of an annuity of £50 for 6 yeart, at ^ per cent mmple
interest.
1 _ 1
1 + i 1.035
1 1
l+3i hl05
1 1
1 + 41*^ 1.14
1_ _ 1
l+5» 1*115
1 _ 1
1 +6i ~ 1.21
= .966184
= .934519
= .904911
c=.. 811193
=: .851064
=: « 826446
5 360443 =:l preaent value of an annuity of £l
*"\ for 6 years
50
268.02215 = ditto £50
To matliematicianB, the tables just mentioned -will be found of great
use, as they contain the factors, squares, cubes, square roots, cube
roots, and reciprocals of all numbers from 1 to 10,000, with other tables,
and an extensive collection of formulae relating to mathematics and
natural philosophy.
COMPOUND INTEREST.
19. When the interest of money, instead of being received as it
becomes due, is added to the principal, increasing the sum each year on
which interest is receivable, then money is said to be put out at Com-
pound Inierett
If the interest of £l00 at £S per cent, instead of bang taken up at
the end of the first year when it becomes due, be added to the principal,
a new principal of £105 is created, which with its interest amounts at
the end of the second year to £l 10 5, this again forms a new prin-
cipal amounting with interest to £115 15 3 at the end of the third
year, and so on for any longer period.
Make « s the amount
p ss the principal
n sa the number of years
t = the interest of £l for one year;
then 1 -t- 1 =: the amount of £l at the end of the first year, and the
amount of any other sum in one year will be in the same proportion,
COMPOUND INTEREST. 11
l.e. M 1 u to i 4- 1, 80 ifi any sum, to itfe amount j in bne year; and
flince 1 + f forms a new |)rincipal, its amoont in one year gives the
amount of £ly the original prindpal at the end of the 2nd year.
• 1 • 1 4- i •• 1 4- i ' (I 4-iYl a™o^nt ^ ^1 at the
..1.1+* .. 1 + t .tl+t;j end of the 2nd year.
1 : (1 + 0 : : (1 + 0" : (1 + 0* ditto 3rd year.
1 : 1 + t :: (1 + if : (1 + 0* ditto 4th year.
and proceeding in the same manner the amount of £l at the end of the
fif^year is (1 + 1) " ; this multiplied by p gives
« s= p (1 4- i) " = the amount of £pmn years,
log « = log j5 + n log (1 -f i).
Rule, Raise the amount of £l at the end of the first year, to the
same power as the number, of years, and multiply the result by the
principal.
Example. What is the amount of «f 325 in 4 years at 5 per cent
compound interest ?
|y = 325 iis4 l+ts L05.
1.05
1.05
5 25
105
1. 1025 = (1.05)*
1. 1025
55125
22050
11025
11025
1. 21550625 = (.105)*
523
3646518
243101
60175
395.0394 = £3% 0 9^
In this example the amount of .£1 in 4 years is multiplied by what is
termed contracted multiplication, the rule for which may be found in
(ArUhmetic and Algebra^ Art 167).
Calculation by logarithms.
Log * = log j» + n log (1 + i).
Log (1 4- 0 = log 1.05 == 0.0211893
n log (1 + i) - 0.0847572
log 325 gs 2.5118834
log/y + n log (1 + 0 = 2.5966406 395,0394 = ^£395 0 9^
Rules for logarithmic calculations may be found prefixed to nearly al(c
the di&ient collections of tables of logarithms, among the best and most
12 ON THB VALUE OF ANNUITIES.
extensiTe of which are Hutton's, Callet'Sy^Taylor's, and Babbage's; the
latter of which will be found the best for this subject, as it contains the
logarithms of numbers only, and is the most correct.
Example. What sum will £349 7 6 amount to in 29 years at
£3 6 8 per cent compound interest ?
log 31 = 1.49136169
CO. log 30 = 2.52281875*
log (1 + 0 = 0.01424044
n = - 29
12816396
2848088
nlog(l +0 = 0.41297276
1<^ 349,375 = 2.5432918
logp + n log (1 + 0 = 2.9562646 904,200 = £904 4 0
20. In Table 3 are given the amounts of £l for any number of
years not exceeding 100 at the rates of 2. 2^. 3. 3j^. 4. 4^. 5. 6. 7. 8. 9.
and 10 per cent from Smart's Collection of Tables, published by him
in 1726; when the amount is required for a greater number of years
than 100 multiply the amount opposite 100 by the amount opposite to
the number of years equal to the excess above 100 ; if the amount of
£l in 130 years be required at 3 percent, (1.03)*"* x (1.03)* =
(1.03)**^. Opposite 100 in the column headed 3 per cent we find
(1.03) *••= 19.21863198, and opposite 30 in the same column
(1.03)"= 2,42726247, therefore( 1.03)*" =19.21863198 X 2.42726247
= 46.64866412, the amount of £l in 130 years. As an example of
the use of the tables —
What is the amount of £325 in 4 years at 5 per cent compound
interest ?
In 5 per cent column opposite 4 years we find
(1.05)* = 1.215506
523 = p inverted
3.646518
243101
60775
395,0394 = ^£395 0 94
* The logarithm the reciprocal of any quantity is eqoal to the logarithm of that
quantity taken from the logarithm of unity, which ii 0. In the preeent instance the
logarithm of -^ being — 1.47712125> in order to have the decimal positive, we
30
have— 1.47712125 = -2 + (2—1.47712125) = 2.52287876. VjUU^IC
COMPOUND INTEREST. 13
As the excess of the amount at the end of the term ahove the original
principal arises from the interest of money, we have this rule : — ** From
the amount at the end of the term, subtract the original principal, and
the difference b equal to the interest."
21. To find ip) the principal, the rest being given.
By art. 19, « = p (1 + 0"
dividing each side by (1 + i)"
s
P = (1+7)" = * (1 + 0""
Rule, Divide the given amount by the amount of £l in the same
term.
Example. What principal will amount to £395,0394 in 4 years at
5 per cent compound interest f
f = 395.0394, (1+0 = 1.05, n=4, by table 3, (1.05)*= 1.215506
1.215506)395.0394(325
3646518
303876
243101
60775
60775
This example is computed by contracted division, which cuts off one
figure at each step from the divisor instead of annexing to the
dividend.
By logarithms.
Art. 19, log f rs p + w X log (1 + i)
By transposition Ic^ p = log « — n x 1(^ (1 + i)
- log 1.05 = 1.9788107
4
-nlog (1 + t) = i.9L52428
log » = 2.5966406
log p = 2.5118834 ^325
22. To find (n) the number of years, the rest being given.
To obtain this we must use the logarithmic formula
(Art. 19) log. « = logp + n log. (I + a)
By transposition n log (1 + i) = log « — logp
dividing each side by log (1 + i)
logf- logp
"^^logd+O
Hvk. Find the difference between the logarithms of the amount
and of the principal, and divide by the logarithm of the amount of £l
in one year. Digitized by ^^ji^ijv IC
14 ON TBB V^I'UH OF A!ifMUIVIE8.
Emmpk. In how many yean will .632^ amount to £395.0394 at
5 per cent compound interest?
« = 395.0394 p = 325 1 + t = 1.05
log 395.0394 = 2.5966406
log 325. =: 2.5118834
log 1.05 = .0211893)0.0841572(4 years
0841572
23, To find (i) the rate of intereat.
Art. 19. i^pil + iy
dividing each side hyp (1 + «)" = —
Extracting the n^ root of each aide, 1 +t = ( — J"
By transposition i s= f — J • — 1
The readiest way of finding f — T* is hy logarithms.
Rule. Divide the difference hetween the logarithms of the princ^pdl
and of the amount^ hy the numher of years, and from the numher cor-
responding to the quotient subtract one, the result is the interest oi£l ;
this multiplied by 100 gives the rate per cent.
Example. At what rate per cent will £325 amount at compound
interest to £395.0394 in 4 years ?
n = 4 ir=: 395.0394 p=!325
log ts= 2.5966406
1(^^ = 2.5118834
4)0.0847572
logg — logp_ 0.0211893 1.05
1
.05 = i
100
5 per cent.
24, When interest is payable half-yearly, quarterly, &c.
If the intervals at which interest is receivable be shorter than a
year, and at each interval the interest be added to the principal as it
becomes due, the amount at compound interest will evidently be greater
Digitized by N^UU V IC
eOMPOUND INTSB99T. )4
than when interest is only payable yearly. £100 at 5 per cent, payable
half-yearly, will amount at the end of six months to £102 10 ; this
new principal being again put out at interest for the next six months,
will give £l05 1 3, the amount of £100 at the end of the year, which,
if interest were payable yearly ^ would be only £l05.
The interest in this case for the year is £5 I 3, from which it
appears that where interest is payable at shorter intervals than a year,
the expression rate per cent^ denotes, not the interest of £100 in a y^ar,
but the sum of which the same proportion must be taken ^ find the
rate per cent for one interval, as each interval is of a year.
' Using the same notation as in art. 19, and calling m the number of
intervals, we have
[ 1 + - j the amount of £l attheendof the 1st interval; reason-
ing as in Art. 19 we find ( 1 + -" ) do. of £1 at the end of one year.
(-i)'
do. £l n years.
multiplying by p
# = p ( 1 + — ) do. £p n years.
by logarithms, log« = log p + mn x log f 1 + - \
Rule. Find the amount of £l at the end of the first interval, and
raise it to a power equal to the product of the number of years and of
intervals at which interest is payable in the year, and then multiply by
the principal.
Example. What will be the amoimt of £325 1 9 in 25 years at 4
per cent compound interest payable half-yearly ?j <
p S3 325.0815, iss .04, n s: 25, m = 2, .^ mn = 50
and the formula becomes 325.0875 x (1.02)^..
by art. 19, (1 . 02)'* == amount of £1 in 50 years at 2 per cent, payable
yearly.
Table 3, ( 1 . 02)" = 2 . 691 58803
5780.523
8074764
538318
134579
2153
188
13
875,0015 = £8^^ j,^qi,oogle
16 ON THE VALUE OF ANNUITIES.
By logarithms^
log 1.02 = 0.008600ni
50 = mn
log (I.02)~ = 0.43000855
logp = 2.5120004
log« =: 2.9420090 SIS.OOl as before.
A person invests £5000 in the 3 per cent consols when stocks are 90 :
what will this sum amount to in 15 years, supposing the interest as it
becomes due to be always invested at the same rate ?
3 1
p = 5000, i = — =— , n = 15, III = 2, the interest in the funds
90 oO
being payable half-yearly, (l + i)"" = (l + -)" = Q J
1(^61 = 1.785329835
log 60 = 1.718151250
log fl + -") = 0.007178585
\ mJ 3Q
log (l + ~ j = 0.21535755
\ogp = 3.6989700
log t = 3.9143276 = 8209.706 s ^£8209 14 1^
25. The fluctuations in the prices of the funds prevent us from
ascertaining with precision what will be the amount of an investment
with the accumulated dividends in a given time, as it is not probable
that the dividends will all be invested at the original rate ; it is there-
fore necessary, if we wish to anticipate what the amount will be, to
assume a probable average rate of interest on which our calculation shall
be grounded.
26. The advantage derived from the interest of money being received
at more intervals than one in the year, will not be of much importance
for the term of one year ; but when money is put out in this way for a
long time, the difference becomes more considerable. The foUowing
formula will show the difference in the amount of interest of £1 for one
year.
f 1 + — j ~ (1 +0 • ^^c fifst part of the expression being expanded
by the binomial theorem (^Arith. and Alg. 275), and the remuning part
• ^ ij-xv m — 1., m— 1 TO — 2.. .m— 1
subtracted, it becomes—- t" + —- • "^ t' + — -r .
2to ^ 2m 3 TO 2m
TO — 2to — 3.. .„ ,.,
— r- — . — I +, &c., which, as the series converges very fast, is
equal to -rr i* nearly. ^ x
2*» Digitized by LjOOgie
COMPOUND INTEREST. 17
When m equals 2 the difference is -j , ivhen m equals 4 it becomes
8 ^ 16^256*
21. The greater the number of intervals at which interest is payable,
the more nearly do ^-, , &c. approximate to unity. If then
we write the limit unity for each of these fractions, we have the amount
of £l m one year on the supposition that there is no portion of time,
however small, but what produces some interest. The series then
Incomes 1 + i + j^ + j^3 + y;^ + TXiXi'*^''^'^''
series, as shewn by writers on lograrithms, is equal to the number that
has t for its Naperian logarithm, or i x .434294482 for its logarithm
in the common system.
Example. What will be the amount of £300 in one year at 4 per
cent, compound interest payable momently ?
p = 300 f = .04 .434294482
.04
^(^+i T= .01737171928 1 .04081 {"""^^^l ^/^
\ tn / I lu one year.
300
312.243= £312 4 10.
When m is infinite, the formula ( 1 + - ) when expanded, becomes
^+"'+1:2+1x3 + 1:2:3:4+ r:2:3:4:5'+*'=' "^''^ '*"^'
is equal to the number that has in for its Naperian logarithm, or in
X .434294482 for its logarithm in the common system?
Example. What will be the amount of <f 300 in 40 years at 5 per
cent compound interest payable momently ?
p = 300, i = .04, n = 40
.04
in=i 1.6
.43429448
6A =f n inverted
43429448
^^ 26057669
.95303
300
• \«- 26057669
log(l + — ) =.69487117 4.!
1485.909
28. In the first of these examples the amount of £l in one year7ff ^^
interest were payable yearly, would be 1 . 04 ; the difference between this
c
IB ON THB VALUE OF ANKUTTIBS.
and the amount. of J^l in the example, is only «00081, or .^43 for J&300,
which is very inconsiderahle ; but in the latter example, the amount of
£l in 40 years, interest payable yearly, is 4.80102, shewing a dif-
ference of •15201 in the amount of if 1 for that time, or for the sum of
£300 a difference equal to ^45,603.
29. To find (p) the principal.
Arta4..«p(l + i)""
dividing each side by f 1 + — J
s
P =
by logarithms, log jpi =3 log f - mn ^ log f 1 + — ]
Rule, Divide the given amount by the amount of £l in the time*
Example. What sum will amount to £690 in 15 years at 8 per
cent compound interest payable quarterly?
s = 690, n = 15, m = 4,'i = ,08,
M ^ lT =: (1.02)'« 2= 3.281031 by Table 3, under 2 per cent
(Art. 24.)
3.281031)690 (210.299 = £210 6 0
.... 6562062
337938
9835
6662
3273
2953
320
295
25
By logarithms.
'^(■■^i)
= log 1,02 5= .008600n
60
log (l + ~) == log (1.02)^= 0.5160102
logp =
log 690 =2.8388491
log p — lo^ { 1 + i- V * '= 2 . 3228389 210. 299 = Pi
\ .">/ ^ Digitized by VjOOgle
COMPOUND DiTBRSST. i \. - ■ 1»
30. To find (rt) the number of years. \
(Art. 24.) log » = log p + wn X log ( 1 + - )
\ fit'
(Arith«and Alg. 109) hy tran8poii(ion,flm.l<^ ( 1 + — )=: log' - log;?
dividing each aide by m. log (l + ^)
^ _ log # — log p
m X log (\ + i-^
Buk, Divide the difference of the logarithms of the principal and the
amount by the logarithm of the sum to which £\ will amount at the
fint interval the interest is convertible, multiplied by the number of
periods of conversion in the year.
Example. In how many years will £210 6 0 amount to £690 at
8 per cent compound interest payable quarterly ?
p = 210.3 «=:690 i=:.08 m = 4
log (l +^) .00860011
log 8 = 2 . 8388491 ±_
logp= 2.3228393 ,n. logri+— j = .03440068
.03440068)0.5160098(15 years
3440068
1*120030
1720030
31 r To find (fn) the number of periods at which interest is convert-
ible in the year :
Extracting the Tith root^
(l +*--) =( — )~t which equation there is no direct method of
wiring, but we can approximate sufficiently near by the following
Biethod:
Expanding by the binomial theorem
1 + I H — I* + —- — 1"
'2m 2m Sm
2m 3m 4m \p J o
c2
20 ON THK VALUE OP ANNUITIES.
By transposition,
=(7y--<'
(i>-a.o
As this series converges very fast we shall be sufficiently accurate if
we omit all the terms but the first two ; we then have the equation
m--l m--l m-2^ /f\L ,, , ..
Multiply by 6 m', and dividing by i*
3m«- 3m + tm« — 3tm + 2t = 6 mS ^ ^ ^
I-
TO« {3 + 1 - 6 ^^^ ^ J - (3 + 30m = — 2i.
This equation is a quadratic, and if we substitute for t, Sj and p their
values in figures, and solve the equation (Arith. & Alg. 206) we shall
have the value of m very nearly.
32. To find (i) the rate of interest
(Art. 24.) $=:p(l + i-)"
dividing each side by p,
extracting the mnth root of each side,
m \pj
by transposition, — = f — j-* — 1.
Multiply each side by m :
( -y^ is found by logarithms : log T — j"^ = .<^* - ^P .
Rule. Divide the difference between the logarithms of the amount
Ktid.principcU^ by the product of the number of years and of periods of
conversion of interest in a year; the quotient is a logarithm; find the
corresponding number, and from it subtract one, and multiply the differ-
ence by the number of periods interest is convertible in a year.
Example, At what rate per cent will £210 6 0 at compound inte-
rest payable quarterly, amount to £690 in 15 years ? zpd by vjuu^ic
COMPOUND INTEREST. '21
;> = 210.3 «==690 7i=sl5 m=4
log<= 2.8388491
log;>= 2.3228393
60)0.5160098
.0086002 1.02=1+7
1 ^
'.02
4
i08 = interest of £l for one year.
•08 X 100 = 8 per cent.
33. These equations might have heen obtained more readily, if in the
formula found when interest is convertible annually, the interest for one
interval had been substituted for the annual interest^ and the number
of periods of conversion for the number of years : this will appear
evident on examining the demonstration in Art. 19, where the amount
of £l in one year is called (1 + i), and the amount of £l in n years
is shown to be (1 + f)"; tliese expressions do not depend upon the
time being reckoned in years, for by adopting the same mode of reason-
ing, if (1 + 0 represent the amount of £l at the expiration of any
other portion of time, (1 + 0' would be the amount at the expiration
of twice that period, and (1 +0" at the expiration of n times that
period ; in whatever way, therefore, we express the amount of £l for a
term at the end of which interest is convertible ; the amount at the
end of any number of the same equal periods may be found by raising
that amount to the power represented by the number of periods.
When interest is convertible at m equal intervals in a year, there are
mn of these intervals in n years, and the amount of «f 1 at the expira-
tion of the first of them is f 1 + — \ this raised to the mnih power,
gives ( 1 H ) > the amount at the end of n years^ or mn terms.
34. When we are in possession of the proper tables, the amount
of £l may be found by looking under the rate of interest produced by
dividing the annual rate of interest by the number of times interest is
convertible in one year, opposite to the number of years obtained by
multiplying the periods of conversion in a year by the number of years ;
if the annual rate of interest be 4 per cent, the amount of £30 in 12
years when interest is payable half-yearly, is obtained by looking in the
Table under 2 per cent, opposite 24 years, where we find 1 . 60843,
which multiplied by 30, gives 48.2529 = the amount ; the same sum
for a similar term when the annual rate is 6 per cent, payable, 3 times
a year, by looking under 2 per cent, opposite 36 years, where we have
2.03988, and multiplying by 30, gives 61 . 196 for the amount.
If we have a table of the logarithms of the expressign^. X b\ vfeuu^lc
82
ON THB VALUB OF ANNUITIES.
for different rates of intet^st, by multiplying this by the number of years,
we find the logarithm of £l in that term.
The following table gives the amounts And their logarithms of £l in
one year, payable yearly, half-yearly, quarterly, and momently, for dif-
ferent rates of interest, and is thus formed :
When interest is 3i^ per cent, the amount payable yearly is 1.035,
the logarithm of which is .0149403497, {Mutton's Logs., Table 3);
when interest is payable half-yearly we have
('-i)"=(-,ol^)"=('-i^J=Q"
100 X 2y
= 1.035306
'^^CiSsJ^^ 2{log401-log400}
:= 2(2.6095944092 — 2.6020599913} t=: '0150688358;
when interest is payable quarterly
0+iH'+ii^)'=(>+i^)'=P*
== 1.035462;
log(g^J= 4{log 801 - log 800}
=: 4{2. 9068735347 - 2.9030899870} = .0151341908.
When interest b payable momently, we have '035 x '4342944819
c= '01520030687 for the logarithm, the number corresponding to
which is 1.035620
Nominal
rate of
Interest.
1
Amount
of ^1 in
one yeah
Logarithms of
rach amount.
Nominal
rate of
Interest
!
Anonnt
of £1 in
one year.
Logarithms of
snch amount.
2
per cent.
9
m
1.020000
1.020100
1.020150
1.020201
.0086001718
.0086427476
.0086642470
.0086858896
5
per cent
I
9
1.050000
1.050625
1.050946
1.051271
.0211892991
.0214477308
.0215801275
.0217147241
per cent.
i
9
1.025000
1.025156
1.025235
1.025315
.0107238654
.0107900638
.0108235735
.0108573620
6
per cent.
9
m
1.060000
1.060900
1.061364
1.061837
.0253058653
.0256744494
.0258641690
.0260576689
3
per cent.
I
9
m
1.030000
1.030225
1.030339
1.030454
.0128372247
.0129320845
.0129802193
.0130288345
7
per cent
9
m
1.070000
1.071225
1.071859
1.072508
.0293837777
.0298806996
.0301376716
.0304006137 .
3*
percent
9
m
1.035000
1.035306
1.035462
1.035620
.0149403498
.0150688358
.0151341909
.0152003069
8
per cent.
9
m
1.080000
1.081600
1.082432
1.083287
.0334237555
.0340666786
.0344006870
,0347435586
' 4
per cent.
f
m
1.040000
1.040400
1.040604
1.040811
.0170333393
.0172003435
.0172854951
.0173717793
9
per cent
y
9
m
1 .090000
1.092025
1.093083
1.094175
.0374264979
.0382325809
.0386532667
.0390865034
44
per dsnt.
i
9
m
1.045000
1.045506
1.045765
1.046028
.0191162904
.0193266334
.0194341385
.0195432517
10
per cent
i
9
m
1.100000
1.102500
1.103813
1.105171
.0413926852
.0423785981
.0428954616
.0434294482
fi3
ON THE PRESENT VALUE OF SUMS AT COMPOUND INTEREST.
35. When money is reckoned at compound interest, the turn to be
given in lieu of a payment at a future period, is that which laid out at
interest until the sum is due, would just provide for the payment thereof.
The method of finding the present value is therefore the reverse of find-
mg the amount. By Art. 19, we have the proportion as £1 is to its
amount in one year, so is any other sum to its amount in a year, which
proportion is also true when inverted. As the amount of £l in a year
18 to the £l which produced it, so is the amount of any other sum in a
year to the sum which produced that amount.
Make p ss the present value,
$ z=t iht sum due,
n =s the number of years,
t ts the interest of JSl for one year.
(1 + 0 : 1 ;: i : A-- = •(! + 0" * = |P'?f?' ^"^^^^ ^^ ^^^
1 + » \ at the end of one year.
(1 + 0 : 1 :: (1 + t*)-* : (l + !)"• second year,
(1 + 0:1 :: (l + t)-* : (l + O"* third year.
Generally, (1 + 0~ " = present value of £l due at the end of n years,
which multipUed by t, will give
p^sH + iy-^ *
(1 + i)-;
By logarithms,
log. p = - w log (1 + i) + log «.
Rule. Find the amount of £l in the given time, and by it divide
the sum due.
Example. What is the present value of i^350 due at the end of
10 years, 5 per cent compound interest ?
* = 350 n = 10 p = .05
By Table 3,
(1.05r = 1.628894)350 (214.810 =r f214 11 5
3251788
. 242212
162889
19323
65156
14161
13030
1131
24 ON THE VALUE OF ANNUITIES
By logarithmsy
log 1. 05-; = 1.9788101
10
log 1.05- = 1.1881070
log g = 2.5440680
2.3321750 = 214.870 = f 214 17 5
In the expression (1 + £)"" if i be taken = .02 and n= 1, 2,3,
&c. respectively, the several values ^rhich it represents will be expressed
by the geometrical series 1.02" *, 1 .02" ', 1 .02" ■, &c., which numbers
respectively denote the reciprocals of the amounts of £l at 2 per cent,
in 1, 2, 3, &c. years, the decimal values of which being found, furnish
a table of the present values of £l at 2 per cent ; when i is equal to
.025, .03, .35, &c., and the decimal values are found, the series will
give the present values of £l at 2i, 3, 3j^, &c. per cent. Tables of the
present values of £l due at the expiration of any number of years not
exceeding 100, were calculated by Mr. Smart at the rates of 2, 2]^, 3,
3i, 4, 44, 5, 6, 7, 8, 9, and 10 per cent, to 8 figures of decimals, and
published in his valuable collection of Tables ; they have been copied
from thence, and given in Table 4 of this work, with the whole of the
decimals, which will be found useful where great accuracy is required.
36. To find {s) the sum due,
(Art. 35.) P^-^.
Multiplying each side by (1 + i)" (Arith. and Alg., 110.)
By logarithms, log « = log;? + w.log (1 + i)
Rule, Multiply the present value by the amount of £l in the given
time.
Example. What sum will the present payment of £214,87 entitle
a person to at the expiration of 10 years, compound interest 5 per cent ?
p = 214.87 71 = 10 I = -05
Table 3, (1.05)" = 1.628894
78.412 = p inverted
3257788
162889
65156
13030
1140
350.0003 = iC350.
By logarithms,
Jog 1.05 = 0.0211893
10 = 71
2.5440680 £350 Digitized by GoOglc
log(1.05)»* = 0.2118930
log;? = 2.3321750
COIIFOUND INTEREST. 25
37. To find (n) the number of yean,
(Art 36.) « = 1?(1 + 0";
this equation is solyed in Art. 22 :
log * — log P
log (1 + 0 "
Rule, From the logarithm of the Bum due, subtract the logarithm of
the present value, and divide the difference by the logarithm of the
amount of £l in one year.
Example. A person at the end of a certain number of years, has to
pay £350 for the renewal of a lease, but wishing to pay some time
before the expiration of the term, he is allowed a discount of 5 per cent,
compound interest, which reduces the payment to £214.87 ; how many
years had the lease to run ?
« == 350 pvz 214.87 i = .05
logf = 2.5440680
log;? = 2.3321750
log 1 .05= .0211893)0.2118930 (10 years
2118930
38. To find (Q the rate of interest :
(Art. 36.) « = p (1 + i)",
fiom which is found by the solution of that equation in Art. 23,
Rule, Divide the diffisrence between the logarithms of the sum due
and the present value by the number of years, and from the correspond-
ing number subtract oue, the result is the interest of £l ; this mul-
tiplied by 100, gives the rate per cent.
Example. A debt of £350 is due from A to B, payable at the ex-
piration of 10 years, which A is allowed to discharge by the immediate
payment of £214.87 ; what rate per cent compound interest is allowed ?
?i= 10
« r= 350 p = !
214.87
log*
logp
=: 2.5440680
= 2.3321750
10)0.2118930
.0211893
1.05
1
.05
100
5 percent. /^ t
^ Digitized by LiOOgle
26 ON THB VALUE OF ANNUITIES
39. When interest is convertible m times a year, the amoumt of £l
at the first period of converson is [ 1 H — J ;
then fl +i J : 1 :: 1 : r 1 +— ) » the present value of £\
payable at Xhe ezpimlion of the mth part of a year, and by reasoning as
in Art. 34, we obtain ( 1 + — ) > the present value of £l due at
the end of one year, or at the end of m periods of conversion of interest,
and [1-1 j , the present v^lue of £l due at the end of n yeats,
or mn periods of conversion of interest. Tlds multiplied by 9 gives
By logarithms,
log p = log « - mn log (l + -^j.
This equation is the same as that given in Art. 29, and the expressions
for 8y 7t, m, and i, derived therefrom, as given in Arts. 28, 30, 31, and
32, furnish us with the formulae for obtaining those quantities. They
may also be found by taking the fbrmulae given when interest is payable
yearly, and substituting the number of intervals for the number of years,
and the interest for one interval instead of the annual interest.
40. To find the present value.
The formulae as given above is
,=.(..x)-.
Rule, Find the present value of £\ due at the end of the first inter-
val, and raise it to a power equal to the number of times interest is
convertible before the money becomes due, and multiply by the sum
due.
Or when the interest for one interval is equal to any of the annual
rates for which tables of the present values are given, we have only to
take from those tables at that rate, the present value of .^1 due at the
end of the same number of years as there are intervals of conversion
during the term, and multiply it by the sum due.
Example. What is the present value of £350 due 5 years hence;
allowing 6 per cent compound interest, payable half-yearly ?
Digitized by VjiOOQlC
COMPOUND INTBRST. S7
«s:350 i=:'06 n=r5 ms=2
(\ + -^^ ""=fl + ^V*^*=!=l. 03-" = .744094
2232282
372047
260. 4329 = £260 8 8
By lo^^thmsy
CO log 1*03 = 1.98716278
10
log (1.03)-"= 1.8716278
log 350= 2.5440680
2.4156958 260.433 = £260 8 8
A has a claim upon B of £925 payable [at the end of 6 yean, but
for the present payment thereof allows him a discount at the same rate
as that which may be obtained in the 3 per cents when the price of
stocks is 92^. What sum has B to pay ?
«=:925 n=6 f» = 2
* "^ 92* "*" 185 w "" 185 3 "" 185
— - 1 4- — — —
■*■ m "^ "^ 185 ■" 185
log 185 = 2.2671711
log 188 = 2.2741578
-lc^(n-i)-':=-log(J|)"L 1.9930139
1.9161668
log 925 = 2.9661417
2.8823085 = 762.620 =£762 12 5.
41. To find is) the sum due.
By substituting in the formula of Art. 36, — for h and mn for n,
we have «=:pfl+ — j ,as found also by Art. 28.
By logarithms,
log « = log p + inn . log r 1 + — j.
Rule. Find the amount of £l at the end of the first interval, raise
it to the same power as the number of intervals of conversion in the
time, and multiply by the present value.
Example. £260 8 8 is paid for the present value of a sum to be
received 6 years hence. What will the person making the payment be
then entitled to, allowing 8 per cent compound interest payable quar-
terly? ' Digitized by VjUU vie
\ ON THE VALUE OF ANNUITIES.
p =: 260.433 i = .08 n s= 6 m sr 4
By Table 3, (K02)«* = 1.608437
334.062
3216874
965062
6434
482
48
418.8900 = £418 17 10
By logarithms, '
log 1.02 = 0.00860017
24
3440068
1720034
log 1.02"* = 0.20640408
log p = 2.4156960
2.6221001 418.890
42. To find (n) the number of years.
Substituting in the formula of Art. 37> the logarithm of the amount
of J^l when intorest is payable m times a year for the logarithm of the
amount when interest is payable yearly, it becomes,
^ — log • — log p
71 S2 —
m
log(l + 1)
Rule. Divide the difierence of the logarithms of the present value
and the sum due, by the logarithm of the amount of £l at the end of
the first interval, multiplied by the number of intervals.
Example. £260 8 8 is paid down in lieu of £350, 6 per cent
compound interest payable half-yearly being allowed as discount. How
long was the sum paid before due ?
p =r 260.433 » = 350 « = 06
log « = 2.5440680 log 1.03 = 0.01283722
log;? t= 2.4156958 2
. 02567444)0. 1283722(5 years .02561444
1283722
43. To find (i) the rate of interest
Substituting in the formula of Art. 38, the number of intervals for
the number of years, we have the interest for one interval :
/Google
Digitized by ^
COMPOUND INTEREST. 29
and each side being multiplied by m, gives
t = m |(— ) "* - ll as in Art. 32.
\p / mn
Rule. Divide the difference between the logarithms of the sum due,
and the logarithms of the. present value, by the product of the number
of years multiplied by the number of periods of conversion in a
year; from, the corresponding number subtract unity, and multiply
the difference by the number of periods of conversion, in a year : the
product is the interest of £1^ which multiplied by TOO, gives the rate
per cent.
Example. At what rate per cent compound interest, payable half-
yearly, may a sum of ^350 due 5 years hence, be discharged by the
immediate payment of ^260 8 8?
p = 260.433 « = 350 n = 5 m=:2
log « = 2.5440680
logp =: 2.4156958
10)0.1283722
.0128372 = 1.03
1
.03
2
.06 = interest of £l
100
6 per cent.
44. The following Table, which shews the present value of £l due at
the end of one year when interest is payable yearly, half-yearly, quarterly,
and momently, is found by taking the reciprocals of the numbers in the
Table in page 22, and the corresponding logarithms are the comple-
ments of the logarithms in the same Table.
Digitized by LjOOQ IC
30
ON TBB VAIUS OF ANlfUniX&
Nominal
rate of
Intereat.
percent
per cent
3
per cent
3i
per cent
4
per^cent
per cent
1
Preaent
ralae
ofiClin
one jfear.
.980392
•980296
•980247
.980199
•975610
.975461
.975386
.975310
.970874
.970662
•970554
m
.970445
.966184
•965898
.965752
.965605
.961538
.961169
.960980
.960789
^956938
.956474
9
•956238
m
•955997
Logarithm of
auch preaent
vaiae.
.9913998282
.9913572524
.9913357530
.9913141104
.9892761346
.9892099362
.9891764265
.9891426380
1.9871627753
T.9870679155
T.9870197807
T.9869711655
r.985O596502
r.9849^11642
T.9848658091
r.9847996931
T.9829666607
r. 9827996565
r.9827145049
T.9826282207
T. 9808837096
r.9806733666
r.9805658615
T.9804567483
Ncmlnai
rate of
lotereat.
5
percent
6
per cent
7
percent
8
percent
9
percent
10
percent
Freaent
▼alue
of£l In
one year.
•952381
.951814
•951524
.951230
.949396
.942596
.942184
•941764
.934579
•933511
.932958
•925926
•924556
•923845
•923116
•917431
.915730
.914843
.913931
.909091
•907029
•905950
.904837
Logarithm of
each preaent
value.
1.9788107009
U9785522692
r.9784198725
U97828S2759
r.9746941347
T. 9743255506
r.9741358310
T.9739423311
T.9706162223
r.9701193004
r.9698623284
U969599386a
1.9665762445
1.9659333214
T.9655993130
T. 9652564414
r.9625735021
T.96I7674191
r. 9613467333
T.9609134966
T.9586073148
T.9576214019
1.9571045384
T.0565705518
AMOUNT OF ANNUITIdS AT COMPOUND INTEREST.
45. We now proceed to consider cases in Annuities where compound
interest is allowed.
Let » = the amount of the annuity,
a = the annuity,
fi = the number of years,
i = interest of £l per annum.
From what has been shewn in treating of the amount of Annuities at
simple interest, in Art. 14, it. appears that the amount of an annuity
of £1 in n years is found by summing the respective amounts of £l at
the end of 0,;i, 2, 3, 4. 5, &c. to (n - 1) years. The amount of £l
received at the end of 0 years after due, i, e. received immediately when
COHPOUND INTERISST* di
due is £l, tlie' amount »t the end of one year, is (I -f t) at the end of
two years (1 + 1)'., &c. (Art. 19).
The 8um of the following aeriea will therefore be the amount of £1
per annum in n years.
1 + (I + 0 + (1 + 0" + (1 + 0' + (I + iy
+ ( 1 + i)" -• + (1 + «)•-•+ (1 + 0" -'
This series form a gecunetrical progression which may he summed by
means of the formula r~ : in Art. 151 of the treatise on Arithmetic
r — 1
and Algebra where a denotes the first term, n the number of terms^ r
the common ratio; in the present series the first term is 1, the common
ratio (1 -f- O9 And number of terms n, the sum is therefore by making
the proper substitutions in the formula,
(1 + tT - 1 (1 + 0" - 1 ciy^
., , ^ =-=s -i f = amount of t\ per ann. m n years:
(1+0-1 % ' -^ '
which multiplied by a giYCs
(1 + iy — 1
« = a T- = the amount of an annuity of £a in n years.
Rule. Subtract unity from the amount of £l in n years, multiply the
^Lifference by the annuity, and divide by the interest of £l for one
year.
Esample. What will an annuity of £30 6 4 amount to in 12 years
at 5 per cent compound interest ?
a = 80.31661 n = 12 t = .05
Table 3, 1 . 05*" = 1 . 1958563
1
.1958563
16613.03
23875689
238151
1959
4115
471
55
.05)2412.1712
^482.5542 = £482 11 I
Table 5 contains the amount of £l per annum at the end of any
number of years not exceeding 100, at the several rates of ^, 2}, 3, 3},
4, 4^, 5, 6, 1, 8, 9, and 10 per cent, from which the amount of any
annuity, at those rates may be found, by multiplying the amount, in the
Table by the annuity.
Digitized by
^oogle
32 ON THE VALUE OF ANNUITIES.
Taking the last example ; under the 5 per cent column opposite
12 yean we have 15*917127
this multiplied by the annuity. . 76613.03
47751381
477514
15917
9550
955
m
482.55428 = £482 11 1 as before.
Example. What will be the amount of an annuity of £325 in 9 years
at £3 6 per cent compound interest ?
i = .033 a = 325 n = 9
log (1 +0 =log 1*033 =0.01410032
log 1. 033* = 0. 12690288 1 .339377
.339377
523
1018131
67875
16969
,033)110.2975
3342.348 = £3342 71
nearly. )
Suppose a sinking fund of £1,000,000 per annum is put by towards
the redemption of the national debt for 50 years ; what portion of it will
be discharged at the expiration of that period, assuming the interest of
money at 3h per cent ?
By Table 5, the amount of £l per annum in 50 years at 3j^ per cent
is 130.997910, which multiplied by 1,000,000 gives £130,997,910.
This calculation is made on the supposition that all the dividends
which would have been due on the redeemed stock, are added each year
to the million, and laid out in the purchase of stock to be cancelled.
46. To find (a) the annuity.
dividing each side by
o =
t
(1 +0"-i
(I + 0" - 1
Rule, Multiply the amount of the annuity by the interest of £l for
one year, and divide the product by the amount <^g]^zldW^^)i^J^^^^'°^*
less one. ^
COMPOUND INTEREST. 33
Or by tiie Tabka—
Divide the amount of the annuity by the amount of £l per annum in
the given time.
Example. A person wishes to provide £350 to be paid for the renewal
of a lease at the expiration of 10 years, what sum must he lay by annu-
ally when interest of money is 4 per cent ?
»=.04 jac350 n = 10
Table 3,
(1.04)»
= 1.480244
1
.480244)
350
.04
14.00 (29.
960488
439512
432220
7292
2490
2401
152=:
:£29 3 0
.89
Orthtt»—
By Table 5, the amount of £l per annum in 10 years is 12.006107.
12.006107)350.00000(29.152 = £29 3 0
24012214
10987786
10805496
182290
62229
60031
2198
What annuity accumulating at 3} per cent compound interest for 30
years will amount to £500 ?
,= .0375 log (I + t) = log 1.037a = 0.01598811
*= 500 30
«= 18.75 log(l+t)*=: 0.4796433 3.017472
1
2.01747
2.01747)18.75 (9.294 = £9 5 11
1815723
59277
40349
18928
18157
771
47. To find (n) the number of years.
Art. 45. ,:=a.(^+*>'-^
Digitized by VjOOQ IC
34 ON THE VALUE OF ANNUITIES,
multiplying each side by i aud dividing by a,
is
= (1 + 0" - 1
a
(1 + i) • = J + 1
by tnuisposition,
or by logarithms,
nxlog(l + 0 = log(^-i- l)
dividing each side by log (1 + t)
""^ log (1+0
Rule. Divide the product of the amount of the annuity and the in-
terest of £l for one year, by the annuity ; add one to the quotient, and
divide the logarithm of the result, by the logarithm of the amornit of £l
in one year.
Example. In how many years will a debt of £800,000,000 be dis-
charged by appropriating to that purpose annually a sinking fund of
£3,000,000, supposing the interest of money to be 3^ per cent?
s = 800,000,000 i = .035 a = 3,000,000
is , 800,000,000 X .035 , 800 x .035
1 + — = 1 + Q fxrxn r^Tkrx == ^ +
a 3,000,000 ' 3
28 31
= 1 + --=;— = 10.333333
^3 3
1(^10.33333- 1.0142404 ^^ ^^
log 1.035 = .0149403 = ^'"^^ y^^"-
In how many years will an annuity of £29 3 0 amount to £350 at
4 per cent compound interest ?
a = 29.15 » = 350 i = .04
1 . i!-. 1 . 350 X .04 14 _ 43.15
a ^ 29.15 "•" 29.15 ^ 29.15
log 43.15 = 1.6349808
log 29.15 = 1.4646386
hgfl + ~)= 0.1703422
+ ~) _ O'lW
-, — 7^ —^ "" .01703333 Di^iti^dVv^cJOvl
log (1 + I ) o
logfl +~^ 0.1703422 ,_ ^ , .
\ a J = — ;rT>.^,>^»^ = 10 years nearly, t^
-; ;^ r-A .01703333 Difed by VjOUvIC
COMPOUND INTERKOT. 35
48. To find (f) the rate of interest.
(Art. 45.) s = a (^ +0"— ^
multiplying by i and dividing by a,
Of
the quantity i is so involved in fhis equation, that we cannot directly
find its value by any of the known rules in Algebra; we may, however,
approximate to the value by the following method to any degree of
accuracy.
Let i' be a quantity found by trial somewhat near the true value off,
and call the difference between it and the true value Zi then i=zi' + z.
Substituting this value in the above equation, we have
-^i' + -^«=(l +i' + zy^l
By transposition.
a a
Expanding by the binomial theorem, this last equation becomes
(1 +iO" + n(l +i')"-»2 + ?L^!illil(l + 2')— 2»,&c.
= 1 + -t'+~ Z
a a
As z is a very small quantity, the series converges very fast, and we may
safely rqect the terms affected with the second and higher powers of
z ; the equation then is
(l + aO" + n(l+e')"-'2= 1 + -«' + -«.
a ja
By transposition,
7i(i + i0— '2- i.2=: 1+ l-t'- (1 + ify-^ .
a ' a
Le. zJn(l + t')"-'--l= 1 + -i' - (1 +i')"
I a] a
dividing each side by n (1 + i')"""* we have
1 + -ij'-(i + i')"
€v
7l(l+t')'-*-~ ^ .
® Digitized by LiOOgle
this result being added to the assumed quantity i ', gives the value of
d2
36 ON THE VALUE OF ANNUITIES.
very nearly, and a still nearer approximation may be made, if upon
trial the result is not found sufficiently exact, by proceeding in the same
manner with the value just obtained.
For common purposes, Table 5, containing the amounts of £l per
annum may be used ; for if we divide the amount of the annuity by the
annuity, we obtain the amount of £l per annum, and the nearest quan-
tity to this opposite the given number of years will give (by observing
the rate per cent under which this is found) an approximation to the
rate sought.
At what rate per cent will £20 per annum amount in 10 years to
£232.07?
s 232 07
— = — --^ — =11. 6035 = amount of £l per annum in 10 years :
a 20 r ^
referring to Table 5, we find this sum lies between the amounts of £l
per annum in 10 years at 3 and 3^ per cent.
1 1 . 7314 =: amount of .^'1 per annum at 3J^ per cent . 035
11.4639= .. .. ditto .. .. 3 per cent .03
. 2675 difference in the amounts . OO5I ^*?^"*^^
(of mterest.
11.7314— 11. 6035=. 1279
.2675 : .005 :: .1279 : .00239;
this being added to .03 gives .03239 ;
call this t ', and make the true rate f = i ' + s;
_ ^ a ^ ^ ^ _ 1 + .375837 - 1.375425
then z - ^ - 13.32276- 11.6035
n (1 + lO
.000412 ^^„^,
= , H,^» = 00024,
1.7192
t = f + z = .03239 + .00024 = .03263, which result is very near
the truth, the true value being .032625, or £3 5 3 per cent : if .03263
had not upon trial proved sufficiently near, we might then have ob-
tained a still nearer approximation by assuming i' = .03263, and
repeating the process.
The sum . 03239 obtained by adding to the rate per cent the propor-
tional part obtained from the differences, is sufficiently near for most
purposes, it differing only 6cZ. per cent from the true rate.
48. When the annuity is payable m' times a year, and interest is con-
wi
vertible m times, — ; (if a whole number) is the number of periods
m
interest is convertible in the interval between any two payments of
the annuity; the amount of £l in the m'th part of a year is therefore
(-y^-
Digitized by LjOOQ iC
COMPOUND INTEREST. 37
and the following series is therefore the amount of an annuity of .^1
at the expiration of n years, since each payment is £—f,
'A'<^- iy <' ^ ^f <' ^ ^T * ■■■■
Suhstituting, as in Art. 44, we have here 1 = the first term^ m^n zz
the number of terms, and f 1 + — j *^ = the common ratio, and the
sum of the series will be
1
('-
mj
— 1
m'
A
mJ
^ 1
m
mJ
- 1
when m = m' then — = 1, and the formula becomes
m
= a
What will an annuity of £20 amount to in 12 years at 6 per cent
compound interest, wften annuity and interest are payable half-yearly ?
a = 20 i^ .06 » = 12 w = 2
By Table 3, (1.03)" = 2.032794
1.032794
20
,06)2.065588 ^ i
344.265 = £m'^'y^^S^^
39 ON THE VALUE OF ANNUITIES.
We may also find the amount by multiplying by 10 the amount of £\
per annum in 24 yean at 3 per cent
34.4264'?
10
344.2647 s £344 5 3.
PRESENT VALUES OF ANNUITIES AT COMPOUND INTEREST.
49. The present value of £l payable at the end of one year, (Art. 35.)
is (1 + 0" ', at the end of two years, (1-i- i)" *, and generally at the
end of n years (1 + i)" * ; and the present value of an annuity being
equal to the aggregate of the present values of the several payments,
the following series will be the present value of £l per annum for
n years:
(1 + o-» + (1 + 0-* + (1 + !)-• + (1 + 0"*+----
.... + (i + 0-^-*^ + (1 + t)-^— *> + (l+i)-"i
the first term of which is (1 -(- i)" *, the common ratio (1 + i)"" \ ^^^
the nmnber of terms n ; the sum of the series by the formula .
{Arith. and Alg. 115.), where a denotes the first term, n the number
of terms, and r the common ratio will be found equal to
^ ^ j^ — rn > which becomes, by multiplying nume-
1 •- C^ + V
rator and denominator by (1 + t),
1 - (1 + Q-". ^ 1-0 + Q-"
(1 + 0-1 . i
Let us now make p = present value,
a = annuity,
n := number of years,
i == interest of £l for one year.
50. To find (p) the present value —
Multiplying the present value of i^l per annum just found by a, we
have the present value of £ a per annum
1 - (1 +f)-" '
P T=l a. ; .
I
Rule, Subtract from unity the present value of £l due at the expi-
ration of the number of years the annuity has to continue, and divide
the diflference by the interest of £l for one year; the quotient multi-
plied by the annuity gives its present value.
Example. A holds for the term of 20 years an estate by lease, of the
value of £250 per annum, for which he pays an annual J^^^gL^O.
COMPOUND INTSSES^ 39
What Bom ought he to require for the disposal of his title, supposing
him to have 5 per cent interest ?
Deducting £80 from ^250 leaves -CnO, the annuity of which we
have to find the value —
a= no » = .05 n = 20
Table 4, 1 .05" * = •31688948
1 — .37688948 = .62311052
071
62311052
43617736
.05)105.928788
2118.5757 - ^2118 11 6.
51. Table 6 contains the present values of £l per annum, at the rates
of 2, 2j, 3, 3i, 4, 44, 5, 6, 7, 8, 9, and 10 per cent, for any number
of years not exceeding 100, from which we may find the value of any
other annuity at any of the above rates, by multiplying the value in the
Table by the aiinuity of which the value is to be found. Taking the
example above ; opposite 20 years under the column of 5 per cent is
12.462210 the present value of £l per annum for 20 years
071
12462210
8723547
£2118.5757 = the amount as before.
What sum would be required for the purchase of an annuity of £20
to continue 10 years, when interest of money is £3 5 per cent ?
a s=5 20 I = .0325 w = 10
- log 1.0325 =1.98610994
71= 10 1.
log(l + 0""= 1.8610994 .7262721
.2737279 = 1 - (I +0""
20
.0325) 5.474558 ( 168.448 = dei68 9 0
325
2224
1950
.2745
2600
Digitized by LjOOQ IC
40 ON THE VALUE OF ANNUITIES.
52. To find (a) the annuity —
1~(1 +!)-•
(Art. 50.) p^a.
dividing each side by
t
t
1 - (1 + i)-
Rule. Multiply the present value by the interest of £l for a year,
and divide the product by the difference between unity and the present
value of «Sl, due the same number of years the annuity has to continue.
Or by the Tables-
Divide the purchase money by the present value of £l per annum,
given in the Tables.
Example. What annuity, to continue 20 years, may be purchased
for £500 when the interest of money is 4 per cent ?
By Table 6, 13.590326 is the present value of £l per annum for
20 years.
13.590326)500 (36.191 = £36 15 10
40770978
9229022
8154196
1074826
951322
123504
122313
1191
If if; were proposed in lieu of the 3^ per cent stock to give an equiva-
lent annuity to continue 60 years, what annuity per cent should be
granted, supposing the stock at par ?
I = .085 n = 60 p c= 100
1.— .035
Table 4, 1.035"'^= .126934 100
.873066 )3.5.. (4.009 =:£4 0 2nearly.
3492264
7736
53. To find (^i) the number of years—
(Art. 50.) prz a ^ "" ^^.'^ *^— .
Midtiplying by t, and dividing by a,*
•^ rS 1 — (1 + 0""* Digitized by Google
COMPOUND INTERBST. 41
By tran8poBiti(m»
(1 + «•)-" = i--^i
Of
by logarithms,
-nlogO +O = log;(l- ^j
or*log(l+0 = -log(l- ^),
dividiog eacli ride by log (1 + O9
^ "" log (1 + i) '
For how many yean may an animity of .^80 be purchased for
JE551 15 3, when interest of money is 3^ per cent?
p s= 551.1625 a 3 30 » =: .035
,035
27588125
16552875
30) 19>31 16875
.64372291 = -^
1^^ « .
.35627709 = 1 — -^
^^ V a) 2 0.4482121 _
log (1+0 ^ .0149403 ^ ^ y^'*
54. To find (t) the rate of interest—
(Art 50.) p ^ a. i-=-iL±Jl
multiplying eachWe by t, and dividing by a,
by transposition,
f = 1 - (i + O-j
a
(1+0-=: 1-^.
As there is no direct mode of solving this equation by any of the
kmnm rules of algebra, we must approximate to the value of t by the
following method, similar to that in Art. 48 : r^ \
Let t' be a quantity found by trial somewhat near the true value of
42 ON THE VALUE OF ANNUITIES.
t, and let 2 be its difference from the trae value, then t = i' 4- z, and
the above equation becomes
a a
expanding the first side by the binomial theorem {Ariih, and Alg, 2*75.)
= 1 - ^' - ^.
Since z must be some very small quantity, the result will be very little
affected, if we reject those tetms in which the second and higher powers
of 2 enter, which makes the equation
(l+i')"" - n (1 + 10"^"+*^ 3 = 1 - ??! - £5.
a a
By transposition,
£i _ „ (1 + ,')-(.+., J _: J _ ^ _ (1 + i^->
a a
' z {I - n (1 + 0-c- + »>} = 1 _ ^ _ (I ^. tV)--;
dividing each side by - — n (1 :t ^')-(«+o^
1 - ^' - (1 + 0-"
2 =- .
a
this being added to t' will give an approximation to the value of i ; and
if upon trial it should not be found sufficiently correct, a value may be
found still nearer by taking the value just found, and repeating the
process.
The Long Annuities, which have 30 years to run, are now sold at 19
years' purchase ; what rate of interest does the purchaser obtain for his
money ?
By Table 6, we find the rate lies between 3 and 3^ per cent.
19.600441 = No. years' purchase at 3 per cent
18.392045 = ditto 3j per cent
1.208396 = difference
.035 19.600441
.03 19^^
As 1.208396 : 005 :: .600441 : .0024828
Letf = .03 + .0024828= .0324828;
then assume i = i' + ar = .0324828 •{- z /- t
Digitized by LjOOQ IC
z =
COMPOUND INTERKST.
1 — ^ — (1 + »0""
a
a
43
1 - 19 X .0324828- 1.0324828-*°,
- .0000913
19-30(1.0324828)-"
% = .0324828 - .0000513 = .0324315 = interest of £l
.0324315 X 100= 3.24315 = £3 4 lOj per cent.
55. When interest is convertible m times a year, and the annuity
a
payable m' times, each payment being — , the present value of the first
payment is — j [ 1 + — W ; the number of payments in n years is
m'tiy and the present value of the annuity is the sum of the series
<^.*ir\
where the first term is ( 1 + — ) "^ , the common ratio ( IH ) "^,
and the number bf terms m'n, which being substituted in the formula
1 -r
-, as in Art. 49., the present value of the annuity becomes
lultiplying numerator and denominator by ( 1 + — y y
p= — X
m
a
o = — X
^ m
becomes
P =
when m and m' are equal, this
m
i(-i)-
= — X
m
m
=r a.
-(■-0
Digitized by VjOOQ IC
44 ON THE VALUE OF ANNUITIES,
What sum would be required to purchase an annuity of £20 to con-
tinue 15 years in the Government Office, when the price of the 3 per
cent consols is such as to yield an interest of £3 5 per cent ?
Here the annuity and interest are both convertible half-yearly.
/. m = 2 a = 20 i = ,0325 n = 15
2). 0325
.01625
1.
— log 1.01625 = 1.99299944
30 = mn
1 .7899832 .616511 = (1 + «)"""
K
.383429= l-(l + 0-*"
20
. .0325)7.66858(235.956 = £235 19 1
^^^ which a(^«cwith the rate in-
1 1 iSQ serted in tiie OoTeniment scale
^ ^ ^ for granting life aaniutiea.
• 1935
1625
3108
2925
PERPETUITIES.
; 56. When the annuity is to continue for ever, it ia called a perpetuity,
in which case n is infinite, and in the formulae = a ^ — ,
* i
given in Art. 50, the value of the quantity (1 + t)-" is less than any
that can be assigned ; that part of the formula therefore vanishes, and
the expression becomes
P
=: a.-T- = -r =, the present value.
Rule. Divide the annuity whose value is to be found by the interest
of •^l per annum.
What is the present value of an estate in fee simple of ^^434 |)er
annum, when interest of money is 4 per cent?
^ = £10850. '
Digitized by LjOOQ iC
COMPOUND INTKREST. 45
57. To find (0 the annuity— '
(Art. 56.) ;? = 4-,
multiplying eacli Bide by t,
a = ip/
Rule. Multiply the present value by the interest of £1 per annum.
Example. What perpetuity will £925 purchase when money bears
5 per cent interest ?
p = 925 i = .05
.05
46.25 = -^46 5 0
58. To find (t) the interest—
(Art. 51.) a = ip, '
dividing by p,
I • = — s= , interest of £\ per annum
V
lt)0 % s= ^ = ditto per cent.
P
Hide. Multiply the annuity by 100, and divide by the principal,
which gives the rate per cent.
What rate per cent is obtained when £925 secures a perpetuity of
£46 5 per annum?
o = 925 a^ 46.25
100
925)4625(5 per cent.
4625
When the annuity is payable m! times in a year, and interest is con-
vertible m times, ( 1 + — ) vanishes in the formula of Art. 55.,
when the annuity is perpetual, and the expression then becomes
a 1
p = — X
{^*iy-^--
if the annuity is always payable when interest is convertible, then
m = m' and the formida becomes
« = — X r-r = — X — r- = -:-, wluch coincides
with the formula for finding the present value when the annuity and
interest are payable yearly. ^^.^.^^^ ^^ ^uu^Ic
46 ON THE VALUE OF ANNUITIEa
REVERSIONS.
59. When an annuity is not to be entered upon until after the
expiration of a certain number of years, it is caUed a Bevernonary or
Deferred Annuity^ the present value of which may be obtained by
finding the present value of an annuity to be entered upon immediately
and continue until the expiration of the reversion, and subtracting
therefrom the present value of an annuity to be continued only until
the time of entering on possession of the reversion ; for it is evident
that if an annuity be deferred d years, and then continue n years, its
present value will be less than that of an annuity to be received during
both the d years and the n years by the present value of an annuity for
d years.
Let p = the present value,
a = the annuity,
n = number of years the annuity continues,
d = number of years deferred,
i = annual interest of £l ;
then Art. 50. p = a. ^ . a. ^ .
= a, :
t
Rule, From the present value of £1, due the number of years de-
ferred, subtract the present value of £l, due at the same time as the last
payment of the reversionary annuity, midtiply the difference by the
annuity, and divide by the annual interest of £l.
Example. What is the present value of the reversion of £30 per
annum for 8 years, to be entered upon after the expiration of the next
10 years; interest 5 per cent?
(1 + 0"** = 1.05-" =: .613913
(1 + 0"^**+'^ = 1.05-" = .415521
.198392*
30
.05)5.95176
60. To find (a) the annuity.
(Art. 59.)jP=o-
multiply by
119.035= £119 0 8.i
(1 + 0-
■" - (1 + l)-'-*")
i
i
0 +»■)-"
- (1 +»)-"'+"
ip
(I + 0-' -(1 + 0-^'+"^
Ruk. Divide the product of the present value of the annuity and
the annual interest of £1 by the difference between the present value
REVERSIONS. 47
of £l due the number of years the annuity is deferred, and the present
value of £l due when the last year's annuity becomes payable.
Example, What annuity to continue 8 years after the expiration of
tbe next 10 years may be purchased fcur £l 19 0 8j^ when the interest of
money is 5 per cent ?
/» = 119 0 8i = 119.035 d = 10 n = 8 i = .05
Table 4, 1.05-»* = .613913 p =. 119.035
1.05-" = .415521 t=: 05 ^
. 198392 ) 5 . 95175(30 annuity.
5 95176
61. To find (n) the number of years.
t
multiply by i and divide by a,
(1+i)--- (1 + i) -<'+•) =^
a
by transposition, (1 + t) -* — ^ = (1 + «)-<' + •>
multiply each side by (1 + i) '
but(l+i)»=l,
/. (i + 0"" = i--f 0 + 0'
by logarithms - n X log (1 + 0 = log {l - -^ (1 + 0'}
dividing each side by — log (1 + t),
- log {l - f (1 + 0-}
"^ log (1 + 0
Emmple. The sum of £ll9 0 8^ is given for the purchase of an
aniniity of £30 to be entered upon after the expiration of 10 years ;
how long will the annuity continue, reckoning interest at 5 per cent ?
p = 119.035 71 = 10 i = .05 a = 30
^P,. . ^«r 1 119.035 X .05 X 1.05"
1.^(1 + , V=l ~
Table 3, 1.05 " = 1 .628895.
ip,, ^^ , 119.035. X .05 X 1.628895
...1 « ^ (I + I) = 1
n =
= 1 - .323157= .676843 Digitized by GoOglc
48 ON THE VALUE OF ANNUITIES.
* I g ^ ^ ^ ( _ —log .676843
log(l + 0 log 1.05
.169512 „
=:o2ii89=^y^-
62. To find (d) the number of years deferred.
Art. 61, (1 + i)-' - (1 + 0 -^'+-> = ^;
a
i-cd+o-Mi -(i + t)-} =-^.
by logarithms, - d Xlog(l+ 1) + log{l - (1 + 0 "'} = log ~;
by transposition, d log (1 + 0 = log {1 — (1 + i) --} - log -2;
a
dividing by log (1 + 0
log{l-(l+0-}-log^
d =
log (I + 0
Example, A deferred annuity of £30 to continue 8 years is pur-
chased for £119 0 8^- when the interest of money is 5 per cent; it is
required to determine how many years the annuity is deferred.
;>= 119.035 n = 8 i=.05 a = 30
1.00000000 119.035
Table 4, 1.05-' .67683936 ,05
1 - 1.05-« = .32316064 30)5.95175
.198392 =^
a
logll - (1 +»^"""} — 1<«-^ ,
^ ^- log .82316064 - log .198392 _
log (1 + 0 log 1.05 ^
.50941 - .29752 _ ,21189 _
.021189 ■" .021189^ lOyears.
63. To find (0 the annual rate of interest.
(Art.59.)p=a<L+0-^-O + 0-^^"-\
multiply each side by -,
(l+i)-''-(l + 0-^'+"' = -^- ^
^ Digitized by Google
REVERSIONS.. 49
Let t' be a quantity found by trial somewhat near the true value of t,
ind let t = t' + z, then by substituting this value in the above equa-
tion, it will become
(1 + »•' + 2)— -(1 + .' + 2)-w+') = ? (i' + «);
bjthe binomial theorem,
{(1+ iO + 2}- =(1 + tO-' - d(l + i')-^'+»z +
did + l)
-<'+«) - (d + n)
(1 + i')-^*+'+*>2* — &e.
2
{(1 + 10 + *}-''+* = (1 + iO"^'*"' - (d + n)(l +iO-'***+"«
^ (d + «) (d + n + 1)
2
aibtncting the second series from the first and rejectiog the terms
iffiicted with the second and higher powers of x, we obtain
(1 + i')-*- (1 + i')-<*+'^ - d (I + i')-^'+» z
+ («l+ n) (1 + ,')-«'+•+ 0* = ^ + £?.
by tnnspoMtion, ^ + <l(l + %')-» + » « — (d+n)(l + i')-<''+"+"«
= (1 +»')-'- (1 + ^0-''+"'-^;
dividing each side by ^+d(l + »')-'*+" -(d + n)(l + 1')-''+'+«
we obtain
I +dO +iO"^'+'^ — (4 + n)(l +«')-('+"+o
a
Example, At what rate of interest will £645.174 purchase an
annuity of £lOO to be entered upon after the expiration of 8 years, and
then continue 10 years ?
By a few trials we find the interest is between 3 per cent and 3]^ per
cent; let us then make i' = .03.
l+i'=1.03 rf=8 n=10 a = 100 21 = 645.174
Tablc4, (1.03)-* = .789409 =(1 +iO"^' .03
(1.03)"*'= .587395 = (1 + iO"^''+"> 100)19.3552
.202014 .193552=*-^
. 193552 «
. 008462= (1 + i')-''-(l +t')-c-+-)- IP
?=.!>iyi4= 6.45174.
Digitized by VjOOQIC
50 ON THE VALUE OF ANNUITIES.
Table4, (1.03)-«= .766417 = (1 + iO-^^+*^
8
6.131336 =:d(l +t')-<^+'>
6.45174
12.58307=^ + d(l +»^ -<-+»>
Table4, LOS-^s .570286= (I +«')-<'+"+«
81
570286
456229
10.26515 2= (d + n) (1 + {')-<*+*+'>
12.58307
2.31792 =^+d(l+tO-^^'^-(rf+w) (1+0"^'^*^*^
2.318).008462(.0036 = z
6954
1508
i = i' + 2 =: .0336, which on trial will be found extremely near
the true value, which is .0333.
64. When the reversion is in perpetuity ^ (1 + a) -<^ + «> in the for-
mula of Art. 59. vanishes, and the equation becomes
^(1+0-"
^ = -—'
Rule. Multiply the present value of £l, due the number of years the
perpetuity is deferred, by the annuity, and divide by the annual interest
ofiCl.
Example. What is the present value of the reversion of a perpetuity
of £50 per annum after 10 years, at 5 per cent interest ?
a = 50 rf = 10 f = .05.
Table 4,. (1 +0"'= (1. 05) -^'^s. 613913
50 = a
.05)30.69565
613.913 = £613 18 3.
65. To find (a) the annuity,
multiplying by i and dividing by (1 + t") "" '
Rule. Multiply the present value of the reversion by the annual
interest of £l and by the amount of £l at the end of the term the per-
petuity is deferred. Digitized by kjkjkj^ ic
KSVERSIONS. 61
EsDample. The reversion of a fee simple estate after 10 years is sold
for £613 18 3^, what annual return should it produce to allow the
purchaser 5 per cent interest for his money?
d = 16 i zri .05 p = 613.914
.05
30.6951
98826.1
30696
18417
614
245
24
3
49.999 Answer £50.
66. To find (<f ) the number of years deferred.
Art. 64. O =: — ^^ r-^
miiltiplying by i and dividing by a,
a
by logarithms,
-dxlog(l+t) = log^,
a
log I
log (1 + 0
Example. If an annuity of £50 be purchased for ^^613 18 3^ at
5 per cent interest, what period must expire before the annuity is
entered upon ?
p = 613 18 3J =613.914 i= .05 o = 50
■ 05
50)30.6957 = ip
.613914=^-
a
— log ^
a —log .613914 .211892
-A = —ill nx = -F^rrahTT = ^^ y^^ars.
log (1 + 0 log 1.05 .0211892
67. To find (0 the annual rate of interest.
Art. 64. (1 +0-**-^
^ Digitized by Google
B 2
52 ON THE VALUE OF ANNUITIES,
assume t' as a quantity somewhat near the true value of i| and let the
true value be i = i ' + z ; then the equation becomes
a a
expanding {l +i' + z)^' by the binomial theorem {Ariih. and
ii/^.275.) we have"
(1 + i')-' - d (1 + tO-^' + '>2 + ^ili:i2(i+i0-(^+«2t-,&c.
a a
rejecting the second and higher powers of z, which being very small,
will not much affect the result.
(I + i')-- -. d (1 +0-^^+^^ 2 = ^ +^i
a a
by transposition, d (I + iO"" ^' "^ *^ « + - « = (1 + O " ' — — ;
a J a
dividing each side by d (1 + O""^' "^^^ + -.
a
z =
d(l+£/)-^'+«+?.
Example. What rate of interest is allowed when £923 2 5 will
purchase a perpetuity of £40 per annum, to be entered upon ader the
expiration of 8 years?
By a few trials the rate of interest is found to be between 3 and 3^
per cent; let us make i' = .03.
(1 + 2')--= 1.03-«=. 789409 • 923.1208X .03.
.692341 =ili = ^±tllf^^±.
a 40
-rf pi'
.097068 =:(! + 10-'' -
a
dO +i')-^^ + ^) +5 = 8 xl.03-* +
923.1208
a ' 40
= 8 X .766417 + 23.07802 = 6. 131336 + 23.07802 = 29.20936,
Digitized by ^^UUV IC
REVBRSIONS. 53
« .097068 __
= .0033,
d(l + 0-^-+^^+^ 29.20936
i= .03 + .0033= .0333
100
3.33 per cent.
RENEWAL OF LEASES.
68. The fine to be required for renewing any number of years ex-
piitd in a lease will be the present value of an annuity deferred for the
unexpired term of the lease, and then to continue for the period re-
newed ; we ha?e therefore the following rule :
Rule. From the present value of an annuity to continue from the
present time until the expiration of the renewed term subtract the
present value of an annuity to expire with the original term of the lease.
Example, Fifty years having expired in a lease for the term of 60
years, what sum should be paid for renewing them, supposing the estate
to produce a clear rental of £90 per annum, and the interest of money
5 per cent?
By Table 6,— the value of £l per annum for 60 years is 18.9293
ditto for 10 years, the unexpired term 7 . 7217
11.2076
90
j£l008 13 8 1008.684
Example 2. Thirty years having expired in a lease for 40 years,
required to know the fine for renewing 10 years of the same, supposing
the yearly rental .£60, and the rate of interest 5 per cent.
40 — 30 = 10 = unexpired time,
10 + 10 = 20 = number of years until the expiration of the
renewed term.
By Table 6, — the value of ^^1 per annum for 20 years 12.4622
ditto, for 10 years, the unexpired time 7.7217
4.7405
60
^284 8 7 284.430
69. The following Tables show the number of years' purchase that
ought to be paid at different rates of interest for the renewal of any
number of years lapsed in a lease for the original term of 10, 20, 21,
and 40 years :
Digitized by VjOOQ IC
Tablb for renewing any namber of years lapied in a
Lease for Ten Yean.
Ycm.
3 per cent
i per cent
5 per cent
6 pet cent
8 per cent*
10 per cent
1
.7441
.6756
.6139
.5584
.4632
.3855
2
1.5105
• 1.3782
1.2585
1.1503
.9634
.8096
3
1.2999
2.1088
1.9354
1.7777
1.5037
1.2761
4
3.1130
2.8688
2.6469
2.4428
2.0872
1.7893
5
3.9505
3.6591
3.3923
3.1477
2.7174
2.3538
6
4.8131
4.4810
4.1758
3.8950
3.3980
2.9747
7
5.7016
5.3358
4.9985
4.6871
4.1330
3.6577
8
6.6167
6.2248
5.8623
5.5267
4.9268
4.4090
9
7.5593
7.1494
6.7694
6.4167
5.7842
5.2355
10
8.5302
8.1109
7.7217
7.3601
6.7101
6.1446
Table for renewing any number of years lapsed in a Lease for Twenty Years.
Ttan.
3 per cent
i per cent
6 per cent
6 per cent
8 per cent
10 per cent
1
.5537
.4564
.3769
.3118
.2145
.1466
2
1.1240
.9310
.7726
.6423
.4463
.3122
3
1.7114
1.4247
1.1881
.9927
.6965
.4920
4
2.3164
1.9380
1.6244
1.3640
.9668
.6899
5
2.9395
2.4719
2.0826
1.7577
1.2587
.9075
6
3.5814
3.0272
2.5636
2.1749
1.5739
1.1469
7
4.2425
3.6047
3.0686
2.6172
1.9144
1.4102
8
4.9235
4.2053
3.5990
3.0861
2.2821
1.6999
9
5.6249
4.8298
4.1558
3.5830
2.6792
2.0185
10
6.3473
5.4794
4.7405
4.1098
3.1081
2.3690
11
7.0914
6.1550
5.3544
4.6682
3.5713
2.7545
12
7.8578
6.8576
5.9990
5.2601
4.0715
3.1786
13
8.6472
7.5883
6.6758
5.8875
4.6118
2.6451
14
9.4603
8.3482
7.3865
6.5526
5.1953
4.1583
15
10.2978
9.1385
8.1327
7.2576
5.8254
4.7228
16
11.1604
9.9604
8.9163
8.0048
6.5060
5.3437
17
12.0489
10.8152
9.7390
8.7969
7.2410
6.0267
18
12.9640
11.7042
10.6028
9.6365
8.0349
6.7780
19
13.9066
12.6288
11.5098
10.5265
8.8922
7.6045
20
14.8775
13.5903
12.4622
11.4699
9.8181
8.5136
Table for renewing any number of years lapsed in a Lease for Twenty-one Years.
1_
Y-r.
3 per cent.
4 per cent.
5 per cent
6 per cent.
8 per cent
10 per cent
1
.5375
.4388
.3589
.2942
.1987
.1351
2
1.0912
.8952
.7358
.6060
.4132
.2838
3
1.6615
1.3699
1.1316
.9365
.6449
.4473
4
2.2489
1.8635
1.5471
1.2868
.8952
.6271
5
2.8539
2.3769
1.9834
1.6582
1.1654
.8250
6
3.4771
2.9108
2.4415
2.0518
1.4573
1.0426
7
4.1190
3.4660
2.9225
2.4691
1.7726
1.2820
8
4.7801
4.0435
3.4276
2.9114
2.1130
1.5453
9
5.4610
4.6441
3.9579
3.3802
2.4807
1.8350
10
6.1624
5.2687
4.5147
3.8772
2.8778
2.1536
11
6.8848
5.9183
5.0994
4.4040
3.3067
2.5041
12
7.6289
6.5938
5.7133
4.9624
3.7699
2.8897
13
8.3953
7.2964
6.3579
5.5543
4.2702
3.3138
14
9.1847
8.0271
7.0348
6.1817
4.8104
3.7803
15
9.9978
8.7870
7.7455
6.8468
5.3939
4.2934
16
10.8353
9.5773
8.4917
7.5517
6.0241
4.8579
17
11.6979
10.3993
9.2752
8.2990
6.7047
5.4788
18
12.5864
11,2541
10.0979
9.0911
7.4397
6.1618
19
13.5016
12.1431
10.9617
9.9307
8.2335
6.9132
20
14.4442
13.0676
11.8688
1.08207
9.0909
7.7396
21
15.4150
14.0292
12.8211
1.17641
10.0168
8.6487
BBNEWAL OF LBASSS.
55
Table for renewing any number of yearg lapsed in a lease for Forty years.
1
3 per cent.
4 per cent.
5 per cent.
6 per cent
a per cent.
10 per cent.
.3066
.2083
.1420
.0972
.0460
.0221
2
.6223
.4249
.2922
.2003
.0957
.0464
3
.9475
.6502
.4478
.3095
.1494
.0731
4
1.2825
.8845
.6122
.4253
.2074
.1025
5
1.6276
1.1282
.7849
.5481
.2700
.1349
6
1.9829
1.3816
.9662
.6782
.3377
.1705
7
2.3490
1.6451
1.1565
.8161
.4107
.2096
8
2.7260
1.9192
1.3564
.9622
.4896
.2527
9
3.1143
2.2043
1.5663
1.1172
.5748
.3000
10
3.5143
2.5007
1.7866
1.2815
.6668
.3521
11
3.9263
2.8091
2.0180
1.4556
.7662
.4094
12
4.3507
3.1297
2.2610
1.6401
.8735
.4725
13
4.7877
3.4632
2.5161
1.8358
.9894
.5418
14
5.2379
3.8100
2.7839
2.0431
1.1146
.6181
15
5.7016
4.1707
3.0651
2.2629
1.2498
.7020
16
6.1792
4.5458
3.3604
2.4959
1.3959
.7943
17
6.6712
4.9359
3.6705
2.7429
1.5536
.8958
18
7.1779
5.3417
3.9961
3.0047
1.7239
1.0075
19
7.6997
5.7636
4.3379
3.2822
1.9078
1.1304
20
8.2373
6.2024
4.6969
3.5764
2.1065
1.2655
21
8.7910
6.6588
5.0738
3.8882
2.3210
1.4141
22
9.3613
7.1335
5.4695
4.2187
2.6527
1.5776
23
9.9487
7.6271
5.8850
4.5690
2.8030
1.7575
24
10.5537
8.1405
6.3213
4.9404
3.0732
1.9553
25
11.1768
8.6744
6.7794
5.3340
3.3651
2.1730
26
11.8187
9.2297
7.2604
5.7513
3.6804
2.4124
27
12.4798
9.8071
7.7655
6.1936
4.0208
2.6757
28
13.1608
10.4077
8.2958
6.6625
4.3885
2.9654
29
13.8621
11.0323
8.8527
7.1594
4.7856
3.2840
30
14.5846
11.6819
9.4374
7.6862
5.2145
3.6345
31
15.3287
J12.3574
10.0513
8.2446
5.6777
4.0200
32
16.0951
13.0000
10.6959
8.8365
6.1780
4.4441
33
16.8845
13.7907
11.3727
9.4639
6.7182
4.9106
34
16.6976
14.5506
12.0834
10.1290
7.3017
5.4238
35
18.5351
15.3410
12.8296
10.8339
7.9319
5.9883
36
19.3977
16.1629
13.6131
11.5812
8.6125
6.6092
37
20.2862
17.0177
14.4358
12.3733
9.3475
7.2922
38
21.2013
17.9067
15.2997
13.2129
10.1413
8.0435
39
22.1439
18.8312
16.2067
14.1029
10.9987
8.8700
40
23.1148
19.7928
17.1591
15.0463
11.9246
9.7791
Digitized by VjOOQ iC
56 ON THE VALUE OF ANNUITIES.
70. If a lease be granted for n years, subject to a fine of £1 every v
years, the presen^value of the future fines will be
(1+0- + (1 + 0 — + (1+0-''+.. ..+(1+0-^-*^;
the sum of which may be found, as in Art. 49. equal to
(1 + t')-'--(l +t)-" _ 1 — (1 +0"<«~»
l-(l+t)-' - (l + 0*~l '
there being no fine at the expiration of the lease, and - being a whole
number. .
f 1
71. When n is infinite the formula becomes ,, . ^ . — 7, the
(I + 0 — 1
present value of the perpetuity of all such fines.
72. The amount and present values of annuities might have been
obtained without the aid of geometrical series, by using the ingenious
mode of reasoning which Mr. Milne has given in his treatise.
The annual interest of £l being i, the present value of a perpetuity
of £i per annum will be £l.
i : 1 :: a I Ti the present value of a perpetuity of £«, as in Art. 56.
73. If the perpetuity be deferred n years,' the party entitled will, at
the expiration of that time, enter upon the perpetuity which is equiva-
lent to a single payment of -; the present value of a perpetuity of £a
deferred n years may therefore be considered as the present value of the
sum of £-7, t
aiX +0-"
sum of £-7, to be received at the end of n years, which is equal to
-, as in Art. 64.
74. If A be entitled to a perpetuity of £a to be entered upon imme-
diately, and B be entitled to a similar perpetuity, to be entered upon at
the expiration of n years, A will be entitled to an immediate annuity for
n years more than B, the difference between the value of A's title and of
B's will therefore be the present value of an annuity of £a for n years ;
i.e«
a a(l+0~" l-(l + 0"" . A^ ^n
^ — 7-^ — = a. ~ — ' — , as m Art. 50.
% % X
75. If the annuity forn years is not to be entered upon until the
expiration of A years, the party entitled may be considered as coming
then into possession of a sum equal to o. : — , which mul
Digitized by ^^UUV
le
REVERSIONS. , . ^7
tiplied by ( 1 + i) ~~ '> ^^^ present value of J^l due at the enaof d yatn^
gives the present value of the deferred annuity, viz.
a. -^^ ' r , as m Art. 59.
t
76. The amount of £l in n years is (1 + 1) * ; this result is made
up of the original £l, an annuity of £i, and the interest on the annuity ;
if, therefore, the original £l be subtracted, the difference (1+i)"— 1
vrill be the amount of the annuity £t, with the interest thereon, and
the amount of any other annuity will be in the same proportion.
i : (I + 0 * — l::a : a.— "tl^H-L , as in Art. 45.
RECAPITULATION OF FORMULiE.
SIMPLE INTEREST.
7*7. Let s = the amount, p the principal, n = number of years,
and i = interest of £l for one year.
* = P (1 + wO,
P =
1 + inr
n = — : ,
tp
i = LIZ-P.
np
DISCOUNT.
78. Let d = the discount, p = the present value, s = the sum due,
n =: the number of years, t = the interest of £l for one year.
p
r=
1 +in
s
=
Pil +
in).
n
=
s-p
ip ^
i
=
s^p
np
d = «-——-
I + tn
Digitized by VjOOQ iC
68 ON THE VALUB OF ANNUITIES.
AMOUNT OF ANNUITIES AT SIMPLE INTEREST.
Let s = the amount, a = the annuity, n = the number of years, i =
annual interest of £ I .
J , n(n - 1) 1
2«
a =
2n + 71 (n — 1) £'
n =:
^8ii+(2-t)«-(2«»);
2}
<=<H.-
71 (n — 1)
AMOUNT OF SUMS AT COMPOUND INTEREST.
80. Let 8 = the amount, p = the principal, n = number of years,
i =: annual interest of .^1.
When the interest is payable yearly.
« = 1> (1 + 0 " log » = nlog (1 + t) + logp,
7? = * (1 + »)- " log j» = — 71 log (1 + 0 + log «,
logjj-logp
log (1 + 0 *
i = ^yl^ 1 log \/r=: i2glziIoiP.
81. When interest is convertible m times a year.
8 = ;?M + -^j log J? = mn. log (I + ~- j + log^,
^"\* "^ W ^^gi'="-'^^log(l+^) + log»;
j^ _ log < - log p
_log g — log p
7.l0g(^l+±)i
m:
;:=„{fi\=_a 1 /A^^ log. -logy ^
IW i ^W D^«ed by Google
RECAPITULATION OF FORMULA* 59
PRESENT VALUES OF SUMS AT COMPOUND INTEREST.
82. Let p = the present value, s = the sum due, n = the number
of years, i =: the annual interest of J^l.
p == « (1 + 0 " " log j9 = — n log (1 + i*) + log «,
» = P (1 + 0" log » = 71. log (1 + 0 + log p,
_log^ — logj?
«=V^i-I.
83. When interest is convertible m times a year.
p = » ^1 + -1-j log 7? = — mn log Tl + -^ j + log*,
' = 1' n + ^j log « = mn. log f 1 + —■) + log J»>
n =
m
_ log g - log ;?
^ log ^ - log ;?
n
AMOUNTS OF ANNUITIES AT COMPOUND INTEREST.
84. Let s = the amount, a = the annuity, n = the number of
jeais, and i =: the annual interest of £l.
When annuity and interest are payable once a year —
(l+^)•-l
s = a.
a —
t
is
(1 + ^r - 1'
log a + i)
* ^ 12 + 2 (n + 1)/J ' ^'^^^/^ - l^an; *'
PRESENT VALUE OF ANNUITIES AT COMPOUND INTEREST.
85. Let p = the present value, a = the annuity, n = the number
of years, and i = interest of £l for one year.
* For tho investigation of this fonnula see Baily's << Doctrine of Interest and
Digitized by VjiOOv IC
60 ON THE VALUE OF ANNUITIES.
1- (l + O-
p ^ a.
a =
t
i-(i + o-;
log (1 + 0
12 — 2 (« - \)fi *
where fi = f -f?Vn — l.
86. When the annuity is a perpetuity.
a
P= J.
o =: tp.
PRESENT VALUES OF DEFERSED ANNUITIES.
87. Let j> = the present value, a = the annuity, n = the number
of yean the annuity is to be received, d = the number of yean it ia de-
ferred, t s the annual interest of £l.
«-- (i-}-0-''-(i-f 0-^^+^
p-a. -.
ip
n =
d =
log (1 + 1-)
ip
log{i - (i^.,-)-}- log -21
a
log (1 + 0 '
{i2;-(ft'-i))8}/t
12-2 (n« - l)y8 '*
where « = 2rf+ n + 1 &j3 = ^— Y> — 1.
88. When the deferred annuity is a perpetuity.
p - -. ,
* Vide Baily'f " Doctrine of Intetett and Annuitiei."
t Vide do. do. Digitized by Google
REeAPTTUlATION OP FORMULAE. 61
d =
log (1 + 2^ »
{6 + (5d+ l)fi}fi
6+4(2(f+l)i3, •
where /3= ('^±-^')7. « i •.
PRACTICAL RULES AND EXAMPLES.
SIMPLE INTEREST.
89. To find tlie interest of a sum for any number of years.
Rule, Multiply the sum by the interest of £l for one year, and the
product by the number of years.
Example I. What is the interest of ^£462 10 0 for 6 years at 4 per
cent simple interest?
462 10 0= 462.5
M
18.500
6
111.000 Answer £111 0 0.
90. Example 2. What will £925 amount to in 8 years at 4i per
cent simple interest ?
925
.045
4625
3700
41.625
8
333.000 ==
£333 0 0 = interest,
925 0 0
1258 0 0 Answer.
91. To find the interest of a given sum for any number of days.
Rule, Find in Table 2 the decimal part of a year corresponding to
the number of days, multiply it by the sum and by the interest of £l
for one year.
• Baily's " Doctrioe of Interest and Annuiti«».^'''^ bydOOglC
62 ON THE VALUE OF ANNUITIES:
Example. What is the interest of £500 for 123 days at 5 per ceDt
simple interest ?
In Table 2, opposite 123 days, we have .336986
this midtiplied by .05
gives .0168493
which multiplied by 500
gives 8.42465 s=
Answer £8 8 6.
92. When the interest is to be found for a given number of years
and days, prefix the number of years to the decimal parts of a year cor-
responding to the number of days, and multiply as before.
Example. What is the interest of £500 for 4 years and 123 days at
5 per cent ?
Prefixing 4 to the decimal for 123 days, we have 4.336986
this multiplied by .05
gives = .2168493
which multiplied by 500
gives 108.42465 =
£108 8 6 Answer.
93. To find the interest without the aid of the table, multiply twice
the rate per cent by the number of days, then multiply the principal by
the result and divide by 73000.'
Example. What is the interest of J&500 for 123 days at five .per
cent?
500
10
5000
123
73.000)615.000(8.424 = 886
584
310
292
180
146
340
Or, instead of dividing by 73000, we may divide first by 100000,
then the result by 3, and this quotient again by 10, and the result again
by 10, the sum of the quotients will be the interest required.
Required the interest of £715 8 6 for 120 days alf^f per^n8
PRACmCAL RULES AND EXAMPLES. 63
113 8 6 = 115.425
I
5007.975
120
100000)600957.
+ 6.00957
tV 2.00319
tV 20032
2003
8.23311 ^848.
COMPOUND INTEREST.
94. To find the Amount of a sum in any number of years.
Look in Table 3, under the given rate per cent opposite the number
of years for the amount of £l, then multiply it by the sum of which the
amount is required.
Example, Required the amount of .f 835 in 12 years at 4j^ per cent
compound interest.
In Table 3, under 4j^ per cent opposite 12 years, we find 1 .69586
this multiplied by 835 .
gives 1416.060=
j£l416 1 2, the amount required.
95. To find the Present Value of a sum to be received at the end
of any number of years.
Look in Table 4, under the given rate per cent opposite the number
of years for the present value of £l, which multiplied by the sum will
give the present value required.
Example, What is the present value of £835 to be received at the
end of 12 years, reckoning at 5 per cent compound interest ?
In Table 4, under 5 per cent opposite 12 years, we find .556837
which multiplied by 835
gives 464.964=
£464 19 3, the present value required.
ANNUITIES AT COMPOUND INTEREST.
96. To find the amount of an annuity in any number of years.
In Table 5, under the given rate per cent opposite the number of
years, find the amount of £l per annum and multiply by the annuity.
Example, What is the amount of £80 per annum in 12 years, at 4
per cent compound interest ? Digitized by vjuu^Ic
64 OK THE VALUE OF ANNUITIES.
In Table 5, opposite 12 yean under 4 per cent, we find 15.0258
which multiplied by 80
gives 1202.064 =
£1202 1 3.
9*7. To find the present value of a Temporary Annuity.
Find in Table 6 the present value of £l per annum and multiply it
by the annuity.
Example. What is the present value of .^80 per annum for 12 years
at 4 per cent compound interest?
In Table 6, under 4 per cent opposite to 12 years, we find 9 . 3850
which multiplied by 80
gives 150.800=
£750 16 0, the present value required.
98. To find what Annuity a given sum will purchase.
Divide the sum by the present value of £1 per annum found in
Table 6. .
Example. What annuity may be purchased for £750 16 0 for 12
years at 4 per cent compound interest?
£
9.385)750.80(80
750.80
99. To find the present value of a Deferred Annuity.
Find in Table 6 the present value of £l per annum, to be entered
upon immediately, and continued until the expiration of the deferred
annuity, and subtract from it the present value of £l per annum for the
term the annuity is deferred.
Example. What is the present value of £60 per annum, to be
entered upon at the expiration of 12 years, and then continued for 9
years at 4^^ per cent compound interest ?
12+ 9 = 21.
In Table 6 we find the present value of £l per annum) , « AfiAn
for 2 1 years | 1 3 . 4U4 7
for 12 years 9.1186
the difference 4.2861
multiplied by the annuity 60
gives 257.166
= £257 So^tizedbyVjUUvlC
DEFERRED ANNUITIES. 65
100. To find the value of a Perpetuity.
Multiply the perpetuity by 100 and divide by the rate per cent.
Example. A person is about to purchase a freehold estate producing
J^90 per annum, what sum should he give to allow him 4 per cent interest
for his money ?
The annuity 90
multiplied by 100
gives 9000
which divided by the rate per cent, gives
9000 ^^^^
4
101. To find the present value of a Deferred Perpetuity,
Multiply the present value of £l due at the end of as many years
as the perpetuity is deferred, by the perpetuity and by 100, and divide
by the rate per cent.
Example. A holds a freehold estate producing £300 per annum, on
which he has granted a lease which has 10 years to run, what sum
ought B to give him to come into possession of the estate at the end
of that time so as to receive 5 per cent interest for his money?
In Table 4 under 5 per cent opposite 10 years, i g, „g, „
we find '. ) .oidyid
this multiplied by 300 X 100 = 30000
gives 18417.39
which divided by 5, gives 3683.478 =
£3683 9 1.
Digitized by VjOOQ IC
66 TABU I.
The Decimal Parts of a Pound coneipoiifiDg to bmj noaber Df ShiUiiigf, &e.
Decimal.
.00104167
.00208333
.003125
.00416667
.00520833
.00625
.00729167
.00833333
.009375
.01041667
.01145833
.0125
.01354167
.01458333
.015625
.01666667
.01770833
.01875
.01979167
.02083333
.021875
.02291667
.02395833
.025
.02604167
.02708333
.028125
.02916667
.03020833
.03125
.03229167
.03333333
.034375
.03541667
.03645833
.0375
.03854167
.03958333
.040625
.04166667
.04270833
.04375
.04479167
.04583333
.04f)«;75
.0479166
.04895833
.05
lOJ
11
m
Hi
2 0
Decimal.
.05104167
.05208333
.0^125
.05416667
.05520833
.05625
.05729167
.05833333
.059375
.06041667
.06145833
.0625
.06354167
.06458333
.065625
.06666667
.06770883
.06875
.06979167
.07083333
.071875
.07291667
.07395833
.075
.07604167
.07708a33
.078125
.07916667
.08020833
.08125
.08229167
.08333333
.084375
.08541667
.08645833
.0875
.08854167
.08958333
.090625
.09166667
.09270833
.09375
.09479167
•09583333
.096875
.09791667
.09895833
.1
111
Decimal.
0104167
0208333
03125
0416667
0520833
0625
0729167
0833333
09375
1041667
1145833
125
1354167
1458333
J 5625
1666667
1770833
1875
1979167
2083333
21875
2291667
2395833
25
2604167
2708333
28125
2916667
3020833
3125
3229167
3333333
34375
3541667
3645833
375
3854167
3968333
40625
4166667
4270833
4375
4479167
4583333
46875
4791667
4895833
5
3 llj
3 lU
3 11|
4 0
nipitivJHhuV ^^
DeeimaL
5104167
5208333
53125
5416667
5520833
5625
5729167
5833333
59375
6041667
6145833
626
6354167
6458333
65625
6666667
67708S3
6875
6979167
7083333
71875
7281667
7395833
75
7604167
7708333
78125
7916667
8020833
8125
8229167
8333333
84375
8541667
8645833
875
8854167
8958333
90625
9166667
9270833
9375
9479167
9583333
96875
9791667
9895833
,2
^
TABLB L 67
Tb« D«ein«l Fnte of • Fmm^, wrmpoiidiiig to any number of ShiUing^y fte.
Detimal.
DeoliiMU
DeotmaU
4
4
4
4
4
4
4
4
0»
1
8
4 3
4 4
4 4(
43
4 5
4 U
4 6l
4 5]
4 6
4
4
4
4
4
4
4
4
4 ^
4 8l
4 8|
4 9
4 M
4 M
4 9|
4 10
4 IM
4 ]0|
4 10|
4 11
4 Hi
4 UX
4 Itf
5 0
.20104167
.20208333
.203125
.20416667
.20620833
.20625
.20729167
.20833333
.209375
.21041667
.21145833
.2125
.21354167
.21458333
»215625
.21666667
.21770633
.21875
.21979167
.22063333
.221875
.22291667
.22395833
.225
.22604167
.22708333
.2228125
.22916667
.23020833
.23125
.23229167
.23333333
.234375
.23541667
.23645833
.2375
.23854167
.23958333
.240625
.24166667
.24270833
.24375
.24479167
.24583333
.246875
.24791667
.24895833
.25
5 10^
5 lOX
5 lOf
5 11
iij
5
5
5 111
6 0
.25104167
.25208333
.253125
.25416667
.25520833
.25625
.25729167
.25833333
.259375
.26041667
.26145833
•2625
.26354167
.26458333
.265625
.26666667
.26770833
.26875
.26979167
.27083333
.271875
.27291667
.27395833
.275
.27604167
.27708333
.278125
.27916667
.28020833
.28125
.28229167
.28333333
.284375
.28541667
.98645833
.2875
.28854167
.28958333
.290625
.29166667
.29270833
.29375
.29479167
.29583333
.296875
.29791667
.29895833
.3
6 10^
6 10A
6 lOf
6 11
6 m
6 Uj
6 Hi
7 0
.30104167
.30208333
.303125
.30416667
.30520833
.30625
.30729167
.30833333
.309375
.31041667
.31145833
.3125
.31354167
.31458333
.315625
,31666667
.31770833
.31875
.31979167
,32083333
.321875
.32291667
,32395833
.325
.32604167
,32708333
.328125
,32916667
.33020833
.33125
.33229167
.33333333
.334375
.33541667
.33645833
.3375
.33854167
.33958333
.340625
.34166667
.34270833
.34375
.34479167
.34583333
.3468:^5
.34791667
.34895833
.35
n
.35104167
.35208333
.353125
.35416667
.35520833
.35625
.35729167
.35833333
.359375
.36041667
.36145833
.3625
.36354167
.36458333
.365625
,36666667
.36770833
.36875
•36979167
.37083333
.371875
.37291667
.37395833
.375
.37604167
.37708333
.378125
.37916667
.38020833
.38125
.38229167
.38333333
.384375
.38541667
.38645833
.3875
.38854167
.38958333
.390625
.39166667
.39270833
.39375
.39479167
•39583333
.396875
.39791667
.39895833
.4
f2
.A^
QDgle
68 TABLE I.
Th« Daeimal Partt of a Poundi coneipondiog to any nnmber of Slultiiigi, &e.
8 8
DedmaL
.40104167
.402083^3
.403125
.40416667
.40520833
.40625
.40729167
.40833333
.409375
.41041667
.41145833
.4125
.41354167
.41458333
.415625
.41666667
.41770833
.41875
,41979167
.42083333
421875
42291667
.42395833
.425
.42604167
,42708333
.428125
.42916667
.43020833
.43125
.43229167
.43333333
.434375
,43541667
.43645833
,4375
.43854167
.43958333
.440625
.44166667
.44270833
.44375
.44479167
.44583333
.446875
.44791667
.44895833
.45
lit
Dednul.
.45104167
.45208333
.453125
.45416667
.45520633
.45625
.45729167
.45833333
.459375
.46041667
.46145833
.4625
.46354167
.46458333
.465625
.46666667
.46770833
.46875
.46979167
.47083333
.471875
.47291667
.47395833
.475
.47604167
,47708333
,478125
47916667
,48020833
,48125
48229167
48333333
,484375
,48541667
.48645833
,4875
.48854167
,48959333
,490625
.49166667
.49270833
.49375
,49479167
.49583333
.496875
.49791667
.49895833
.5
^ A
0 0^
0 o|
0
0 2
II
0 2}
0 24
0 2}
0 3
11
DedmaL
50104167
,50208333
,503125
.50416667
,50520833
,50625
,50729167
,50833333
.509375
.51041667
,51145833
.5125
.51354167
.51458333
,515625
.51666667
.51770833
,51875
,51979167
.52083333
.521875
,52291667
,52395833
.525
52604167
,52708333
528125
.52916667
,53020833
53125
.53229167
,53333333
,534375
.53541667
.53645833
.5375
,53854167
.53958333
.540625
,54166667
,54270833
.54-375
,54479167
.54583333
.546875
.54791667
.54895833
.55
nipitiTmril hylaJtuMi
JL ±
I
5
I
7
8
DMlmaL
.55104167
55208333
553125
.55416667
.55520833
.55625
.55729167
.55833333
.559375
.56041667
.56145833
.5625
.56354167
.96458333
.565625
.56666667
.56770833
56875
.56979167
57083333
.571875
.57291667
.57395833
.575
.57604167
.57708333
.578125
.57916667
.58020833
.58125
.58229167
.58333333
.584375
.58541667
.58645833
.5875
.58854167
.58958333
.590623
.59166667
.59270833
.59375
.59479167
.59583333
.596875
.59791667
.59895833
.6
H
TABLE L
69
Tbe Decimal Paits of a Pound, corresponding to any Number of Shillings, &c
12 Oi
12 oX
12 0}
12 1
12 U
12 U
12 If
12 2
12 2i
12 22
12 2|
12 3
12 3}
la sl
12 3f
12 4
12
12
12
12
12 M
12 5}
12 3|
12 6
12 6}
12 el
12 6}
12 7
12 7i
12 7|
12 7j
12 8
12 8^
12 8^
12 81
12 9
12 94
12 9i
12 9f
12 10
12 lOi
12 104
12 lOi
12 11
12 Ui
12 11}
12 Hi
13 0
Decimal.
.60104167
.60208333
.603125
.60416667
.60520833
.60625
.60729167
.60833333
.609375
.61041667
.61145833
.6125
.61354167
.61458333
.615625
.61666667
.61770833
.61875
.61979167
.62083333
.621875
.62291667
.62395833
.625
.62604167
.62708333
,628125
.62916667
.63020833
.63125
.63229167
.63333333
.634375
.63541667
.63645833
.6375
.63854167
.63958333
.640625
.64166667
.64270833
.64375
.64479167
.64583333
.646875
,64791667
.64895833
,65
13 Oi
13 Oi
13 Of
13 1
H
13
13 9|
13 9*
13 10
13 10}
13 104
13 10}
13 11
13 Hi
13 lU
13 m
14 0
Decimal
.65104167
,65208333
.653125
.65416667
.65520833
.65625
,65729167
.65833333
.659375
,66041667
.66145833
,6625
,66354167
.66458333
,665625
.66666667
.66770833
.66875
.66979167
.67083333
.671875
.67291667
.67395833
.675
.67604167
.67708333
678125
.67916667
.68020833
,68125
.68229167
.68333333
,684375
,68541667
.68645833
.6875
.68854167
,68958333
690625
,69166667
,69270833
.69375
.69479167
.69583333
.696875
.69791667
.69895833
.7
14 Oi
14 0|
14 Of
14 1
14 11
14 1}
14 1}
14 2
14 2^
14 2|
14 2|
14 3
14 3i
14 34
14 3|
14 4
14 4i
14 4}
14 4}
14 5
14 51
14 5}
14 51
14 6
14 6}
14 6}
14 6]
14 7
14 7i
14 7i
14 79
14 8
DedmaL
.70104167
.70208333
,703125
.70416667
.70520833
.70625
.70729167
.70833333
.709375
.71041667
.71145833
.7125
,71354167
.71458333
.715625
.71666667
.71770833
.71875
.71979167
.72083333
.721875
.72291667
.72395833
,725
,72604167
,72708333
.728125
.72916667
.73020833
.73125
,73229167
.73333333
.734375
,73541667
73645833
.7375
.73854167
.73958333
.740625
.74166667
.74270833
.74375
.74479167
,74583333
.746875
,74791667
,74895833
.75
15 1
15 64
15 6}
15 6}
15 7_
15 7J
15 7|
15 7}
15 8
15
15
15 8}
15 9
15
15
15 9}
15 10
15 1
15 1
15 lOf
15 11
Decimal.
.75104167
.75208333
.753125
.75416667
.75520833
.75625
.75729167
.75833333
.759375
.76041667
.76145833
.7625
.76354167
.76458333
.765625
.76666667
.76770833
.76875
.76979167
.77083333
.771875
.77291667
.77395833
.775
.77604167
.77708333
.778125
.77916667
.78020833
.78125
.78229167
.78333333
.784375
.78541667
.78645833
.7875
.78854167
.78958333
.790625
.79166667
.79270833
.79375
.79479167
.79583333
.796875
.79791667
.79895833
.8
byVjUUV
le
70 TABLB 1.
ne Dacbnal Paiti off a Pooad, i»ixMpQiiduig to anj Nomb^i of
9. d.
DtdmaL
.80104167
.80208333
.803125
.80416667
.80520833
.80625
.80729167
.80833333
.800375
•81041667
.81145833
.8125
.81354167
.81458333
.815625
.81666667
.81770833
.81875
•81979167
.82083333
.821875
.82291667
.82395833
.825
.82604167
.82708333
.828125
•82916667
.83020833
.83125
.83229167
.83333333
.834375
.83541667
.83645833
.8375
.83854167
.83958333
.840625
.84166667
.84270833
.84375
.84479167
.84583333
.846875
.84791667
.84895833
85
t. d.
lit
DteimaL
.85104167
.853125
.85416667
.85520833
.85625
.85729167
.85833333
•859375
.86041667
.86145833
.8625
.86354167
.86458333
.865625
.86666667
.86770833
.86875
.86979167
.87083333
.871875
.87291667
.87395833
.875
.87604167
.87708333
.878125
.87916667
.88020833
.88125
.88229167
.88333333
.884375
.88541667
.88645833
.8875
.88854167
.88958333
.890625
.89166667
.89270833
.89375
.89479167
.89J63333
.896875
.89791667
.89895833
.9
a. d
DtdmaL
.90104167
.90208333
.903125
.00416667
.90520833
.90625
,90729167
•90833333
.909375
.91041667
.91145833
.9125
.91354167
.91458333
.915625
.91666667
.91770833
.91875
.91979167
.92083333
.921875
.92291667
.92395833
.925
.92604167
.92708333
.928125
.92916667
.93020833
.93125
.93229167
.93333333
.934375
.93541667
.93645833
.9375
.93854167
.93958333
.940625
.94166667
.94270833
.94375
.94479167
.94583333
.946875
.94791667
.94695833
.95
Digitized
t. 4.
19 0^
19 01
19 0|
19 1
19 U
19 \l
19 li
19 2
19 2^
19 2}
19 2}
19 3
19 3^
19 4
19 3f
19 4
19 4^
19 4
19 4|
19 5
19 bl
19 5|
19 5}
19 6
19 7i
19 7i
19 7|
19 8
DedmaL
.95104167
.95208333
.953125
.95416667
.95520a33
.95625
.95729167
.95833333
•959375
.96041667
•96145833
.96-25
.96354167
•96458333
.965625
.96666667
.96770833
.96875
.96979167
.97083333
.971875
.97291667
.97395833
.975
.97604167
.97708333
.978125
.97916667
.98020833
.98125
.98229167
.98333333
.984375
.98541667
.98645833
.9875
.98854167
.98958333
.890625
.99166667
.99270833
.99375
.99479167
.99583333
.996875
.99791667
.90895833
1.
WC
TABLE n. n
TIn Deefanal puti of a Tear, eorrespondiDg to any number of Dayi, ftc
D«y*
ty^OnuH
Dmyi.
BedmaL
D»y.
D^eimaL
Day..
Decimal.
1
.0027 3973
51
•1397 2603
101
.2767 1233
151
.4136 9863
2
•0054 7945
52
.1424 6575
102
.2794 5205
152
.4164 3836
3
.0082 1918
53
•1452 0548
103
.2821 9178
153
.4191 7808
4
.0109 5890
54
.1479 4521
104
.2849 3151
154
.4219 1781
5
.0136 9863
55
.1506 8493
105
.2876 7123
165
.4246 5753
6
.0164 S836
56
.1534 2466
106
.2904 1096
156
.4273 9726
7
.0191 7808
57
.1561 6438
107
.2931 5068
157
.4301 3699
8
.0219 1781
58
.1589 0411
108
.2958 9041
158
.4328 7671
9
.0246 6753
59
.1616 4384
109
.2986 3014
159
•4356 1644
10
•0273 9726
60
.1643 8356
110
.3013 6986
160
.4383 5616
11
•0301 3699
61
.1671 2329
111
.3041 0959
161
•4410 9589
12
.0328 7671
62
.1698 6301
112
.3068 4932
162
.4438 3562
13
.0356 1644
63
.1726 0274
113
.3095 8904
163
.4465 7534
14
.0383 5616
64
.1753 4247
114
.3123 2877
164
.4493 1507
15
.0410 9589
65
.1780 8219
115
.3150 6849
165
.4520 6479
16
.0438 3562
66
.1808 2192
116
.3178 0822
166
.4547 9452
17
.0465 7534
67
.1835 6164
117
.3205 4795
167
.4575 3425
18
.0493 1507
68
.1863 0137
118
.3232 8767
168
.4602 7397
19
.0520 5479
69
.1890 4110
119
.3260 2740
169
.4630 1370
20
.0547 9452
70
.1917 8082
120
.3287 6712
170
.4657 5342
21
.0575 3425
71
.1945 2055
121
.3315 0685
171
.4684 9315
22
.0602 7397
72
•1972 6027
122
.3342 4658
172
.4712 3288
23
.0630 1370
73
.2000 0000
123
.3369 8630
173
.4739 7260
24
.0657 5342
74
.2027 3973
124
.3397 2603
174
.4767 1233
26
.0684 9315
75
.2054 7945
125
.3424 6575
175
.4794 5205
26
.0712 3288
76
.2082 1918
126
.3452 0548
176
,4821 9178
27
.0739 7260
77
.2109 5890
127
.3479 4521
177
.4849 3151
28
.0767 1233
78
.2136 9863
128
.3506 8493
178
.4876 7123
29
.0794 5205
79
.2164 3836
129
.3534 2466
179
.4904 1096
30
.0821 9178
80
.2191 7808
130
.3561 6438
ISO
.4931 5068
31
.0849 3151
81
.2219 1781
131
.3589 0411
181
.4958 9041
32
.0876 7123
82
.2246 5753
132
.3616 4384
182
.4986 3014
33
.0904 1096
83
.2273 9726
133
.3643 8356
183
.5013 6986
34
.0931 5068
84
.2301 3699
134
.3671 2329
184
.5041 0959
35
.0958 9041
85
.2328 7671
135
.3698 6301
185
.5068 4932
36
.0986 3014
86
.2356 1644
136
•3726 0274
186
.5095 8904
37
.1013 6986
87
.2383 5616
137
.3753 4247
187
.5123 2877
38
.1041 0959
88
.2410 9589
138
.3780 8219
188
.5150 6849
39
.1068 4932
89
.2438 3562
139
.3808 2192
189
.5178 0822
40
.1095 8904
90
.2465 7534
140
.3835 6164
190
.5205 4795
41
.1123 2877
91
.2493 1507
141
.3863 0137
191
.5232 8767
42
.1150 6849
92
.2520 5479
142
.3890 4110
192
.5260 2740
43
.1178 0822
93
.2547 9452
143
.3917 8082
193
.5287 6712
44
.1205 4795
94
.2575 3425
144
.3945 2055
194
.5315 0685
45
.1232 8767
95
.2602 7397
145
.3972 6027
195
.6342 4658
46
.1260 2740
96
.2630 1370
146
«4000 0000
196
.5369 8630
47
.1287 6712
97
.2657 5342
147
.4027 3973
197
.5397 2603
48
.1315 0685
98
.2684 9315
148
.4054 7945
198
.5424 6575
49
.1342 4658
99
.2712 3288
U9
.4082 1918
199
.5452 0348
50
.1369 8630
100
.2739 7260
150
.4109 5890
200
.6479 4521
DigTtizedbyVJtJOV
le
72 TABLE II.
The decimal parti of a Teari ooneeponding to any number of Dayi, fte.
Days.
DeeimaL
Day..
DeeimaL
Days.
DedmaL
Days.
DMimaL
201
.5506 8499
251
.6876 7123
301
.8246 5753
351
.9616 4384
202
.5534 2466
252
.6904 1096
302
.8273 9726
352
.9643 8356
203
.5561 6438
253
.6931 5068
303
.8301 3699
353
.9671 2329
204
.5589 0411
264
.6958 9041
304
.8328 7671
354
.9698 6301
205
.5616 4384
255
.6986 3014
305
.8356 1644
355
.9726 0274
206
.5643 8356
256
.7013 6986
306
.8383 5616
356
.9753 4247
207
.5671 2329
257
.7041 0959
307
.8410 9589
357
.9780 8219
208
.6698 6301
258
.7068 4932
308
.8438 3562
358
.9808 2192
209
.5726 0274
259
.7095 8904
309
.8465 7534
359
.9835 6164
210
.5753 4247
260
.7123 2877
310
.8493 1507
360
.9863 0137
211
.5780 8219
261
.7150 6849
311
.8520 5479
361
.9890 4110
212
.5808 2192
262
.7178 0822
312
•8547 9452
362
.9917 8082
213
.5835 6164
263
.7205 4795
313
.8575 3425
363
.9945 2055
214
.5863 0137
264
.7232 8767
314
.8602 7397
364
.9972 6027
215
.5890 4110
265
.7260 2740
315
.8630 1370
365
Year.
1.0000 0000
216
.5917 8082
266
.7287 6712
316
.8657 5342
A
.062500
217
.5945 2055
267
.7315 0685
317
.8684 9315
A
.083333
218
.5972 6027
268
.7342 4658
318
.8712 3288
A
.100000
219
.6000 0000
269
.7369 8630
319
.8739 7260
i
•125000
220
.6027 3973
270
.7397 2603
320
.8767 1233
221
.6054 7945
271
.7424 6575
321
.8794 5205
.166666
222
.6082 1918
272
.7452 0548
322
.8821 9178
1 1
.187500
223
.6109 5890
273
.7479 4521
323
.8849 3151
•200000
224
.6136 9863
274
.7506 8493
324
.8876 7123
.250000
225
.6164 3836
275
.7534 2466
325
.8904 1096
226
.6191 7808
276
.7561 6438
326
.8931 5068
i
.300000
227
•6219 1781
277
.7589 0411
327
.8958 9041
.312500
228
.6246 5753
278
.7616 4384
328
.8986 3014
1
.333333
929
.6273 9726
279
.7643 8356
329
.9013 6986
.375000
230
.6301 3699
280
.7671 2329
330
.9041 0959
231
.6328 7671
281
.7698 6301
331
.9068 4932
.400000
232
.6356 1644
282
.7726 0274
332
.9095 8904
n
.416666
233
.6383 5616
283
.7753 4247
333
.9123 2877
A
.437500
234
.6410 9589
284
.7780 8219
334
.9150 6849
f
.500000
235
.6438 3562
285
.7808 2192
335
.9178 0822
236
.6465 7534
286
.7835 6164
336
.9205 4795
A
.562500
237
•6493 1507
287
.7863 0137
337
.9232 8767
A
.583333
238
.6520 5479
288
.7890 4110
338
.9260 2740
I
.600000
239
.6547 9452
289
.7917 8082
339
.9287 6712
1
.625000
240
.6575 3425
290
.7945 2055
340
.9315 0685
241
.6602 7397
291
.7972 6027
341
.9342 4658
)
•666666
242
.6630 1370
292
.6000 0000
342
.9369 8630
t
.687500
243
.6657 5342
293
.8027 3973
343
.9397 2603
•700000
244
.6684 9315
294
.8054 7945
344
.9424 6575
}
.750000
245
.6712 3288
295
.8082 1918
345
.9452 0548
J
.800000
246
.6739 7260
296
.8109 5890
346
.9479 452)
if
.812500
247
.6767 1233
297
.8136 9863
347
.9506 8493
1
.833333
248
.6794 5205
298
.8164 3836
348
.9534 2466
1
•875000
249
.6821 9178
299
.8191 7808
349
.9561 6438
X
.900000
250
.6849 3151
300
.8219 1781
350
.9589 0411
^
.916666
*
.937500
Digitized by N^UUV IC
TABLB ni.
Th6 amoimt of £1 in aaj number of Yean*
13
Yem.
Sper oent.
Si per cent
Spereent
8*p«rMit
1
1 .0200 0000
1.0250 0000
1.0300 0000
1.0350 0000
2
1.0404 0000
1.0506 2500
1.0609 0000
1.0712 2500
3
1.0612 0800
1.0768 9062
1.0927 2700
1.1087 1787
4
1.0824 3216
1.1038 1289
1.1255 0881
1.1475 2300
5
1.1040 8080
1.1314 0821
1.1592 7407
1.1876 8631
6
1.1261 6242
1.1596 9342
1.1940 5230
1.2292 5533
7
1.1486 8567
1.1886 8575
1.2298 7387
1.2722 7926
8
1.1716 5938
1.2184 0290
1.2667 7008
1.3168 0904
9
1.1950 9257
1.2488 6297
1.3047 7318
1.3628 9735
10
1.2189 9442
1.2800 8454
1.3439 1638
1.4105 9876
11
1.2433 7431
1.3120 8666
1.3842 3387
1.4599 6972
12
1.2682 4179
1.3448 8882
1.4257 6089
1.5110 6866
13
1.2936 0663
1.3785 1104
1.4685 3371
1.5639 5606
14
1.3194 7876
1.4129 7382
1.5125 8972
1.6186 9452
15
1.3458 6834
K4482 9817
1.5579 6742
1.6753 4883
16
1.3727 8570
1.4845 0562
1.6047 0644
1 .7339 8604
17
1.4002 4142
1.5216 1826
1.6528 4763
1.7946 7555
18
1.4282 4625
1.5596 5872
1.7024 3306
1.8574 8920
19
1.4568 1117
1.5986 5019
1.7535 0605
1.9225 0132
SO
1.4859 4740
1.6386 1644
1.8061 1123
1.9897 8886
21
1.5156 6634
1.6795 8185
1.8602 9457
2.0594 3147
22
1.5459 7967
1.7215 7140
1.9161 0341
2.1315 1158
23
1.5768 9926
1,7646 1068
1.9735 8651
2.2061 1448
24
1.6084 3725
1.8087 2595
2.0327 9411
2.2833 2849
25
1.6406 0599
1.8539 4410
2.0937 7793
2.3632 4498
26
1.6734 1811
1.9002 9270
2.1565 9127
2.4459 5856
27
1.7068 8648
1.9478 0002
2.2212 8901
2.5315 6711
28
1.7410 2421
1.9964 9502
2.2879 2768
2.6201 7196
29
1.7758 4469
2.0464 0739
2.3565 6551
2.7118 7798
30
1.8113 6158
2.0975 6758
2.4272 6247
2.8067 9370
31
1.8475 8882
2.1500 0677
2.5000 8035
2.9050 3148
32
1.8845 4059
2.2037 5694
2.5750 8276
3.0067 0759
33
1.9222 3140
2.2588 5086
2.6523 3524
3.1119 4235
34
1.9606 7603
2.3153 2213
2.7319 0530
3.2208 6033
35
1.9998 8955
2.3732 0519
2.8138 6245
3.3335 9045
36
2.0398 8734
2.4325 3532
2.8982 7833
3.4502 6611
37
2.0806 8509
2.4933 4870
2.9852 2668
3.5710 2543
38
2.1222 9879
2.5556 8242
3.0747 8348
3.6960 1132
39
2.1647 4477
2.6195 7448
3.1670 2698
3.8253 7171
40
2.2080 3966
2.6850 6384
3.2620 3779
3.9592 5972
41
2.2522 0046
2.7521 9043
3.3598 9893
4.0978 3381
42
2.2972 4447
2.8209 9520
3.4606 9589
4.2412 5799
43
2.3431 8936
2.8915 2008
3.5645 1677
4.3897 0202
44
2.3900 5314
2.9638 0808
3.6714 5227
4.5433 4160
45
2.4378 5421
3.0379 0328
3.7815 9584
4.7023 5855
46
2.4866 1129
3.1138 5086
3.8950 4372
4.8669 4110
47
2.5363 4351
3.1916 9713
4.0118 9503
5.0372 8404
48
2.5870 7039
3.2714 8956
4.1322 5188
5.2135 8898
49
2.6388 1179
3.3532 7680
4.2562 1944
5.3960 6459
50
2.6915 8803
3.4371 0872
4.3839 0602
5.5849 2686
Qogle
H
Tht
T1BUIIIL
Tam.
4perfl«it
4iiwroaU
»P««0bL
• iwroa.1.
1
1.0400 0000
1.0450 0000
1.0500 0000
1.0600 0000
a
1.0816 0000
1.0920 2500
1.1025 0000
1.1*238 0000
a
1.1248 6400
1.1411 6619
1.1576 2500
1.1910 1600
4
1.1698 5856
1.1925 1860
1.2155 0625
1.2624 7696
5
1.2166 5290
1.2461 8194
1.2762 8156
1.3382 2558
6
1.2653 1902
1..3022 6012
1.3400 9564
1.4185 1911
7
1.3159 3178
1.3608 6183
1.4071 0042
1.5036 3026
8
1.3685 6905
1.4221 0061
1 .4774 5544
1.5938 4807
9
1.4233 1181
1.4860 9514
1.5513 2822
1.6894 7896
10
1.4802 4428
1.5529 6949
1.6288 9463
1.7908 4770
11
1.5394 5406
1.6228 5306
1.7103 3936
1.8989 9856
12
1.6010 3222
1.6958 8143
1.7958 5633
2.0121 9647
13
1.6650 7351
1.7721 9610
1.8856 4914
2.1329 2826
14
1.7316 7645
1.8519 4492
1.9799 3160
2.2609 0:i96
15
1.8009 4351
1.9352 8244
2.0789 2818
9.396S 5819
16
1.8729 8125
2.0223 7015
2.1828 7459
2.5403 5168
17
1.9479 0050
2.1133 7681
2.2920 1832
2.6927 7279
18
2.0258 1652
2.2084 7877
2.4066 1923
2.8543 3915
19
2.1068 4918
2.3078 6031
2.5269 5020
3.0255 9950
90
2.1911 2314
2.4117 1402
2.6532 9771
3.2071 3547
91
2.2787 6807
2.5202 4116
2.7859 6259
3.3995 6360
92
2.3699 1879
2.6336 5201
2.9252 6072
3.6035 3742
93
2.4647 1555
2.7521 6635
3.0715 2376
3.8197 4966
94
9.5633 0417
2.8760 1383
3.2250 9994
4.0489 3464
95
2.6658 3633
3.0054 3446
3.3863 5494
4.2918 7072
96
2.7724 6979
3.1406 7901
3.5556 7269
4.5493 8996
97
9.8833 6858
3.2820 0956
3.7334 5632
4.8223 4594
98
2.9987 0332
3.4296 9999
3.9201 2914
5.1116 8670
99
3.1186 5145
3.5840 3649
4.1161 3560
5.4183 8790
90
3.2433 9751
3.7453 1813
4.3219 4238
5.7434 9117
31
3.3731 a341
3.9138 5745
4.5380 3949
6.0881 0064
32
3.5080 5875
4.0899 8104
4.7649 4147
6.4.'>33 8668
33
3.6483 8110
4.2740 3018
5.0031 8854
6.8405 8983
84
3.7943 1634
4.4663 6154
5.2533 4797
7.2510 2528
35
3.9460 8899
4.6673 4781 |
5.5160 1537
7.6860 8679
36
4.1039 3255
4.8773 7846
5.7918 1614
8.1472 5900
37
4.2680 8986
5.0968 6049
6.0814 0694
8.6360 8712
38
4.4388 1345
5.3262 1921
6.3854 7729
9.1542 5235
39
4.6163 6599
5.5658 9908
6.7047 5115
9.7035 0749
40
4.8010 2063
5.8163 6454
7.0399 8871
10.2857 1794
41
4.9930 6145
6.0781 0094
7.3919 8815
10.9028 6101
42
5.1927 8391
6.3516 1548
7.7615 8755
11.5570 3267
43
5.4004 9527
6.6374 3818
8.1496 6693
12 2504 5463
44
5.6165 1508
6.9361 2290
8.5571 5028
12.9854 8191
45
5.8411 7568
7.2482 4843
8.9850 0779
13.7646 1083
46
6.071S 2271
7.6744 3961
9.4342 5818
14.5904 8748
47
6.3178 1062
7.yi52 6849
9.9059 7109
15.4659 1673
48
6.5705 2824
8.2714 5^57
10.4012 6965
16.3938 7173
4^
5.fe3J3 4937
8,6436 7107
10.9213 3313
17.3775 0403
5(1
r.lOCC 5335
y,0326 3627
11.4673 9978
18.4201 5427
TABtB IIL
TiM amooBt of £1 in any nnmbu of Toon.
H
Ymn.
7peT«eiit.
8 per e«nt
9 per cent
10 per cent.
1
K0700 0000
1.0800 0000
1.0900 0000
1.1000 0000
2
1.1449 0000
1.1664 0000
1.1881 0000
1.2100 0000
3
1.2250 4300
1.2597 1200
1.2950 2900
1.3310 0000
4
1.3107 9601
1.3604 8896
1.4115 8161
1.4641 0000
5
1.4025 5173
1.4693 2808
1.5386 2395
1.6105 1000
6
1.5007 3035
1.5868 7432
1.6771 0011
1.7715 6100
7
1.6057 8148
1.7138 2427
1.8280 3912
1.9487 1710
8
1.7181 8618
1.8509 3021
1.9925 6264
2.1435 8881
2.3579 4769
9
1.8384 5921
1.9990 0463
2.1718 9328
10
1.9671 5136
3.1589 2500
2.3673 6367
2.5937 4246
11
2.1048 5195
2.3316 3900
2.5804 2641
2.8531 1671
12
2.2521 9159
2.5181 7012
2.8126 6478
3.1384 2838
13
2.4098 4500
2.7196 2373
3.0658 0461
3.4522 7121
14
2.5785 3415
2.9371 9362
3.3417 2703
3.7974 9834
15
2.7590 3154
3.1721 6911
3.6424 8246
4.1772 4817
16
2.9521 6375
3.4259 4264
3.9703 0588
4.5949 7299
17
3.1588 1521
3.7000 1805
4.3276 3341
5.0544 7028
18
3.3799 3228
3.9960 1950
4.7171 2042
5.5599 1731
19
3.6165 2753
4.3157 0106
5.1416 6125
6.1159 0904
20
3.8696 8446
4.6609 5714
5.6044 1077
6.7274 9995
21
4.1405 6237
5.0338 3372
6.1088 0774
7.4002 4994
22
4.4304 0174
5.4365 4041
6.6586 0043
8.1402 7494
23
4.7405 2986
5.8714 6365
7.2578 7447
8.9543 0243
24
5.0723 6695
6.3411 8074
7.9110 8317
9.8497 3268
25
5.4274 3264
6.8484 7520
8.6230 8066
10.8347 0594
26
5.8073 5292
7.3963 5321
9.3991 5792
11.9181 7654
27
6.2138 6763
7.9880 6147
10.2450 8213
13.1099 9419
28
6.6483 3936
8.6271 0639
11.1671 3952
14.4209 9361
29
7.1142 5705
9.3172 7490
12.1721 8208
15.8630 9297
30
7.6122 5504
10.0626 5689
13.2676 7847
17.4494 0227
31
8.1451 1290
10.8676 6944
14.4617 6953
19.1943 4250
32
8.7152 7080
11.7370 8300
15.7633 2879
21.1137 7675
33
9.3253 3975
12.6760 4963
17.1820 2838
23.2251 5442
34
9.9781 1354
13.6901 3361
18.7284 1093
25.5476 6986
35
10.6765 8148
14.7853 4429
20.4139 6792
28.1024 3685
36
11.4239 4219
15.9681 7184
22.2512 2503
30.9126 8053
37
12.2236 1814
17.2456 2558
24.2538 3528
34.0039 4859
38
13.0792 7141
18.6252 7563
26.4366 8046
37.4043 4344
39
13.9948 2041
20.1152 9768
28.8159 8170
41.1447 7779
40
14.9744 5784
21.7245 2150
31.4094 2005
45.2592 5557
41
16.0226 6989
23.4624 8322
34.2362 6786
49.7851 8112
42
17.1442 5678
25.3394 8187
37.3175 3197
54.7636 9924
43
18.3443 5475
27.3666 4042
40.6761 0984
60.2400 6916
44
19.6284 5959
29.5559 7166
44.3369 5973
66.2640 7608
45
21.0024 5176
31.9204 4939
48.3272 8610
72.8904 8369
46
22.4726 2338
34.4740 8534
52.6767 4185
80.1795 3205
47
24.0457 0702
37.2320 1217
57.4176 4862
88.1974 8526
48
25.7289 0651
40.2105 7314
62.6852 3700
97.0172 3378
49
27.5299 2997
43.4274 1899
68.2179 0833
106.7189 5716
50
29.4570 2506
46.9016 1251
74.3575 2008
117.3908 5288
nioitr^r^hyVTtOOgle
1
76
TABLB m.
The amoant of £1 in any number of Tean.
Tean.
Sp«ro0iit.
9i per cent.
8 per cent
S^peromt.
61
2.7454 1979
3.5230 3644
4.5154 2320
5.7803 9930
52
2.8003 2819
3.6111 1235
4.6508 8590
5.9827 1.327
53
2.8563 3475
3.7013 9016
4.7904 1247
6.1921 0824
54
2.9134 6144
3.7939 2491
4.9&41 2485
6.4088 3-202
55
2.9717 3067
3.8887 7303
5.0821 4859
6.6331 4114
56
3.0311 6529
3.9859 9236
5.2346 1305
6.8653 0108
57
3.0917 8859
4.0856 4217
5.3916 5144
7.1055 8662
58
3.1536 2436
4.1877 8322
5.5534 0098
7.3542 8215
59
3.2166 9685
4.2924 7780
5.7200 0301
7.6116 8203
60
3.2810 3079
4.3997 8975
5.8916 0310
7.8780 9090
61
3.3466 5140
4.5097 8449
6.0683 5120
8.1538 2408
62
3.4135 8443
4.6225 2910
6.2504 0173
8.4392 0793
63
3.4818 5612
4.7380 9233
6.4379 1379
8.7345 80-20
64
3.5514 9324
4.8565 4464
6.6310 5120
9.0402 9051
65
3.6225 2311
4.9779 5826
6.8299 8273
9.3567 0068
66
3.6949 7357
5.1024 0721
7.0348 8222
9.6841 8520
67
3.7683 7304
5.2299 6739
7.2469 2868
10.0231 3168
68
3.8442 5050
5.3607 1658
7.4633 0654
10.3739 4129
69
3.9211 3551
5.4947 3449
7.6872 0574
10.7370 2924
70
3.9995 5822
5.6321 0286
7.9178 2191
11.1128 2526
71
4.0795 4939
5.7729 0543
8.1553 5657
11.5017 7414
72
4.1611 4037
5.9172 2S06
8.4000 1727
11.9043 3624
73
4.2443 6318
6.0651 5876
8.6520 1778
12.3209 8801
74
4.8292 5045
6.2167 8773
8.9115 7832
12.7522 2259
75
4.4158 3545
6.3722 0743
9.1789 2567
13.1985 5038
76
4.5041 5216
6.5315 1261
9.4542 9344
13.6604 9964
77
4.5942 3521
6.6948 0043
9.7379 2224
14.1386 1713
78
4.6861 1991
6.8621 7044
10.0300 5991
14.6334 6873
79
4.7798 4231
7.0337 2470
10.3309 6171
15.1456 4013
80
4.8754 3916
7.2095 6782
10.6408 9056
15.6757 3754
81
4.9729 4794
7.3898 0701
10.9601 1727
16.2243 8835
82
5.0724 0690
7.5745 5219
11.2889 2079
16.7922 4195
83
5.1738 5504
7.7639 1599
11.6275 8842
17.3799 7041
84
5.2773 3214
7.9580 1389
11.9764 1607
17.9882 6938
85
5.3828 7878
8.1569 6424
12.3357 0855
18.6178 5881
86
5.4905 3635
8.3608 8834
12.7057 7981
19.2694 8386
87
5.6003 4708
8.5699 1055
13.0869 5320
19.9439 1580
88
5.7123 5402
8.7841 5832
13.4795 6180
20.6419 5285
89
5.8266 0110
9.0037 6227
13.8839 4865
21.3644 2120
90
5.9431 3313
9.2288 5633
14.3004 6711
22.1121 7595
91
6.0619 9579
9.4595 7774
14.7294 8112
22.8861 0210
92
6.1832 3570
9.6960 6718
15.1713 6556
23.6871 1568
93
6.3069 0042
9.9384 6886
15.6265 0652
24.5161 6473
94
6.4330 3843
10.1869 3058
16.0953 0172
25.3742 3049
95
6.5616 9919
10.4416 0385
16.5781 6077
26.2623 2856
96
6.6929 3318
10.7026 4395
17.0755 0559
27.1815 1006
97
6.8267 9184
10.9702 1004
17.5877 7076
28.1328 6291
98
6.9633 2768
11.2444 6530
18.1154 0388
29.1175 1311
99
7.1025 9423
11.5255 7693
18.6588 6600
30.1366 2607
100
7.2446 4612
11.8137 1635
19.2186 3198
31.1914 0798
-BtgrtiztjU by \_iiUU*iLC
TABLB III.
The amoont of £1 in any number of Teart.
71
T««i.
4 per cent.
4* per cent.
6 per cent
6 per cent.
51
7.3909 5068
9.4391 0490
12.0407 6977
19.5253 6353
52
7.6865 8871
9.8638 6463
12.6428 0826
20.6968 8534
53
7.9940 5226
10.3077 3853
13.2749 4868
21 .9386 9846
64
8.3138 1435
10.7715 8677
13.9386 9611
23.2550 2037
55
8.6463 6692
11.2563 0817
14.6356 3092
24.6503 2159
56
8.9922 2160
11.7628 4204
15.3674 1246
26.1293 4089
57
9.3519 1046
12.2921 6993
16.1357 8308
27.6971 0134
58
9.7259 8688
12.8453 1758
16.9425 7224
29.3689 2742
59
10.1150 2636
13.4233 5687
17.7897 0085
31.1204 6307
60
10.5196 2741
14.0274 0793
18.6791 8589
32.9876 9085
61
10.9404 1251
14.6586 4129
19.6131 4519
34.9669 5230
62
11.3780 2901
15.3182 8014
20.5938 0245
37.0649 6944
63
11.8331 5017
16.0076 0275
21.6234 9257
39.2888 6761
64
12.3064 7617
16.7279 4487
22.7046 6720
41.6461 9967
65
12.7987 3522
17.4807 0239
23.8399 0056
44.1449 7165
66
13.3106 8463
18.2673 3400
25.0318 9659
46.7936 6994
67
13.8431 1201
19.0893 6403
26.2834 9036
49.6012 9014
63
14.3968 3649
19.9483 8541
27.5976 6488
52.5773 6755
69
14.9727 0995
20.8460 6276
28.9775 4813
55.7320 0960
70
15.5716 1835
21.7841 3558
30.4264 2553
59.0759 3018
71
16.1944 8309
22.7644 2168
31.9477 4681
62.6204 8599
72
16.8422 6241
23.7888 2066
33.5451 3415
66.3777 1515
73
17.5159 6291
24.8593 1759
35.2223 9086
70.3603 7806
74
18.2105 9102
25.9779 8688
36.9835 1040
74.5820 0074
75
18.9452 5466
27.1469 9629
38.8326 8592
79.0569 2079
76
19.7030 6485
28.3686 1112
40.7743 2022
83.8003 3603
77
20.4911 8744
29.6451 9862
42.8130 3623
88.8283 5619
78
21.3108 3494
30.9792 3256
44.9536 8804
94.1580 5757
79
22.1632 6834
32.3732 9802
47.2013 7244
99.8075 4102
80
23.0497 9907
33.8300 9643
49.5614 4106
105.7959 9348
81
23.9717 9104
35.3524 5077
52.0395 1312
112.1437 5309
82
24.9306 6268
36.9433 1106
54.6414 8877
118.8723 7828
83
25.9278 8918
38.6057 6006
57.3735 6321
126.0047 2097
84
26.9650 0475
40.3430 1926
60.2422 4137
133.5650 0423
85
28.0436 0494
42.1584 5513
63.2543 5344
141.5789 0448
86
29.1653 4914
44.0555 8561
66.4170 7111
150.0736 3875
87
30.3319 6311
46.0380 8696
69.7379 2467
159.0780 6708
88
31.5452 4163
48.1098 0087
73.2248 2090
168.6227 4050
89
32.8070 5129
50.2747 4191
76.8860 6195
178.7401 0493
90
34.1193 3335
52.5371 0530
80.7303 6504
189.4645 1123
91
35.4341 0668
54.9012 7503
84.7668 8329
200.8323 8190
92
36.9034 7095
57.3718 3241
89.0052 2746
212.8823 2482
93
38.3796 0979
59.9535 6487
93.4554 8883
225.6552 6431
94
39.9147 9418
62.6514 7529
98.1282 6327
239.1945 8017
95
41.5113 8594
65.4707 9168
103.0346 7644
253.5462 5498
96
43.1718 4138
68.4169 7730
108.1864 1026
268.7590 3027
97
44.8987 1504
71.4957 4128
113.5957 3077
284.8845 7209
98
46.6946 6364
74.7130 4964
119.2755 1731
301.9776 4642
99
48.5624 5018
78.0751 3687
125.2392 9318
320.0963 0520
100
50.5049 4819
81.5835 1803
131.5012 5784
339.3020 8351
TABLB III.
The amon&i of £1 in any wimber of Tcv9«
Teut.
7 per C6iit«
Speromt
9p«rcfiit.
lOpnetot.
51
31.6190 1682
50.6537 4151
81 .0496 9688
129.1299 3817
52
33.7253 4799
54.7060 4083
88.3441 6960
142.0429 3198
53
36.0861 2235
59.0825 2410
96.2951 4487
156.2472 2518
54
38.6121 5092
63.8091 2603
104.9617 0790
171.8710 4770
55
41.3150 0148
68.9138 5611
114.4082 6162
189.0591 4247
56
44.2070 5159
74.4269 6460
124.7050 0516
207.9650 5672
57
47.3015 4520
80.3811 2177
135.9284 5563
228.7615 6239
58
50.6126 5336
86.8116 1151
148.1620 1663
251.6377 1863
59
54.1555 3910
93.7565 4043
161.4965 9813
276.8014 9049
60
57.9464 2683
101.2570 6367
176.0312 9106
304.4816 3954
61
62.0026 7671
109.3576 2876
191.8741 0S24
334.9296 0350
62
66.3428 6408
118.1062 3906
209.1427 7798
368.4227 8385
63
70.9868 6457
127.5547 3819
227.9656 2800
405.2650 6223
64
75.9559 4509
137.7591 1724
248.4825 3452
445.7915 6845
65
81.2728 6124
148.7798 4662
270.8459 6262
490.3707 2530
66
86.9619 6153
160.6822 3435
295.2220 9926
539.4077 9783
67
93.0492 9884
173.5368 1310
321.7920 8819
593.3485 7761
68
99.5627 4976
187.4197 5814
350.7533 7613
652.6834 3537
69
106.5321 4224
202.4133 3880
382.3211 7998
717.9517 7891
70
113.9893 9220
218,6064 0590
416.7300 8618
789.7469 5680
71
121.9686 4965
236.0949 1837
454.2357 9393
868.7216 5248
. 72
130.5064 5513
254.9825 1184
495.1170 1539
955.5938 1773
73
139.6419 0699
275.3811 1279
539.6775 4677
1051.1531 9950
74
149.4168 4047
297.4116 0181
588.2485 2598
1156.2685 1945
75
159.8760 1931
321.2045 2996
641.1908 9332
1271.8953 7140
76
171.0673 4066
346.9008 9235
698.8980 7372
1399.0849 0853
77
183.0420 5450
374.6529 6374
761.7989 0035
1538.9933 9939
7S
195.8549 9832
404.6252 0084
830.3608 0139
1692.8927 3933
79
209.5648 4820
436.9952 1691
905.0932 7351
1862.1820 1326
80
224.2343 8758
471.9548 3426
986.5516 6813
2048.4002 1459
81
239.9307 9471
509.7112 2100
1075.3413 1826
2253.2402 3604
82
256.7259 5034
550.4881 18G8
1172.1220 3690
2478.5642 5965
83
274.6967 6686
594.5271 6S18
1277.6130 2022
2726.4206 8561
84
293.9255 4054
642.0893 4163
1392.5981 9204
2999.0627 5418
85
314.5003 2838
693.4564 8896
1517.9320 2933
3298.9690 2959
86
336.5153 5136
748.9330 0808
1654.5459 1196
3628.8659 3255
87
360.0714 2596
808.8476 4873
1803.4550 4404
3991.7525 2581
88
385.2764 2578
673.5554 6062
1965.7659 9801
4390.9277 7839
89
412.2457 7558
943.4398 9747
2142.6849 3783
4830.0205 5623
90
441.1029 7987
1018.9150 8927
2335.5265 8223
5313.0226 1185
91
471.9601 8846
1100.4282 9641
2545.7239 7463
5844.3248 7303
92
505.0188 0166
1188.4625 6013
2774.8391 3235
6428.7573 6034
93
540.3701 1777
1283.5395 6494
3024.5746 5426
7071.6330 9637
94
578.1960 2602
1386.2227 3013
3296.7863 7314
7778.7964 0601
95
618.6697 4784
1497.1205 4854
3593.4971 4672
8556.6760 4661
96
661.9766 3019
1616.8901 9242
3916.9118 8993
9412.3436 5127
97
708.3149 9430
1746.2414 0782
4269.4339 6002
10353.5780 1640
98
757.8970 4390
1885.9407 2044
4653.6830 1643
11388.9358 1804
99
810.9498 3697
2036.8159 7808
5072.5144 8790
12527.8293 9984
100
867.7163 2556
2199.7612 5632
5529.0407 9181
13780.6123 3988
Digitized by ^
T4Sf<B Vf. n
n* yiMent Talw of £1 diM at the end of aay VnaiMr of Tean.
YeMn
t per cent.
Mp«roent
OiwroBirt.
SipWlBMlt.
1
.9803 9216
.9756 0976"
.9708 7379
.9661 8357
2
.9611 6878
.9518 1440
.9425 9591
.9335 1070
3
.9423 2233
•0285 9941
.9151 4166
.9019 4270
4
.9238 4543
.9059 5064
.8884 8705
.8714 4223
5
.9057 3081
•8838 5429
.8626 0878
•8419 7317
6
.8879 7138
•8622 9687
.8374 8496
.8135 0064
7
.8705 6018
.8412 6524
.8130 9151
.7859 9096
8
.8534 9037
•8207 4657
.7894 0923
•7594 1156
9
.8367 5527
.8007 2836
.7664 1673
.7337 3097
10
.6203 4830
.7811 9840
.7440 9391
.7089 1881
11
.8042 6304
.7621 4478
.7224 2126
•6849 4571
IS
.7884 9318
.7435 5539
•7013 7988
•6617 8330
13
.7730 3253
.7254 2038
•6809 5134
.6394 0415
14
.7578 7502
.7077 2720
.6611 1781
.6177 8179
15
.7430 1473
•6904 6556
.6418 6195
.5968 9062
16
•7284 4581
.6736 9493
.6231 6694
.5767 0591
17
. .7141 6256
•6571 9596
•6050 1645
.5572 0378
18
.7001 5937
.6411 6591
.5873 9461
.5383 6114
19
•6864 3076
.6255 9779
.5702 8603
•5201 5569
90
•6729 7133
•6102 7094
.5536 7575
•5025 6588
91
•6597 7589
.5953 8629
•5375 4928
.4855 7090
99
.6468 3904
•5808 6467
.5218 9260
.4691 5063
93
.6341 5592
•5666 9724
.5066 9175
.4532 8563
94
.6217 2149
.5528 7535
.4919 3374
.4379 5713
95
.6095 3087
.5393 9069
•4776 0556
.4231 4699
96
.5975 7998
.5262 3472
•4636 9473
.4088 3767
97
.5858 6204
.5133 9973
.4501 8966
.3950 1224
98
.5743 7455
.5008 7778
.4370 7675
.3816 5434
99
.5631 1231
.4886 6125
.4243 4636
•3687 4815
30
•5520 7089
•4767 4269
.4119 8676
.3562 7841
SI
.5412 4597
.4651 1481
•3999 8714
.3442 3035
39
.5306 3330
.4537 7055
.3883 3703
,3325 8971
33
.5202 2873
.4427 0298
.3770 2625
.3213 4271
34
•5100 2817
.4319 0534
.3660 4490
.3104 7605
35
.5000 2761
.4213 7107
.3553 8340
•2999 7686
36
•4902 2315
.4110 9379
•3450 3248
.2898 3272
37
.4806 1093
.4010 6795
.3349 8294
.2800 3161
38
.4711 8719
•3912 8492
.3252 2615
.2705 6194
39
.4619 4822
•3817 4139
.3157 5355
.2614 1250
40
.4528 9042
.3724 3062
•3065 5684
.2525 7247
41
•4440 1091
.3633 4695
.2976 2800
.2440 3m
42
.4353 0413
.9544 8483
.2889 5929
•2357 7910
43
.4267 6875
•3458 3886
.2805 4294
.2278 0590
44
.4184 0076
•3374 0376
.2723 7178
•2201 0231
45
•4101 9680
•3291 7440
•2644 3862
.2126 5924
46
.4021 5373
.3211 4576
•2567 3659
.2054 6787
47
.3942 6836
.3133 1294
.2492 5877
.1985 1968
48
.3865 3761
.3056 7116
•2419 9380
.1918 0645
49
.3789 5844
.2982 1576
.2349 5029
.1853 2024
50
.3715 2788
.2909 4221
.2281 0708
.1790 5337
eogle
$0 TABLE IV.
The pntent Value of £1 doeattheaiidof any Number of Tean.
TMIt.
4 per cent
4iptrewt
Spereeni
epereaat.
1
.9615 3846
•9569 3780
.9523 8095
.9433 9623
8
.9245 5621
.9157 2995
•9070 2948
•8899 9644
3
•8889 9636
.8762 9660
.6638 3760
•8396 1928
4
.8548 0419
.8385 6134
•8227 0247
.7920 9366
5
.8219 2711
.8024 5105
.7835 2616
.7472 5817
6
.7903 1453
•7678 9574
•7462 1540
.7049 6054
7
.7599 1781
•7348 2846
.7106 8133
.6650 5711
8
.7306 9020
.7031 8513
.6768 3936
.6274 1237
9
.7025 8674
.6729 0443
.6446 0892
.5918 9846
10
.6755 6417
.6439 2768
.6139 1325
.5583 9478
11
• 6495 8093
.6161 9874
.5846 7929
.5267 8753
12
.6245 9705
.5896 6386
.5568 3742
.4969 6936
13
.6005 7409
.5642 7164
.5303 2135
.4688 3902
14
.5774 7508
.5399 7286
.5050 6795
.4423 0096
15
•5552 6450
•5167 2044
•4810 1710
•4172 6506
16
•5339 0818
.4944 6932
•4581 1152
.3936 4628
17
.5133 7325
.4731 7639
•4362 9669
.3713 6442
18
•4936 2812
.4528 0037
.4155 2065
.3503 4379
19
.4746 4242
.4333 0179
.3957 3396
.3305 1301
80
•4563 8695
.4146 4286
.3768 8948
.3118 0473
21
.4388 3360
.3967 8743
•3589 4236
.2941 5540
22
.4219 5539
.3797 0089
.3418 4987
.27/5 0510
23
.4057 2633
.3633 5013
•3255 7131
.2617 9726
24
.3901 2147
.3477 0347
.3100 6791
.2469 7855
25
.3751 1680
.3327 3060
.2953 0277
.2329 9863
26
.3606 8923
•3184 0248
.2812 4073
.2198 1003
27
.3468 1657
.3046 9137
.2678 4832
.2073 6795
28
.3334 7747
.2915 7069
.2550 9364
.1956 3014
29
.3206 5141
.2790 1502
.2429 4632
.1843 5674
30
.3083 1867
•2670 0001
.2313 7745
•1741 1013
31
.2964 6026
.2555 0241
.2203 5947
.1642 5484
32
.2850 5794
.2444 9991
.2098 6617
.1549 5740
33
.2740 9417
.2339 7121
.1998 7254
.1461 8622
34
.2635 5209
.2238 9589
.1903 5480
.1379 1153
35
.2534 1547
.2142 5444
.1812 9029
.1301 0522
36
.2436 6872
.2050 2817
.1726 5741
•1227 4077
37
.2342 9685
.1961 9921
.1644 3563
.1157 9318
38
.2252 8543
•1877 5044
•1566 0536
.1092 3885
39
.2166 2061
.1796 6549
•1491 4797
.1030 5552
40
.2082 8904
.1719 2870
.1420 4568
•0972 2219
41
.2002 7792
.1645 2507
.1352 8160
.0917 1905
42
.1925 7493
.1574 4026
•1288 3962
.0865 2740
43
•1851 6820
.1506 6054
.1227 0440
.0816 2962
44
•1780 4635
.1441 7276
•1168 6133
.0770 0903
45
.1711 9841
.1379 6437
•1112 9651
.0726 5007
46
.1646 1386
.1320 2332
.1059 9668
.0685 3781
47
.1582 8256
.1263 3810
.1009 4921
.0646 5831
48
.1521 9476
.1208 9771
.0961 4211
.0609 9840
49
.1463 4112
.1156 9158
.0915 6391
.0575 4566
50
.1407 1262
.1107 0965
.0872 0373
.0542 8836
ui^iyg^^uvvjuuvii^
TABLE IV. 81
The preieut Value of £\ due at the eud of any Number of Yeart.
Yean.
7 per Mnt.
8 per cent
9 per cent
10 per cent.
1
•9345 7944
.9259 2593
.9174 3119
.9090 9091
2
.8734 3873
.8573 3882
.8416 7999
.8264 4628
3
.8162 9788
.7938 3224
.7721 8348
.7513 1480
4
.7628 9521
.7350 2985
.7084 2521
.6830 1346
S
.7129 8618
.6305 8320
.6499 3139
.6209 2132
6
.6663 4222
.6301 6963
.5962 6733
.5644 7393
7
.6227 4974
•5834 9040
.5470 3424
.5131 5S12
8
.5820 0910
.5402 6888
.5018 6628
.4665 0738
9
.S439 3374
.5002 4897
.4604 2778
.4240 9762
10
.5033 4929
•4631 9349
.4224 1081
.3855 4329
11
.4750 9280
.4288 S286
.3875 3285
.3504 9390
12
.4440 1196
.3971 1376
.3:)55 3473
,3186 3082
13
.4149 6445
,3676 9792
.3261 7865
.2896 643S
14
.3878 1724
.3404 6104
.2992 4647
.2633 3125
15
.3624 4602
.3152 4171
.2745 3804
.2393 9205
16
.3387 3460
.2918 9047
.2518 6976
.2176 2914
17
.3165 7439
,2702 6895
.2310 7318
.1978 4407
18
.2958 6392
.2502 4903
.2119 9374
•1798 5879
19
.2765 0833
.2317 1206
.1944 8967
.1635 0799
20
.2584 1900
.2145 4821
.1784 3089
. 1486 4363
21
.2415 1309
.1986 5575
.1636 9806
.1351 3057
22
.2257 1317
.1839 4051
.1501 8171
.1228 4597
23
.2109 4688
.1703 1528
.1377 8139
,1116 7816
24
.1971 4662
.1576 9934
.1264 0494
.1015 2560
25
.1842 4918
.1460 1790
.1159 6784
.0922 9600
26
.1721 9549
.1352 0176
.1063 9251
.0839 0545
27
.1609 3037
.1251 8082
.0976 0781
.0762 7768
23
.1504 0-221
.1159 1372
.0895 4845
.0693 4335
'i9
.1405 62S2
.1073 2752
.0821 5454
.0630 3941
30
.1313 6712
.0993 7733
.0753 7114
.0573 0855
31
•1227 7301
.0920 1605
.0691 4783
.0520 9868
32
.1147 4113
.0852 0005
.0634 3838
.0473 6244
33
.1072 3470
.0783 8893
.0582 0035
.0430 5676
34
.1002 1934
.0730 4531
.0533 9481
.0391 4251
35
.0936 6294
.0676 3454
.0489 8607
.0355 8410
36
.0875 3546
.0626 2458
.0449 4135
•0323 4918
37
.0818 0884
.0579 8572
.0412 3059
.0294 0835
:{S
.0764 5686
.0530 9048
.0378 2623
.0267 3186
yj
.0714 5501
.0497 1341
.0347 0296
.0243 0442
40
.0667 8038
.0460 3093
.0318 3758
.0220 9493
41
.0624 1157
.0426 2123
.0292 0879
.0200 8030
42
.0583 2857
.0394 6411
.0267 9706
.0182 6027
43
.0545 1268
.0365 4084
.0245 8446
.0166 0025
41
.0509 4643
.0338 3411
.0225 5455
.0150 9113
45
•0476 1349
.0313 2788
.0206 9224
.0137 1921
4G
.0444 9859
.0290 0730
.0189 8371
.0124 7201
47
.0415 8747
.0268 5861
.0174 lf52.>
.0113 3819
48
.0388 6C79
.02-18 6908
.0159 7821
,0103 0745
49
:0363 2410
.0230 261)3
.0146 5S91
.0003 7041
50
.0339 4776
.0213 2123
.0134 4854 ,
.0085 1855
^^^^^^oTOOgle
M TABLE IV.
Hie preient Value of £1 due at the end of any Number of Yean.
Year*.
S per c«Qt.
Si per oent.
8 per c«nt.
Slperent
51
.3642 4302
.2838 4606
.2214 6318
,1729 9843
52
.3571 0100
.2769 2'J98
.2150 1280
.1671 4824
53
.3500 9902
.2701 6.S76
.2087 5029
.1614 9589
51
.343i 3433
.2635 7928
.2026 7019
,1560 8467
55
.3363 04-25
.2571 6052
.1967 6717
.1507 6814
56
.3299 0613
.2508 7855
.1910 3609
.1456 6004
57
.3*J34 3738
.2447 5957
.1854 7193
.1407 3433
58
.3170 9547
.23S7 8982
.1800 6984
.1359 7520
59
.3108 7791
.2329 6568
.1748 2508
.1313 7701
60
.3047 8227
.2272 8359
.1697 3J09
.1269 3431
61
.2088 0614
.2217 4009
.1647 8941
.1226 4184
62
.2929 47'JO
.2163 3179
.1599 8972
.1184 9453
63
.2872 0314
.2110 5541
.1553 2982
.1144 8747
64
.2815 7170
.2059 0771
.1508 0565
.1106 1591
65
.2760 5069
.2008 8557
.1464 1325
.1068 7528
66
.2/06 3793
.1939 8593
.1421 4879
.1032 6114
67
.2653 3130
.1912 0578
.1380 0853
.0997 6922
68
.2601 2873
.1865 4223
.1339 3887
.0963 9538
69
.2550 2817
.1819 9242
.1300 8628
.0931 3563
70
.2500 2761
.1775 5358
.1262 9736
.0899 8612
71
.2451 2511
.1732 2300
.1226 1880
.0869 4311
72
•2403 1874
.1689 9805
-1190 4737
.0840 0300
73
.2336 0661
.1648 7611
.1155 7998
.0811 623ir
74
.2309 8687
.1608 5478
.1122 1357
.0784 1770
75
.2264 5771
.1569 3149
.1089 4521
.0757 6590
76
•2220 1737
.1531 0389
.1057 7205
.0732 0376
77
.2176 6403
.1493 6965
.1026 9131
.0707 2827
78
.2133 9616
.14->7 2649
.0997 0030
.0683 3650
79
.2092 1192
.1421 7218
.0967 9641
.0660 2560
80
.2031 0973
.1387 0457
.0939 7710
.0637 9285
81
.2010 8797
.1353 2153
.0912 3990
.0616 3561
82
.1971 4507
.1320 2101
.0885 8-243
.0595 5131
83
.1932 7948
.1288 0098
.0860 0236
.0575 3750
84
.1894 3969
.1256 5949
.0834 9743
.0555 9178
85
.1857 7420
.1225 9463
.0810 6547
.0537 1187
86
.1821 3157
.1196 0452
.0787 04^4
.0518 9553
87
.1785 6036
.1166 8733
.0764 1198
.0501 4060
88
.1750 5918
.1138 4130
.0741 8639
.0484 4503
89
.1716 2665
.1110 6468
.0720 2562
.0468 0679
90
.1682 6142
.1083 5579
.0699 2779
.0452 2395
91
.1649 6217
.1057 1297
.0678 9105
.0436 9464
92
.1617 2762
.1031 3460
.0659 1364
.0422 1704
<J3
.1585 5649
.1006 1912
.0639 9383
.0407 8941
94
.1554 4754
.0981 6500
.0621 2993
.0394 1006
95
.1523 9955
.0957 7073
.0603 2032
.0380 7735
96
.1494 1132
.0934 3486
.0585 6342
.0367 8971
97
.1464 8169
.0911 5596
.0568 5769
,0355 4562
98
.1436 0950
.0889 3264
.0552 0164
.0343 4358
99
.1407 9363
.0867 6355
.0535 9383
.0331 8221
100
.13150 3297
.0846 4737
.0520 3284
.0320 6011
Digitized by^^UUVlC
TABLE IV.
Th« preieBt Valat of £1 due at the end of koj Number of Yeare.
63
Ye»f.
4 per cent
4i per cent
5 per cent
6 per cent.
61
•1353 0059
•1059 4225
.0830 5117
.0512 1544
58
.1300 9672
.1013 8014
.0790 9635
.0483 1645
63
.1250 9300
.0970 1449
.0753 2986
.0456 8156
54
.1202 8173
.0928 3683
.0717 4272
.0430 0147
55
.1156 5551
.0888 3907
•0683 2640
.0405 6742
56
•1112 0722
.0850 1347
.0650 7276
.0382 7115
67
.1069 3002
.0813 5260
.0619 7406
.0361 0486
58
.1028 1733
.0778 4938
.0590 2291
.0340 6119
59
.0988 6282
.0744 9701
.0562 1230
.0321 3320
60
.0950 6040
.0712 8901
.0535 3552
.0303 1434
61
.0914 0423
.0682 1915
.0509 8621
.0285 9843
63
.0878 8868
.0652 8148
.0485 5830
.0269 7965
63
.0845 0835
•0624 7032
.0462 4600
.0254 5250
64
.0312 5903
.0597 8021
.0440 4381
.0240 1179
65
.0781 3272
.0572 0504
•0419 4648
.0226 5264
66
.0751 2760
.0547 4253
.0399 4903
.0213 7041
67
.0722 3809
.0:)23 8519
•0380 4670
.0201 6077
63
.0694 5970
.0501 2937
.0362 3495
.0190 1959
69
.0667 8818
.0479 7069
.0345 0948
.0179,4301
70
•0642 1940
•0459 0497
.0328 6617
.0169 2737
71
•0617 4942
.0439 2820
.0313 0111
.0159 6921
78
.0593 7446
.0420 3655
•0298 1058
.0150 6530
73
.0570 9081
.0402 2637
•0283 9103
.0142 1254
74
.0548 9501
•0384 9413
.0270 3908
.0134 0806
75
.0527 8367
.0368 3649
.0257 5150
.0126 4911
76
.0507 5353
.0352 5023
.0245 2524
.0119 3313
77
.0488 0147
•0337 3228
.0233 5737
.0112 5767
78
.0469 2449
.0322 7969
.0222 4512
.0106 2044*
79
.0451 1970
.0308 8966
.0211 8582
.0100 1928
80
.0433 8433
•0295 5947
.0201 7698
.0094 5215
81
.0417 1570
.0282 8658
.0192 1617
.0089 1713
88
.0401 1125
.0270 6850
.0183 0111
.0084 1238
b3
.0385 6851
.0259 0287
.0174 2963
.0079 3621
84
.0370 8510
.0247 8744
.0165 9965
.0074 8699
£5
.0356 5875
.0237 2003
.0158 0919
.0070 6320
86
.0342 8726
.0226 9860
.0150 5637
.0066 6340
87
•0329 6862
.0217 2115
.0143 3940
.0062 8622
88
.0317 0050
.0207 8579
.0136 5657
.0059 3040
89
.0304 8125
.0198 9070
.0130 0626
.0055 9472
90
.0293 0890
.0190 3417
.0123 8691
.0052 7803
91
.0281 8163
.0182 1451
.0117 9706
.0049 7928
9-1
.0270 9772
.0174 3016
.0112 3530
.0046 9743
93
.0260 5550
.0166 7958
.0107 0028
.0044 3154
94
.0-250 5337
.0159 6132
.0101 9074
.0041 8070
95
.0240 8978
.0152 7399
.0097 0547
,0039 4405
96
.0231 6325
.0146 1626
.0092 4331
.0037 2081
97
.0222 7235
•0139 8685
.0088 0315
.0035 1019
99
.0214 1572
.0133 8454
.0083 8395
.0033 1150
99
.0205 9204
.0128 0817
.0079 8471
.0031 2406
100
.0198 0004
.0122 5663
.0076 0449
.0029 4723
DigitI
ftjby^oogle
84 TABLE IV.
The present value of £1 due at the end of any Nnmber of Yean.
Year*.
7 per cent.
8 per cent
9 per cent.
10 per eent.
51
.0317 2688
.0197 4188
.0123 3811
.0077 4414
52
.0296 5129
.0182 7952
.0113 1937
.0070 4013
53
.0277 1148
.0169 2548
.0103 8474
.0064 0011
54
.0238 9858
.0156 7174
.0095 2728
.0058 1S29
55
.0242 0428
.0145 1087
.0087 4063
.0052 8935
56
.0226 2083
.0134 3599
.0080 1892
.0048 0850
57
,0211 4096
.0124 4073
.0073 5681
.0043 7136
58
.0197 5791
.0115 1920
.0067 4937
.0039 7397
59
.0184 6533
.0106 6692
.0061 9208
.0036 1270
60
,0172 5732
.0098 7585
.0056 8081
.0032 8427
61
.0161 2834
.0091 4431
.0052 1175
.0029 8570
G2
.0150 7321
.0084 6696
.0047 8142
.0027 1427
63
.0140 8711
.0078 3977
.0043 8663
.0024 6752
64
.0131 6553
.0072 5905
.0040 2443
.0022 4320
65
.0123 0423
.0067 2134
•0036 9214
.0020 3927
G6
.0114 9928
.0062 2346
.0033 8728
.0018 5388
67
.0107 4699
.0057 6247
.0031 0760
.0016 8535
68
.0100 4392
.0053 3562
.0028 5101
.0015 3214
6'J
.0093 8684
.0049 4039
.0026 1560
.0013 9285
70
.0087 7275
.0046 7443
.0023 9963
•0012 6623
71
.0081 9883
.0042 3558
.0022 0150
.0011 5112
72
.0076 6246
•0039 2184
.0020 1972
.0010 4647
73
.0071 6117
.0036 3133
.0018 5296
.0009 5134
74
.0006 9269
.0033 6234
.0016 9996
.0008 6485
75
.0062 5485
.0031 1328
.0015 5960
•0007 8623
76
.0058 4565
.0028 8267
.0014 3082
.0007 1475
77
.0054 6323
.0026 6914
.0013 1268
.0006 4978
78
.0051 0582
.0024 7142
.0012 0430
.0005 9070
79
.0047 7179
.0022 8835
.0011 0486
.0005 3700
80
.0044 5962
.0021 1885
.0010 1363
.0004 8819
81
.0041 6787
.0019 6190
.0009 2994
.0004 4381
82
.0038 9520
.0018 1657
.0008 5315
.0004 0346
83
.0036 4038
.0016 8201
.0007 8271
.0003 6678
84
.0034 0222
.0015 5742
.0007 1808
.0003 3344
85
.0031 7965
.0014 4205
.0006 5879
•0003 0313
86
.0029 7163
.0013 3523
.0006 0440
.0002 7557
87
.0027 7723
.0012 3633
.0005 5449
.0002 5052
88
.0025 9554
.0011 4475
.0005 0871
.0002 2774
89
.0024 2574
.0010 5995
.0004 6670
.0002 0704
90
.0022 6704
.0009 8144
.0004 2817
.0001 8822
91
.0021 1873
.0009 0874
.0003 9282
.0001 7111
92
.0019 8012
.0008 4142
.0003 6038
.0001 5555
93
.0018 5068
.0007 7910
.0003 3063
.0001 4141
94
.0017 2952
.0007 2138
.0003 0333
.0001 2855
95
.0016 1637
.0006 6795
.0002 7828
.0001 1687
96
.0015 1063
.0006 1847
.0002 5530
.0001 0624
97
.0014 1180
.0005 7266
.0002 3422
.0000 9658
98
.0013 1944
.0006 3024
.0002 1488
.0000 8780
99
.0012 3312
.0004 9096
.0001 9714
.0000 7982
100
.0011 5245
.0004 6459
.0001 808G
.0000 7257
Digitized by Vj\^*^V IC
TABLB V.
The amoant of £1 per annum ia any number of Years.
8A
Yean.
2 per cent.
9i per cent
3 per oeot
3i per cent.
1
1.000000
1.000000
1.000000
1.000000
2
2.020000
2.025000
2.030000
2.035000
3
3.060400
3.075625
3.090900
8.106225
4
4.121608
4.152516
4.183627
4.214943
5
5.204040
5.236329
5.309136
5.362466
6
6.308121
6.387737
6.468410
6.550152
7
7.434283
7.547430
7.662462
7.779408
8
8.582969
8.736116
8.892336
9.051687
9
9.754628
9.954519
10.159J06
10.368496
10
10.949721
11.203382
11.463879
11.731393
11
12.168715
12.483466
12.807796
13.141992
12
13.412090
13.795553
14.192030
14.601962
13
14.680332
15.140442
15.617790
16.113030
14
15.973938
16.518953
17.086324
17.676986
15
17.293417
17.931927
18.598914
19.295681
16
18.630285
19.380225
20.156881
20.971030
17
20.012071
20.864Z30
21.761588
22.705016
IS
21.412312
22.386349
23.414435
24.499691
19
22.840559
23.946007
25.116868
26.357181
20
24.297370
25.544658
26.870374
28.279682
21
25.783317
27.183274
28.676486
30.269471
22
27.298984
28.862856
30.536780
32.328902
23
28.844963
30.584427
32.452884
34.4604(4
24
30.421862
32.349038
34.426470
36.666528
25
32.030300
34.157764
36.459264
38.949857
26
33.670906
36.0H708
38.553042
41.313102
27
35.344324
37.912001
40.709634
43.759060
23
37.051210
39.859801
42.930923
46.290627
29
38.792235
41.856296
45.218850
48.910799
30
40.568079
43.902703
47.575416
i^l. 622677
31
42.379441
46.000271
50.002678
54.429471
32
44.227030
48.150278
52.502759
57.334602
33
46.111570
50.354034
55.077841
60.341210
34
48.033802
52.612885
57.730177
63.453152
35
49.994473
54.928207
60.462082
66.674013
,
36
51.994367
57.301413
63.275944
70.007603
37
54.034255
59.733948
66.174223
73.457869
38
56.114940
62.227297
69.159449
77.028895
39
58.237238
64.782979
72.234233
80.724906
40
60.401983
67.402554
75.401260
84.550278
41
62.610023
70.087617
78.663298
88.509537
42
64.862223
72.839808
82.023196
92.607371
43
67.159468
75.660803
85.483892
96.848629
44
69.502657
78.652323
89.048409
101.238331
45
71.892710
81.516131
92.719861
105.781673
46
74.330564
84.554034
96.501457
110.484031
47
76.817176
87.667885
100.396501
115.350973
48
79.353519
90.859582
104.408396
120.388257
49
81.940590
94.131072
108.540648
125.601846
50
84.579401
97.484349
112.796867
130.997910
T
ninitPPflhyViOQgiC
TABLK V.
T1i« amoiuit of £1 per antmm in ray number of Tcftif.
y^
4 per oent
Opcreent.
6 percent.
6 per cent.
X
1.000000
1.000000
1.000000
1.000000
s
2.040000
2.045000
2.050000
2.060000
3
8.121600
3.137025
3.152500
3.183600
4
4.246464
4.278191
4.310125
4.374616
5
5.416323
5.470710
5.525631
5.637093
6
6.632975
6.716892
6.801913
6.975319
7
7.898294
8.019152
8.142008
8.393838
8
9.214226
9.380014
9.549109
9.897468
9
10.582795
10.802114
11.026564
11.491316
10
12.006107
12.288209
12.577893
13.180795
\l
13.486351
13.841179
14.206787
14.971643
n
15.025805
15 464032
15.917127
16.869941
13
16.626838
17.159913
17.712983
18.882138
14
18.291911
18.933109
19.598632
21.015066
19
20.023588
20.784054
21.578564
23.275970
16
21.824531
22.719337
23.657492
25.672528
IJ
23.697512
24.741707
25.840366
28.212880
18
25.645413
26.855084
28.132385
30.905653
19
27.671229
29.063.>62
30.539004
33.759992
20
29.778079
31.371423
33.065954
36.785591
21
31.969202
33.783137
35.719252
39.992727
29
34.247970
36.303378
38.505214
43.392290
23
36.617889
38.937030
41.430475
46.995828
24
39.082604
41.689196
44.501999
50.815577
25
41.645908
44.565210
47.727099
54.864512
26
44.311745
47.570645
51.113454
59.156383
2f
47.084214
50.711324
54.669126
63.705766
28
49.967583
53.993333
58.402.') 83
68.528112
29
52.966286
57.423033
62.322712
73.639798
30
56.084938
61.007070
66.438848
79.058186
31
59.328335
64.752388
70.760790
84.801677
32
62.701469
68.6662 i5
75.298829
90.889778
33
66.209527
72.756226
80.063771
97.343165
34
69 857909
77.030256
85.066959
104.183755
35
73.652225
81.496618
90.320307
111.434780
36
7^.698314
86.163966
95.836323
119.120867
3;
81.702246
91.041344
101.628139
127.268119
38
85.970336
96.138205
107.709,146
135.904206
39
90.409150
101.464424
114.095023
145.058458
40
95.025516
107.030323
120.799774
154.761966
41
99.826536
112.846688
127.839763
165.047684
42
104.819598
118.924789
135.231751
175.950545
43
110.012382
125.276404
142.993339
187.507577
44
115.412877
131.91.3842
151.143006
199.758032
45
121.029392
138.849965
159.700156
212.743514
46
126.870568
146.098214
168.685164
226.508125
47
132.945390
153.672633
178.119422
241.098612
48
139.263206
161.587902
188.025393
256.564529
49
145.833734
169.859357
198.426663
2r2.9:)8401
50
152.667084
178.503028
209.347996
Digitized by
290.335905
TABLE V. ®^
The amoimi of £\ per annum in any number of Teari.
Teatt.
7 per atnU
Spereent
9 per cent.
10 per cent
1.000000
1.000000
1.000000
1.000000
3.070000
2.080000
2.090000
2.100000
3.214900
3.246400
3.278100
3.310000
4.439943
4.506112
4.573129
4.641000
5.750739
5.866601
5.984711
6.105100
7.153291
7.335929
7.523335
7.715610
8.654021
8.922803
9.200435
9.487171
10.259803
10.636628
11.028474
11.435888
11.977989
12.487558
13.021036
13.579477
13.81^448
14.486562
15.192930
15.937425
15.783599
16.645487
17.560293
18.531167
17.888451
18.977126
20.140720
21.384284
20.140643
21.495297
22.95338 >
24.522712
22.55048S
24.214920
26.019189
27.974983
25.129022
27.152114
29.360916
31.772482
27.838054
30.324283
33.003399
35.949730
30.840217
33.750226
36.973705
40.544703
33.999033
37.450244
41.301338
45.599173
37.378965
41.446263
46.018458
51.159090*
40.995492
45.761964
51.160120
57.274999
44.865177
50.422921
56.7G4530
64.002499
22
49.005739
55.466755
62.873338
71.402749
23
53.436141
60.893296
69.531939
79.543024
24
58.176671
66.764759
76.789813
88.497327
25
63.249038
73.105940
84.700896
98.347059
20
68.676470
79.954415
93.323977
109.181765
27
74.483823
87.350768
102.723135
121.099942
28
80.697691
95.338830
112.968217
134.209936
29
87.346529
103.965936
124.135356
148.630930
30
94.460786
113.283211
136.307539
164.494023
81
102.073041
123.345868
149.575217
181.943425
32
110.218154
134.213537
164.036987
201.137767
33
118.933425
145.950620
179.800315
222.251544
34
128.258765
158.626670
196.982344
245.476699
35
138.236878
172.316804
215.710755
271.024368
36
148.913460
187.102148
236.124' 23
299.126805
37
160.337402
203.070320
2 >8. 375948
330.039486
38
172.561020
220.315945
282.629783
364.043434
39
185.640292
238.941221
309.066463
401.447778
40
199.635112
259.056519
337.882445
442.592556
41
214.609570
280.781040
369.291865
487.851811
42
230.632240
304,243523
403 528133
537-636992
43
247.776496
329.583005
440.845665
592.400692
44
266.120851
356.949646
481.521775
652.640761
45
285.749311
386.505617
525.858734
718.904837
46
306.751763
418.426067
574.186021
791.795321
47
329.224386
452.900152
626.86276-2
871.974853
48
353.270093
490.132164
684.280411
960.172338
49
378.999000
530.342737
746.865643
1057.189572
50
406 528929
573.770156
813.083556
1163.908529
Digitized by VjOOQ IC
88 TABLE V.
The amoi:nt o{£,\ per cnnvm in any number of Years.
Years.
2 per cent.
8i per cent.
3 per cent.
3i per cent.
51
87.2709S9
100.921458
117.180773
136.582837
52
90.016409
104.444494
121.696197
142.363236
53
92.816737
108.055606
126.347082
148.345950
54
95.673072
111.756996
131.137495
154.536058
55 .
98.586534
115.550921
136.071620
160.946890
56
101.5.')8264
119.439694
141.153768
167.580031
57
104.589430
123.425687
146.388381
174.4453.32
58
107.681218
127.511329
151.780033
181.550919
59
110.834843
131.699112
157.333434
188.906201
60
114.051539
135.991590
163.053437
196.516883
61
117.332570
140.391380
168.945040
204.394974
62
120.679222
144.901164
175.013391
212.548798
63
124.092806
149.523693
181.263793
220.988006
64
127.574662
154.261786
187.701707
229.722586
65
131.126155
159.118330
194.332758
238.762877
66
134.748679
164.096289
201.162741
248.119577
67
138.443652
169.198696
208.197623
267.803762
f.8
142.2125-25
174.428663
215.443551
267.826894
69
146.056776
179.789380
222.906858
278.200835
70
149.977911
185.284114
230.594064
288.937865
71
153.977469
190.916217
238.511886
300.050690
72
158.057019
196.689122
246.667242
311.552464
73
162.218159
202.606351
255.067259
.323.456800
74
166.462522
208.671509
263.719277
335.777788
75
170.791773
214.88S297
272.630856
348.530011
76
175.207608
221.260504
281.809781
361.728561
77
179.711760
227.792017
291.264075
375.389061
78
184.305996
234.486818
301.001997
389.527678
79
188.992115
241.348988
311.032057
404.161147
80
193.771958
248.332713
321.363019
419.306787
81
198.647397
255.592280
332.003909
434.982524
82
203.620345
262.982087
342.964026
451.206913
83
208.092752
270.550640
354,252947
467.999155
64
213.806607
278.320556
365.880536
485.379125
85
219.143939
286.278570
377.856952
503.367394
86
224.526818
294.435')34
390.192660
521.985253
87
230.017364
302.796422
402.898440
541.254737
88
235.617701
311.366333
415.985393
561.198663
89
241.330055
320.150491
429.464955
581.840606
UO
247.156656
329.154253
443.348904
603.205027
91
253.099789
338.383110
457.649371
625.317203
92
259.161785
347.842(587
472.3788.52
648.203305
93
265.345021
357.538755
487.550217
671.890421
94
271.651921
367.477223
503.176724
696.406585
95
278.084960
377.664154
519.272026
721.780816
96
284.646659
388.10.5758
535.850186
748.043145
97
291.339592
398.808402
552.925692
775.224655
98
298.1663S4
409.778612
570.513463
803.357517
99
305.129712
421.023077
5.S8. 628867
832.475031
100
312.23^306
432.548054
607.287733
862.611657
Digitized by VjOOQIC
TABLE V. 80
The amount of £1 per aimumin any number of Years.
Years.
4 per cent
41 per cent
5 per cent
6 per cent.
51
159.773767
187.535665
220.815395
308.756059
52
167.164718
196.974769
232.856165
323.281422
53
174.851306
206.838634
245.498974
348.978308
54
182.845350
217.146373
258.773922
370.917006
55
191.159173
227.917959
272.712618
394.172027
56
199.805540
239.174268
287.348249
418.822348
57
208.797762
250.937110
302.715662
444.951689
53
218.] 49672
263.229280
318.851445
472.648790
59
227.875659
276.074597
335.794017
502.007713
60
237.990685
289.497954
333.583718
533.128181
61
248.510313
303.525362
372.262904
566.115872
62
259.450725
318.184003
391.876049
601.082824
63
270.828754
333.502283
412.469851
638.147793
64
282.661904
349.509886
434.093344
677.436661
65
294.968381
366.237831
456.798011
719.082861
66
307.767116
383.718533
480.637912
763.227832
67
321.077800
401.985867
505.669807
810.021502
68
334.920912
421,075231
531.953298
859.622792
69
349.317749
441.023617
559.550963
912.200160
70
364.290459
461.8^9680
588.528511
967.932170
71
379.862077
483.653815
618.954936
1027.008100
72
396.056560
506.418237
650.902683
1089.628586
73
412.898823
530.207057
684.447817
1156.006301
74
430.414776
555.066375
719.670208
1226.366679
75
448.631367
581.044362
756.653718
1300.948680
76
467.576621
608.191358
795.486404
1380.005601
77
487.279686
636.559969
836.260725
1463.805937
78
507.770874
666.205168
879.073761
1552.634293
79
529.081708
697.184401
924.027449
1646.792350
80
551.244977
729.557699
971.228821
1746.599391
81
574.294776
763.387795
1020.790262
1852.395885
82
598.266567
798.740246
1072.829775
1964.539638
83
623.197230
835.683557
1127.471264
2083.412016
84
649.125119
874.289317
1184.844827
2209.416737
8j
676.090124
914.632336
1245.087069
2342.981741
86
704.133728
733.299078
956.790791
1208.341422
2484.560646
87
1000.846377
1374.758493
2634.634285
88
763.631041
1046.884464
1444.496418
2793.712342
89
795.176282
1094.994265
1517.721239
2962.335082
90
827.983334
1145.269007
1594.607301
3141.075187
9]
862.102667
1197.806112
1675.337666
3330.539698
92
697.586774
1232.707387
1760.104549
3531.372080
93
934.490245
1310,079219
1849.109777
3744.254405
94
972.869854
1370.032784
1942.565265
3969.909669
95
1012.784649
1432.684259
2040.693529
4209.104250
96
1054.296035
1498.155051
2143.728205
4462.650505
97
1097.467876
1566.572028
2231.914615
4731.409535
98
1142.366591
1638.067770
2365.510346
5016.294107
99
1189.061255
1712.780819
24S4. 785864
5318.271753
100
1237.623705
1790.855956
2610.025157
5638.368059
Uigitized by VjO^
TABLE V.
Jht amount of £1 f€r nmmm in nnj Nnmber of Yean.
T.»
ypnoent
Spereent
f parent
10 per eeat.
51
435.985955
620.671769
889.441076
1281.2993S2
52
467.504971
671.325510
970.490773
1410.429320
58
501.230319
726.031551
1058.834943
1552.472252
64
537.316442
785.114075
1155.130088
1708.719477
55
575.928593
848.923201
1260.091796
1880.591425
66
617.243594
917.837058
1374.500057
2069.650567
6r
661.450646
992.264022
1499.205063
2277.615624
58
708.752191
1072.645144
1635.183518
2506.377186
59
759,364844
1159.456755
1783.295535
2758.014905
60
813.520383
1253.213296
1944.792133
3034.816395
61
871.466810
1354.470360
2120.823425
3339.298035
62
933.469487
1463.827988
2312.697533
3674.227838
63
999.812351
1581.934227
2521.840311
4042.650622
64
1070.799216
1709.488966
2749.805939
4447.915685
65
1146.755161
1847.248083
2998.288474
4893.707253
66
1228.028022
1996.027929
3269.134436
5384.077973
67
1314.989983
2156.710164
3564.356535
59-23.485776
68
1408.039282
2330.246977
3886.148684
6516.834354
69
1507.602032
2517.666735
4236.902000
7169.517789
ro
1614.134174
8720.080074
4619.223180
7887.469568
71
1728.123566
2938.686480
5035.953266
8677.216525
72
1850.092216
3174.781398
5490.189060
9545.938177
73
1980.598671
3429.763910
5985.306075
10501.531995
74
2120.240578
3705.145023
6524.983688
11552.685195
75
2269.657419
4002.556624
7113.232148
12708.953714
76
2429.5334S8
4323.761154
7754.423041
13980.849085
7f
2600.600779
4670.662047
8453.321115
15379.933994
78
2783.642833
5045.315011
9215.120015
16918.927393
79
2979.497831
5449.940211
10045.480817
18611.820133
80
3189.062G80
5886.935428
10950.574090
20474.002146
61
3413.297067
6358.890263
11937.125758
22522.402360
82
3653.227862
6868.601484
13012.467077
24775.642596
83
3909.953812
7419.089502
14184.589114
27*254.206856
84
4184.650579
8013.616770
15462.202134
29980.627542
85
4478.576120
8655.706112
16854.800326
32979.690296
86
4793.076448
9349.162601
18372.732355
36278.659326
87
3129.591799
1009S. 095609
20027.278267
39907.525258
88
5489.663225
10906.943258
21830.733311
43899.277784
89
5S74. 939651
11780.498718
23796.499309
48290.205562
90
6287.185427
12723.938616
25939.184247
53120.226119
91
6728.288407
13742.853705
28274.710829
58433.248730
92
7-200.268595
14843.282002
80820.434804
64277.573603
93
7705.2S7397
16031.744562
33595.273936
7070G. 330964
94
8245.657515
17315.284127
36619.848590
77777.964060
95
8823.853541
18701.506857
39916.634964
85556.760466
96
9442.523288
20198.627405
43^10.132110
94113.436513
97
10104.499919
21815.517598
47427.044000
103525.780164
98
10812.814913
23561.759006
51696.477960
113879.358180
99
11570.711957
25447.699726
56350.160977
1'25'268. 293998
100
12381.661794
27484.515704
61422.675465
137796.123398
Digitized by \
jUUV ic —
TABIiB VL 91
The preteni Value of £1 per mmim tot unj Namber of Tean«
Ye^
fipereent
Si per cent.
6 per eent.
di per cent
1
.980392
.975610
.970874
.966184
2
1.941561
1.927424
* 1.913470
1.899694
3
2.883883
2.856024
2.828611
2.801637
4
3.807729
3.761974
3.717098
3.673079
5
4.713460
4,645828
4.579707
4.515052
6
5.601431
5.508125
5.417191
5.328553
7
6.471991
6.349391
6.230283
6.114544
8
7.325481
7.170137
7.019692
6.873956
9
8.162237
7.970866
7.786109
7.607687
10
8.982585
8.752064
8.530203
8.316605
n
9.786848
9.514209
9.252624
9.001551
12
10.575341
10.257765
9.954004
9.663334
13
11.348374
10.983185
10.634955
10.302738
14
12.106249
11.690912
11.296073
10.920520
15
12.849264
12.381378
11.937935
11.517411
16
13.577709
13.055003
12.561102
12.094117
17
14.291872
13.712198
13.166118
12.651321
IS
14.992031
14.353364
13.753513
13.189682
19
15.678462
14.978891
14.323799
13.709837
20
16.351433
15.589162
14.877475
14.212403
21
17.011209
16.184549
15.415024
14.697974
22
17.658048
16.765413
15.936917
15.167125
23
18.292204
17.332110
16.443608
15.620410
24
18.913926
17.884986
16.935542
16.058368
25
19.523456
18.424376
17.413148
16.481515
26
20.1221036
18.950611
17.876842
16.890352
27
20.706898
19.464011
18.327031
17.285365
28
21.281272
19.964889
18.764108
17.667019
29
21.844385
20.453550
19.188455
18.035767
30
22.396456
20.930293
19.600441
18.392045
SI
22.937702
21.395407
20.0d0428
18.736276
32
23.468335
21.849178
20.388766
19.068865
33
23.988564
22.291881
20.705792
19.390208
34
24.498592
22.723786
21.131837
19.700684
35
24.998619
23.145157
21 .487220
20.000661
36
25.488842
23.556251
21.832252
20.290494
37
25.969453
23.957318
22.167235
20.570525
38
26.440641
24.348603
22.492462
20.841087
39
26.902589
24.730344
22.808215
21.102500
40
27.355479
25.102776
23.114772
21.355072
41
27.799489
25.466122
23.412400
21.599104
42
28.234794
25.820607
23.701359
21.83-1883
43
28.661562
26.166446
23.981902
22.06*2689
44
29.079963
26.503849
24.254274
22.282791
45
29.490160
26.833024
24.518713
22.495450
46
29.892314
27.154170
24.775449
22.700918
47
3U. 286582
27.467483
25.024708
22.899438
48
30.673120
27.773154
25.266707
23.091244
49
31.052078
2S. 07 1369
25.501657
23.276564
50
31.423606
28.362312
25.729764
23.455618
TABLE VI.
The present Valne of £\ p^r annum for any Number of Tears*
Yeart.
4 per cent.
4t per ceot.
5 per cent.
fiperceat.
1
.961538
.956938
.952:^81
.943396
2
1.8S6095
1 .872668
1.859410
1.833393
3
2.775091
2.748964
2.723248
2.673012
4
3.629895
3.587526
3.545951
3.465106
5
4.451822
4.389977
4.329477
4.212364
6
5.242137
5.157872
5.075692
4.917324
7
6.002055
5.892701
5.786373
5.582381
8
6.732745
6.595886
6.463213
6.209794
9
7.435332
7.268790
7.107822
6.801692
10
8.110896
7.912718
7.721735
7.360087
11
8.760477
8.528917
8.306414
7.886875
12
9.385074
9.118581
8.863252
8.383844
13
9.985648
9.682852
9.393573
8.852683
14
10.563123
10.222825
9.898641
9.294984
15
11.118387
10.739546
10.379658
9.712249
16
11.652296
11.234015
10.837770
10.105895
17
12.165669
11.707191
ll.'J740li6
10.477260
18
12.659297
12.159992
11.689587
10.827603
19
13.133939
12.593294
12.085321
11.158116
20
13.590326
13.007936
12.462210
11.469921
21
14.029160
13.404724
12.821153
11.764077
22
14.451115
13.784425
13.163003
12.041:182
23
14.856842
14.147775
13.488574
12.303379
24
15.246963
14.495478
13.798642
12.550358
25
15.622080
' 14.828209
14.093945
12.783356
26
15.982769
15.146611
14.375185
13.003166
27
16.329586
15.451303
14.643034
13.210:i34
28
16.663063
15.742874
14.898127
13.406164
29
16.983715
16.021889
15.141074
13.590721
30
17.292033
16.288889
15.372451
13.764831
31
17.588494
16.544391
15.592811
13.929086
32
17.873552
16.788891
15.802677
14.084043
33
18.147646
17.022862
16.002549
14.230230
34
18.411198
17.246758
16.192904
14.368141
35
18.664613
17.461012
16.374194
14.498246
36
18.908282
17.666041
16.546852
14.620987
37
19.142579
17.862240
16.711287
14.736780
38
19.367864
18.049990
16.867893
14.846019
39
19.584485
18.229056
17.017041
14.949075
40
19.792774
18.401584
17.159086
15.046297
41
19.993052
18.566109
17.294368
15.138016 ♦
42
20.185627
18.723550
17.423208
15.224543
43
20.370795
18.874210
17.545912
15.306173
44
20.548841
19.018383
17.662773
15.383182
45
20.720040
19.156347
17.774070
15.455:>32
46
20.884654
19.288371
17.880067
15.524370
47
21.042936
19.414709
17.981016
15.589028
48
21.195131
19.535007
18.077158
15.650027
49
21.341472
19.651298
18.168722
15.707572
50
21.482185
19.762008
18.255925
15.761861
LiiiVl^
TABLE VI. OS
The preient Valne of £1 per amum for any Number of Yean*
Tean.
7 per cent
8 per cent
9 per cent
10 per cent
1
.934579
.925926
.917431
.909091
2
1.808018
1.783265
1.759111
, 1.735537
3
2.624316
2.577097
2.531295
2.486852
4
3.387211
3.312127
3.239720
3.169865
S
4.100197
3.992710
3.889651
3.790787
6
4.766540
4.622880
4.485919
4.355261
7
5.389289
5.206370
6.032953
4.868419
8
5.971299
5.746639
5.534819
5.334926
9
6.515232
6.246888
5.995247
5.759024
10
7.023582
6.710081
6.417658
6.144567
11
7.498674
7.138964
6.805191
6.495061
12
7.942686
7.r)36U78
7.160725
6.813692
13
8.357651
7.903776
7.486904
7.103356
14
8.745468
8.244237
7.786150
7.3666S7
15
9.107914
8.559479
8.060688
7.606080
16
9.446649
8.851369
8.312558
' 7.823709
17
9.763223
9.121638
8.543631
8.021553
18
10.059087
9.371887
8.755625
8.201412
19
10.335595
9.603599
8.950115
8.364920
20
10.594014
9.818147
9.128546
8.513564
21
10.835527
10.016803
9.292244
8.648694
22
11.061241
10.200744
9.442425
8.771540
23
11.272187
10.371059
9.580207
8.883218
24
11.469334
10.528758
9.706612
8.9S4744
25
11.653583
10.674776
9.822580
9.077040
26
11.825779
10.809978
9.928972
9.160945
27
11.986709
10.935165
10.026580
9.237223
28
12.137111
11.051078
10.116128
9.306567
29
12.277674
11.15H406
10.198283
9.369606
30
12.409041
U. 257783
10.273654
9.426914
31
12.531814
11.349799
10.342802
9.479013
32
12.646555
11.434999
10.406240
9.526376
33
12.753790
11.513888
10.464441
9.569432
34
12.854009
11.586934
10.517835
9.608575
35
12.947672
11.654568
10.566821
9.644159
36
13.035208
11.717193
10.611763
9.676508
37
13.117017
11.775179
10.652993
9.705917
38
13.193473
11.828869
10.690820
9.732651
39
13.264928
11.87H5S2
10.725523
9.756956
40
13.331709
11.924613
10.757360
9.779051
41
13.394120
11.967235
10.7865G9
9.799137
42
13.452149
12.006699
10.813366
9.817397
43
I3.50G962
12.043240
10.837951
9.833998
44
13.557908
12.077074
10.860505
9.849089
45
13.605522
12.108402
10.881197
9.862808
46
13.650020
12.137409
10.900181
9.875280
47
13.691608
12.164267
10.917597
9.886618
48
13.730474
12.189136
10.933575
9.896926
49
13.766799
12.212163
10.9-18234
9.906296
50
13.800746
12.233485
10.961683
9.914814
64 TAttLB VL
The preieut Value of £1 per taumm fur amf Nombw of Yeen.
Yfari.
% per cent.
Si per eent
8pcro8iit
8i per eent.
51
81.787849
28.646158
25.951227
23.626616
52
32.144950
28.923081
26.166240
23.795765
53
32.495049
29.193249
86.374990
23.957260
54
32.838283
29.456829
86.577660
24.113295
55
33.174788
29.713979
26.774428
24.264053
66
83.504694
89.964858
26.965464
24.400713
57
33.828131
30.209617
27.150936
24.550448
58
34.145227
80.448407
27.331005
24.686423
59
84.456104
80.681373
27.505831
24.817800
60
34.760887
30.908656
27.675564
24.944734
61
35.059693
31.130397
27.840353
25.067376
62
35.352640
31.346728
28.000343
25.186870
63
35.639843
31 .657784
28.165673
85.300358
64
35.921415
31.763691
28.306478
26.410974
65
36.197466
31.964577
28.452891
26.517840
66
36.468104
32.160563
28.595040
25.621110
67
36,733435
32.351769
28.733049
25.720880
68
36.993564
32.538311
28.867038
25.817276
6B
37.248392
32.720303
28.997124
25.910411
70
37.496619
32.897857
29.123421
26.000397
71
37.743744
33.071080
29.246040
26.087340
72
37.984063
33.240078
29.365087
26.171343
73
38.219670
33.404954
29.480667
26.262506
74
38.450657.
33.566809
29.592881
26.330923
75
38.677114
33.722740
29.701826
26.406689
76
38.899132
33.875844
29.807598
26.479892
77
39.116796
84.025214
89.910290
86.550621
78
89.330192
34.170940
30.009990
26.618957
79
39.539404
34.313113
30.106786
26.684983
80
39.744514
34.451817
30.200763
26.748776
81
39.945602
84.587139
30.292003
26.810411
82
40.142747
34.719160
30.380586
26.869963
83
40.336026
34.847961
30.466588
26.927500
84
40.525516
34.973620
30.550086
26.983092
85
40.711290
35.096215
30.631151
27.036804
86
40.893429
35.215819
30.709855
27.038699
87
41.071982
35.332507
30.786267
27.138840
88
41.247041
35.446348
30.860454
27.187285
89
41.418668
35.557413
30.932470
27.234092
90
41.586929
35.665768
31.002407
27.279316
91
41.751891
35. 771481
31.070298
27.323010
92
41.913619
35.874616
31.136213
27.365227
83
42.072176
35.975235
31.200206
27.406017
94
42.227623
36.073400
31.262336
27.445427
95
42.380023
36.169171
31.322656
27.483504
96
42.529434
36.262606
31,. 381219
27.520294
97
42.675916
36.353762
31.438077
27.555839
98
42.819525
36.442694
31.493279
27.590183
99
42.960319
36.529458
31.546872
27.623365
100
43.098352
36.614106
31.598906
27.665425
Per^
50.000000
40.000000
33.333333
88.571489
TABLl VI.
The pTMent Vtluo of £1 per mtumm for any Number of Teatf .
Taut.
4 pcf cent
4i percent.
5 per eent
6 per oeot
51
21.617485
19.867950
18.338977
15.813076
52
21.747582
19.969330
18.418073
15.861393
53
21.872675
20.066345
18.493403
15.906974
54
21.992957
20.159181
18.565146
15.949976
55
22.108612
20.246021
18.633472
15.990543
56
22.219819
20.3^3034
18.698545
16.028814
57
22.326749
20.414387
18.760519
16.064919
&8
22.429567
20.492236
18.819542
16.098980
59
22.528430
20.566733
18.875754
16.131113
eo
22.623490
20.63802.)
18.929290
16.161428
61
22.714894
20.706241
18.980276
16.190026
62
22.802783
20.7715i>3
10.028834
16.217006
63
22.887291
20.833993
19.075080
16.242458
64
22.968549
20.893773
10.119124
16.266470
65
23.046682
20.950979
10.161070
J6. 289123
66
23.121810
21.005723
19.201019
16.310493
67
23.194048
21.058107
19.239066
16.330654
68
23.263507
21.108236
19.275301
16.349673
69
23.330296
21.156207
10.309810
16.367617
70
23.394515
21.202112
19.342677
16.384544
71
23.456264
21.246040
19.373978
16.400513
72
23.515639
21.288077
19.403788
16.415578
73
23.572730
21.328303
19.432179
16.429791
74
23.627625
21.366797
19.459218
16.443199
75
23.680408
.21.403634
19.484970
16.455848
76
23.731162
21.438884
19.509495
16.46778!
77
23.779963
21.472616
19.532853
16.479039
78
23.826888
21.504896
19.555098
16.489659
79
23.872008
21.535785
19.576284
16.499679
80
23.915392
21.565345
19.596460
16.509131
81
23.957108
21.593632
19.615677
16.518048
82
23.997219
21.620700
19.633978
16.526468
83
24.035787
21.646603
19.651407
16.534396
84
24.072872
21.671396
19.668007
16.541883
85
24.108531
21.695110
19.683816
16.548947
86
24.142818
21.717809
19.698873
16.555610
87
24.175787
21.739530
19.713212
16.561896
88
24.207487
21.760316
19.726869
16.567827
89
24.237969
21.780207
19,739876
16.573421
90
24.267278
21.799241
19.752262
16.578699
91
24.295459
21.817455
19.764059
16.583679
92
24,322557
21.834885
19.775294
16.588376
93
24.348612
21.851565
19.785994
16.592808
94
24.373666
21.867526
19.796185
16.596988
95
24.397756
21.882800
19.805891
16.600932
96
24.420919
21.897417
19.815134
16.604653
97
24.443191
21.911403
19.823937
16.608163
98
24.464607
21.924788
19.832321
16.611475
99
24.485199
21.937596
19.840306
16.614599
100
24.504999
21.949853
19.847910
16.617546
Petp.
25.000000
22.222222
20.000000
16.666667
-^r^\r>
96 TABLE VI.
The pre«ent Value of £1 fer annum for any number of Year*.
Years.
7 per cent.
8 per coot.
9 per oent
10 per ccut
51
13.832473
12.253227
10.974021
9.92J559
52
13.862124
12.271506
10.985340
9.929599
53
13.889836
12.288432
10.995725
9.935999
54
13.915735
12.304103
11.005252
9.941817
55
13.939939
12.318614
11.013993
9.947107
56
13.962560
12.332050
11.022012
9.951915
57
13.98370]
12.344491
11.029369
9.956286
58
14.003459
12.356010
11.036118
9.960260
59
14.021924
12.366676
11.042310
9.963873
60
14.039181
12.376552
11.047991
9.967157
61
14.055309
12.385696
11.053203
9.97014.1
62
14.070383
12.394163
11.057984
9. 972857
63
14.084470
12.402003
11.062371
9.975325
64
14.097635
12.409262
11.066395
9.97756S
65
14.109940
12.415983
11.070087
9.979607
66
14.121439
12.422207
11 .073475
9.981461
67
14.132186
12.427969
11.076582
9.9S3147
68
14.142230
12.433305
11,079433
9.984679
69
14.151617
12.438245
11.082049
9.986071
70
14.160389
12.442820
11.084449
9.98733S
71
14.168588
12.447055
11.086650
9.988489
72
14.176251
12.450977
11.088670
0.989535
73
14.183412
12.454608
11.090523
9.990487
74
14.190104
12.457971
11.092223
9.9913.M
75
14.196359
12.461084 .
11.093782
9.992138
76
14.202205
12.463967
11.095213
9.992852
77
14.207668
12.466636
11.096526
9.993502
78
14.212774
12.469107
11.097730
9.994093
79
14.217546
12.471396
11.098835
9.994630
80
14.222005
12.473514
11.099849
9.995118
81
14.226173
12.475476
11.100778
9.995562
82
14.230069
12.477293
11.101632
9.995965
83
14.233709
12.478975
11.102414
9.996332
84
14.237111
12.480532
11.103132
9.996666
85
14.240291
12.481974
11.103791
9.996969
86
14.243262
12.483310
11.104396
9.997244
87
14.246040
12.484546
11.104950
9.997495
88
14.248635
12.485691
11.105459
9.997723
89
14.251061
12.486751
11.105926
9.997930
90
14.253328
12.487732
11.106354
9.998118
91
14.2rir)447
12.488641
11.106746
9.9982S9
92
14.257427
12.489482*
11.107107
9.998444
93
14.259277
12.490261
11.107438
9.998586
94
14.261007
12.4909S3
11.107741
9.996714
95
14.262623
12.491951
11.108019
9.998831
96
14.264134
12.4922C9
11.108274
9.99893S
97
14.265546
12.492S42
11.108509
9.999034
98
14.266865
12.493372
11.108724
9.999122
99
14.268098
12.493863
11.108921
9.999.02
luo
14.269251
12.494318
11.109102
9.99li274
Perp.
14.285714
12.500000
11.111111
10.000000
Digitized by VjOOQ IC
TABLS VIL 97
The AnDuity which £1 will purchase for any number of Tean.
Ytm.
S per cent
8i per oent.
8 per cent
3i per cent.
1
1.02000000
1 .02500000
1.03000000
1.03500000
2
0.51504950
0.51882716
0.52261084
0.52640049
3
.34675467
.35013717
.35353036
.35693418
4
.26262375
.26581788
.26902705
.27225114
5
.21215839
.21524686
.21835157
.22148137
6
.17852581
.18154997
.18459750
.18766821
7
.15451195
.15749543
.16050635
.16354449
8
.13650980
.13946735
.14245639
,14547665
9
•12251544
.12545689
.12843386
.13144601
10
.11132653
.11425876
.11723051
.12024137
11
.10217794
.10510596
.10807745
.11109197
12
.09455960
.09748713
.10046209
.10348395
13
.08811835
.09104827
.09402954
.09706157
14
.08260197
. 08553653
.0S852634
.09157073
lb
.07782547
.08076646
.08376658
.08682507
16
.07365013
.07659899
.07961085
.08268483
17
.06996984
.07292777
.07595253
.07904313
18
.06670210
.06967008
.07-270870
.07581684
19
.06378177
.06676062
.06981388
,07294033
20
.06115672
.06414713
.06721571
.07036108
21
.05878477
.06178733
.06487178
.06803659
22
.05663140
.05964660
.06274739
.06593207
23
.05466810
.05769638
.06081390
.06401880
24
.05287110
.05591282
.05904742
.06227283
25
.05122044
.05427592
.05742787
.06067404
26
.04969923
.05276875
.05593829
.05920540
27
.04829309
.05137687
.05456421
.05785241
28
.04698967
.05008793
.05329323
.05660265
29
.04577835
.04889127
.05211467
.05544538
30
.04464992
.04777764
.05101926
.05437133
31
.04359635
.04673900
.04999893
.05337240
32
.04261061
.04576831
.04904662
.05244150
33
.04168653
.04485938
.04815612
.05157242
34
.04081867
•04400675
.0J732196
.05075966
35
.04000221
•04320558
.04653929
.04999835
36
.03923285
.04245158
.04580379
.04928416
37
.03S50678
.04174090
.04511162
.04861325
38
.03782057
.04107012
.044J5934
.04798214
39
.03717114
.04043615
.04384385
.04738775
40
.03655575
.03983623
.04326238
.04682723
41
.03597188
.03926786
.01271241
.04629822
42
.03541729
.03872876
.04219168
.04579828
43
.03488993
.03821688
.04169811
.04)32539
44
.03438794
.03773037
.04122985
.04487768
45
.03390962
•03726751
.04078518
.04445343
46
.03345342
.03682676
.04036254
.04405108
47
.03301792
.03640669
.03996051
.04366919
48
.03260184
.03600599
.03957777
.04330646
49
.03^20396
.0356-2348
.03921314
.04296167
50
.03182321
.03525806
.03886546
.04263371
h' O
le
TABLB VII.
The Aonuify which £1 willpurehaae for any nnmber of Yean.
Ycari.
4 per eent.
4i per cent
5 per eent.
«per oent.
1
1.04000000
1.04600000
1.05000000
1.06000000
2
0.63019608
0.53399766
0.53780488
0.54643689
S
.36034854
.36377336
.36720866
.37410981
4
.27549006
.27874365
.28201183
.28869149
5
i 224627 11
.22779164
.23097480
.23739640
6
.19076190
.19387839
.19701747
.20336263
7
116660961
.16970147
.17281982
.17913502
8
.14352783
.15160965
.15472181
.16103594
9
.13449299
.13757447
.14069008
.14702224
10
.12329094
.12637882
. 129504 >8
.13686796
11
.11414904
.11724818
.12038889
.12679294
12
.10655217
.10966619
.11282541
.11927703
13
.10014373
.10327635
. 10646577
.11296011
14
.09466897
.09782032
.10102397
.10758491
15
.08994110
.09311381
.09634229
.10296276
16
.08582000
.08901537
.09226991
.09895214
17
.08219852
.08541758
.08869914
.09544480
18
.07899333
.08223690
.08554622
•09235654
19
.07613862
.07940734
.08274501
.08962086
29
.07358175
.07687614
.08024259
.08718456
21
.07128011
.07460057
.07799611
.08500456
22
.06919881
.07254565
.07597051
.08304557
23
•• .06730906
.07068249
.07413683
.08127848
24
.06558683
.06898703
.07247090
.07967901
25
.06401196
.06743903
.07095246
.07822672
26
.06256738
.06602137
.06956432
.07690435
27
.06123854
.06471949
.06829186
.07569717
28
.06001298
.06352081
.06712253
.07459266
29
.05887993
.06241461
.06604551
.07357961
30
.05783010
.00139154
.06506144
.07264891
31
i05e85535
.06044345
.06413212
.07179222
32
.05594859
.05956320
.06328042
.07100234
33
.05510357
.05974453
.06249004
.07027293
34
.05431477
.05798191
.06175549
.06959843
35
.05367732
.05727045
.06107171
.06897386
36
.05288688
.05660578
.06043446
.06839483
37
.05223956
.05598402
.05983979
.06785743
38
.05163192
.05540169
.05928423
.06736812
39
.05106083
.05485567
.05876402
.06689380
40
.05052349
.06434315
.05827816
.06646163
41
.05001738
.05386158
.05782229
.06606886
42
.04954020
.05340868
.05739471
.06668342
43
.04908989
.05298236
.05699333
.06533312
44
.04866454
.05258071
.05661625
.06)00606
45
.04826246
.05220202
.05626173
.06470050
46
.04788205
.05184471
.05592820
.06441485
47
.04752189
.05150734
.05561421
.06414768
48
.04718065
.06118858
.05531843
.06389766
49
.04685712
.06088722
.05503966
.06366356
50
.04665020
.06060216
.06477674
.06344429
TABLE Vir. 99
The Annuity whicli £1 will pnrchase for any number of Tears.
Ycus.
7p«rMBt.
8 per ceBt.
9 per cent.
Wpeteent.
1
1.07000000
1.08000000
1.09000000
1,10000000
2
0.55309179
0.56076923
0.56846890
0.57619048
a
.38105166
.38803351
.39505476
.40211480
4
.2952281:2
.30192080
.30866866
.31547080
5
.24389069
.25045645
.25709246
.26379748
6
.20979580
.21631539
.22291978
.22960738
7
. 18555322
.19207240
.19869052
.20540550
8
.16746776
.17401476
.18067438
.18744402
9
.15348647
.16007971
.166798S0
.17364054
10
.14237750
.14902949
.15582009
.16274540
11
.13335690
.14007634
.14694666
.15396314
12
.12590199
.13269502
.13965066
.14676332
13
.11965085
.12652181
.13356656
.14077852
14
.11434494
.12129685
,12843317
,13574622
15
.10979462
.11682954
.12405888
.13147378
16
.10585765
.11297687
.12029991
•12781662
17
.10242519
.10962943
.11704625
•12466413
18
.09941260
.10670210
.11421229
•12193022
\9
.09675302
.10412763
.11173041
•11954687
20
.09439293
.10185221
.10954648
.11745962
21
.09228900
.09983225
.10761663
.11562439
32
.09040577
.09803207
.10590499
.11400506
23
.08871393
.09642217
.1043S188
.11257181
24
.08718902
.09497796
.10302256
.11129978
25
.08581052
.09367878
.•10180625
.11016807
26
.08456103
.09250713
,10071536
.10915904
27
.08342573
.09144810
.09973491
.10825764
28
.08239193
.09048890
.09885205
.10745101
29
.08144865
.08961854
.09805572
.10672807
30
.08058640
.08882743
.09732635
.10607925
31
.07979691
.08810728
.09668560
.10549621
32
.07907292
.08745081
.09609619
.10497172
33
.07840807
.08685163
.09556173
•10449941
34
.07779674
.08630411
.09507660
.10407371
35
.07723396
.08580326
,09463584
.10366971
36
.07671531
' .08534467
.09423505
.10334306
37
.07623685
.08492440
.09387033
. 10302994
38
.07579505
.08453894
.09353820
. 10274692
39
.07538676
.08418513
.09323555
.10249098
40
.07500914
.08386016
.09295961
.10226941
41
.07465962
.08356149
.09270789
.10204980
42
.07433591
.08328684
.09247814
.10185999
43
.07403590
.08303414
.09226937
.10168805
44
.07375769
.08280152
.09207675
.10153224
45
.07349957
.08258728
•09190165
.10139100
46
.07325996
.08238991
.09174160
.10126295
47
•07303744
.08220799
.09159525
.10114682
48
,07283070
.08204027
.09146139
.10104148
49
.07263853
.08188557
.09133893
. 10094590
50
•07245985
.08174286
.09122687
Digitiz(
d.yd«e?^gle
h2
100 TABLE VII.
The Annuity which £1 will purchase for any number of Yean.
Years.
S per cent.
Si per cent.
3 per cent.
3i per oenU
51
.03145856
.03490870
.03853382
.04232156
52
.03110909
.03457446
.03821718
.04202428
53
.03077392
.03425449
.03791471
.04174100
f)4
.03045226
.03394799
.03762558
.04147090
55
.03014337
.03365419
.03734907
.04121323
56
.02984657
.03337243
.03708447
.04096730
&7
.02956120
.03310204
.03683114
.04073245
58
.0292S667
.03284244
.03658848
.04050810
59
.02902243
.03259307
.03635593
.04029366
60
.02876797
.03235340
.03613296
.04008862
61
.02852278
.03212294
.03591908
.03989249
62
.02828643
.03190126
.03571385
.03970480
63
.02805848
.03168790
.03551682
.03952513
64
.02783S55
.03148249
.03532760
.03935308
65
,02762624
.03123463
.03514581
.03918826
66
.02742122
.03109398
.03497110
.03903031
67
.02722316
.03091021
.03480313
.03887892
68
-02703173
.03073300
.03464159
.03873375
69
.02684665
.03056206
.03448618
.03859453
70
.02666765
.03039712
.03433663
.03846095
71
.02649446
.03023790
.03419266
.03833277
71
.02632683
.03008417
.03405404
.03820973
73
.02616454
.02993568
.03392053
.03809160
74
.026007.^6
.02979222
.03379191
.03797816
75
.0i5S5508
.02965358
.03366796
.03786919
76
.02570751
.02951956
.03354849
.03776450
77
.02556-147
.02938997
.03343)31
.03766390
78
.02542576
.02926463
.03332224
.03756721
79
.02.V29123
.02914338
.03321510
.03747426
80
.02516071
.02902605
.03311175
.03738489
81
.02:>03405
.02891248
.03301201
.03729894
82
.02491110
.028802r>4
.03-291576
.03721628
S3
.02479173
.02869608
.03282284
.03713676
84
.024r,75Sl
.02859298
.03273313
.03706025
85
.02436321
.02849310
.032(i4650
.03698662
86
.02445331
.02839633
.03256284
.03691576
87
.02434750
.02830255
.03248202
.036S4756
88
.02424416
.02821165
.03240393
.03678190
89
.02414370
.023123:>3
.03232848
.03671868
90
.02404G02
.02803809
.03225556
.03665781
91
.02395101
.02795523
.03218508
.03659919
92
.02a858:>9
.02787486
.03211695
.03654273
93
.02376868
.02779690
.03205107
.036-J8834
94
.02368118
.02772126
.03198737
.03643594
95
.02359602
.02764786
.03192577
.03638546
96
.02351313
.02767662
.03180619
.03633682
97
.02343242
.02750747
.03180856
.03628995
98
.02335383
.02744034
.03175281
.03624478
99
.02327730
.02737517
.03169886
.03620124
100
.02320274
.02731188
.03164667
.03615927
Perp.
.02000000
.02500000
.03000000
.03500000
TABLE VII. 101
The Annuity which £1 will purchase for any number of Years.
Yews.
4 per cent
ii per cent
5 per cent.
6 per cent
51
.04625885
.05033232
.05452867
.06323880
62
.04598212
.0JD07679
.05429449
.06304617
53
.04571915
.04983469
.05407334
.06236551
54
.04546910
.04960519
.05386438
.06269602
55
.04523124
.04938754
.05366686
.06253696
56
.04500487
.04918105
.05348010
.06238765
57
,04478932
.04898506
.05330343
.06224744
58
.04458401
.04879897
.05313626
.06211573
59
.04438836
.04862221
.05297802
.06199200
60
.04420185
.04845426
.05282818
.06187572
61
.04402398
.04829462
.05268627
.06176642
62
.04385430
.04814284
.05255183
.06166366
63
.04369237
.04799848
.05242442
.06156703
64
.0435^7S0
.04786115
.05230365
.06147615
65
.04339019
.04773047
.05218915
.06139066
66
.04324921
.04760608
.05208057
,06131022
67
.04311451
.04748765
.05197757
.06123154
68
.04298578
.04737487
.05187986
.06116330
69
.04286272
.04726745
.05178715
.06109625
70
.04274506
.04716311
.05169915
.06103313
71
•04263253
.04706760
.05161563
.06097370
72
.04252489
.04697465
.05153633
.06091774
73
.04242190
.04688605
.05146103
.06086505
74
.04232334
.04680159
.05138953
.06081542
75
.04222900
.04672104
.05132161
.06076867
76
.04213868
.04664422
.05123709
.06072463
77
.04205221
.04657094
.05119580
.06068315
78
.04196939
.04650104
.05113757
.06064407
79
.04189007
.04643434
,05108222
.06060724
80
.04181408
.04637069
.05102963
.06057234
81
.04174127
.04630995
.05097963
.06053984
82
.04167150
.04625197
.05093211
.06050903
83
.04160463
.04619662
.05088694
.06047998
84
.04154054
.04614379
.05084399
.06045261
85
.04147909
.04609334
.05080316
.06042681
86
.04142018
.04604516
.05076433
.06040249
87
.04136370
.04599915
.05072740
.06037956
88
.04130953
.04595522
.05069228
.06035795
89
.04125758
.04591325
.05U658S8
.06033757
90
.04120775
.04587316
.05062711
.06031836
91
.04115995
.04583486
.05059689
.06030025
92
.04111410
.04579827
.05056815
.06028318
93
.04107010
.04576331
.05054080
.06026708
94
.04102789
.04572991
.05051478
.06025190
95
.04098738
.04569799
.05049003
.06023753
96
.04094350
.04566749
.05046648
.06022406
97
.04091119
.04563834
.05044407
.0601' 11 35
98
.04087538
.04561048
.05042274
.06019935
99
.04084100
.04558385
.05040245
.06018803
100
.04080800
.04555339
.05038314
.06017736
Perp.
.04000000
.04500000
.05000000
.ooooooomc
lOa TABLB VII.
Tha Aamutj which £1 will purdufe for any number of Tean,
Ycuri.
7 per cent.
8 per cent
9 per cent.
10 per cent
51
.07229365
.08161116
.09112430
.10078046
5!2
.07213901
.08148959
.09103041
.10070900
53
.07199509
.08137735
.09094443
.10064413
54
.07186110
.08127370
.09086570
.10058523
55
.07173633
.08117796
.09079359
.10053175
56
•07162011
.08108952
.09072754
.10048317
57
.07151183
.08100780
,09066702
.10043906
5S
.07141093
.08093226
.09061157
.10039898
59
.07131689
.08086247
.09056076
.10036258
60
.07122923
.08079795
.09051419
.10032951
61
.07114749
.08073830
•09047151
.10029946
(i2
.07107127
.08068314
•09043240
.10027217
63
.07100019
.0S063214
.09039654
.10024736
64
.07093338
.08058497
.09036366
.10022463
65
.07087203
. .08054135
.09033352
.10020434
66
.07081431
.08050100
.09030589
.10018573
67
.07076046
,08046367
.09028056
,10016882
63
.07071021
.08042914
.09025732
.10015345
69
.07066330
.08039719
.09023602
.10013948
70
.07061953
.08036764
.09021649
.10012676
71
.07057866
.08034029
.09019857
.10011524
7i
.07054051
.08031498
.09018214
.10010476
n
.07050490
.08029156
.09016708
.10009522
74
.07047164
.08026990
.09015326
.10008656
7^
,07044060
.03024984
.09014056
.1OO078C8
76
.07041160
.08023128
.09012896
.10007153
71
.07038453
,08021410
.09011821
.10006502
78
.07035924
.08019820
.09010852
.10005911
79
.O7033.i63
.08018349
.09009955
.10005373
60
.07031357
.08016987
.09009132
.10004884
61
.07029297
.08015726
.09008377
.10004440
82
.07027373
.08014559
.09007665
.10004036
83
.07025576
.08013479
.09007050
.10003669
84
.07023897
.0!i012479
.09006467
•10003336
65
.07022329
.03011553
.09005933
.10003032
66
.07020863
.08010696
.09005443
.10002756
87
.07019495
.08009903
.09004993
.10002506
68
.07018216
.08009168
.09004581
.10002276
89
.07017021
.08008489
.09004202
.10002071
90
.07015905
.08007859
.09003855
.10001883
91
.07014863
• .08007277
.09003537
.10001711
92
.07013888
.08006737
.09003245
.10001556
93
.07012978
.08006238
.09002977
.10001414
94
.07012128
.08005775
.09002731
.10001286
95
.07011333
.08005347
.09002505
.10001169
96
.07010J90
.08004951
.09002298
.10001063
97
.07009897
.08004584
.09002109
.10000966
96
.07009248
.08004244
.09001934
.10000878
99
.07008643
.08003930
.09001775
.10000798
100
.07008076
.08003638
.09001628
.10000726
Perp.
•07000000
.08000000
.09000000 ,ed
byVDlli!i^<t
TABLE VIU. 103
LtgmrMm of the Fkofeat Value of £U doe ai tbe end of any nttubev of Yean.
Yem.
' Spereent
2*pwoent.
8 p«r cent
/
8i per oeat '
1
T. 9913998
1.9892761
r.9871628
T. 9850596
2
.9827997
.9785523
.9743256
. .9701193
3
.9741995
.9678284
.9614884
. .9551789
4
.9655993
.9571045
.9486512
.9402386
5
.9569991
. .9463806
. .9358139
.9252983
6
.9483990
.9356568
.9229767
.9103579
7
.9397988
•9249329
. .9101395
.8954176
8
.9311986
.9142090
.8973023
. .8804772
9
. .9225985
. .9034852
.8844650
.8655369
10
. .9189983
.8927613
. .8716278
. .8505965
11
.9053981
. .8820374
. .8587906
. .8356562
12
.8967979
. .8713136
.8459534
.8207158
13
. .8881978
. .8605897
. .8331161
.8057755
14
. .8795976
.8498658
.8202789
.7908351
15
. .8709974
.8391420
. .8074417
.7758948
16
.8623973
. .8284181
.7946045
.7609544
17
.8537971
.8176942
.7817672
.7460141
18
.8451969
. .8069704
. .7689300
.7310737
19
.8365968
. .7962465
.7560928
.7161334
20
. .8279966
. .7855227
. .7432556
.7011930
21
.8193964
.7747988
.7304183
.6862527
22
.8107962
.7640749
.7175811
.6713123
23
.8021961
.7533H1
.7047439
.6563720
24
.7935959
.7426272
.6919067
.6414316
25
.7849957
. .7319033
.6790694
.6264913
26
.7763955
.7211795
.6662322
.6115509
27
.7677954
.7104556
.6533950
.5966106
28
.7591952
.6997317
.6405578
.5816702
29
.7505950
.6890079
.6277205
.5667299
30
. .7419949
.6782840
.6148833
.5517895
31
.7333947
.6675601
.6020461
.5368492
32
.7247945
.6568363
.5892089
.5219088
33
.7161944
.6461124
. .5763716
.5069685
34
.7075942
.6353885
.5635344
.4920-281
35
•6989940
. .6246647
.5506972
.4770878
36
. .6903938
.6139408
.5378600
. .4621474
37
.6817937
.6032169
.5250227
.4472071
38
.6731935
.5924931
. .5121855
.4322667
39
.6645933
.5817692
.4993483
.4173264
40
.6559932
. .5710454
.4865111
, .4U23860
41
.6473930
.5603215
.4736738
.3874457
42
.6387928
. .5495976
.4608366
.3725053
43
.6301927
. .5388738
.4479994
.3575650
44
.6215925
. .5281489
.4351622
.3426246
45
. .6129923
,5174260
.4223249
.3276843
46
.6043921
.5067021
.4094877
.312743$
47
. .5957920
.4959783
.3966505
. .2978035
48
.5871918
.4852544
.3838133
. .2828632
49
.5785916
.4745305
.3709760
. .2679229
iO
.5699914
. .4638067.
.3581388.
.2529825
sdbvVjUUvlC
Digitiz
104 TABLE VIII.
Lojm-iikm of the Ptetent Value of £1, diie at the end of any nmnbor of Yean.
Yean.
• 4 per crnt
i\ ptr cent.
6 per eent'
Spcroent.
1
T.9829667
T.9808837
1.9788107
T.9746941
2
.9659333
.9617674
.9576-214
.9493882
3
.9489000
.9426511
.9364321
.9240824
4
.9318666
•9235348
.9152428
.8987765
5
.9148333
.9044186
.8940535
.8734706
6
.8978000
.8853022
.8728642
.8481643
7
.8807666
.8661859
.8516749
.8228589
8
.8637333
.8470696
.8304856
.7975530
9
.8467000
,8279533
.8092963
.7722472
10
.8296667
.8088371
.7881070
.7469413
11
.8126333
.7897208
.7669177
.7216354
12
.7956000
.7706045
.7457284
.6963296
13
.7785667
.7514882
.7245391
.6710237
14
.7615333
.7323719
.7033498
.6457178
15
.7445000
,7132556
•6821605
.6204120
16
.7274667
.6941393
.6609712
.5951061
17
.7104333
.6750230
.6397819
.5698002
18
.6934000
.6559067
.6185926
.5444943
19
.6763667
.6367904
•5974033
.5191885
20
.6593333
.6176742.
.5762140
.4938826
21
.6422999
.5985579
.5559247
-.4685767
22
.6252666
.5794416
.5338354
.4432709
23
.6082332
.5603253
.5126461
.4179650
24
.5911999
.5412090
.4914558
.3926591
25
.5741666
.5220927
.4702675
.3673533
26
.5571333
.5029764
.4490782
.3420474
27
.5401000
.4838601
.4278889
.3167415
28
.5230667
.4647438
.4066996
.2914357
29
.5060333
.4456275
•38.55103
.2661298
30
.4890000
.4265113
.3643210
.2408239
31
.4719667
.4073950
.3431317
.2155181
32
.4549333
.3882787
.3219424
.1902122
33
.4379000
.3691624
.3007531
.1649063
34
.4208667
.3500461
.2795638
.1396005
36
.4038333
.3309298'
.2583745
.1142946
36
.3868000
.3118135
.2371852
.0889887
37
.3697667
.2926972
.2159959
.0636829
38
.3527333
.2735809
.1948066
.0383770
39
.3357000
.2544646
.1736173
.0130711
40
.3186667
.2353484
.1524280
2.9ii77653
41
.3016133
.2162321
.1312387
.9624594
42
.2846000
.1971158
•1100495
.9371535
43
.267.1667
.1779995
.0888602
.9118477
44
.2505333
.1588832 •
•067C709
.8S65418
45
.2335000
.1397669
.0464816
.8612359
46
.2164607
.1206506
.0252921
.8359301
47
.1994333
•1015343
.0041030
.8106242
4H
.1824000
.0824180
2.9829137
.7853183
49
.1653667
.0633017
.9617244
.7600125
50
.1483333
.0441855
.9405352
.7347066
i*ABLE VUI. 105
Logarithm of tbe Present Value of £1 , due at the end of any mimbcr of Tean.
Yf^im.
7 p«r"cent.
8 per cent.
9 per cent
10 per cent.
1
T.9706162
T. 9665762
1.9625735
T. 9586073
2
.9412324
.9331524
.9251470
.9172146
3
.9118487
.8997287
.8877205
.8758219
4
.8824649
.8663049
.8502940
.8344293
5
.8530811
.8328812
.8128675
.7930366
6
.8236973
.7994574
.7754410
.7516439
7
.7943135
.7660337
.7380145
.7102512
8
.7649298
.7326099
.7005880
.6688585
9
.7355460
.6991862
.6631615
.6274658
10
.7061622
.6657624
.6257350
.5860731
n
.6767784
.6323387
.5883085
.5446805
12
.6473946
.5989149
.5508820
.5032878
13
.6180109
.5^54912
.5134555
.4618951
14
.5886271
.5320674
.4760290
.4*205024
15
.5592433
.4986437
.4386025
.3791097
16
.5298595
.4652199
.4011760
.3377170
17
.5004757
.4317961
.3637495
.2963244
18
.4710920
.3983724
.3263230
.2549317
19
.4417082
.3649486
.2888965
.2135390
20
.4123244
.3315249
.2514700
.1721463
21
.3829406
.2981011
.2140435
,1307536
22
.3535568
.2646774
, .1766170
.0893609
23
.3241731
.2312536
.1391905
.0479682
24
.2947893
.1978299
.1017641
.0065756
25
.2654055
.1644061
.06-13376
2.9651829
26
.2360217
.1309824
_. 02691 11
.9237902
27
.2066379
.097:586
2.9894846
.8823975
23
.1772542
.0641349
.95'20581
.8410048
29
.1478704
_. 0307111
.9H6316
.7996121
30
.1184866
2.9972874
.8772051
.7582194
31
.0891029
.9638636
.8397786
.7168268
32
.0597190
.9304399
.8023521
.6754341
33
.0303353
.8970161
.7649256
.6340414
34
,.0009515
.8635923
.7274991
.5926487
35
2.9715677
.8301685
.6900726
.5512560
36
.9421839
.7967448
.6526461
.5098633
37
.9128001
.7633210
.6152196
.4684706
38
.8834164
.7298973
.5777931
.4270780
39
.8540326
.6964735
.5403666
.3856853
40
.8246488
.6630498
.5029401
.3442926
41
•7952650
.6296260
.4655136
.3028999
42
.7658812
.5962023
.4280871
.2615072
43
.7364975
.5627785
.3906606
.2201145
44
.7071137
.52935J8
.3532311
.1787219
45
.6777299
.4953310
.3158076
.1373292
46
.6483461
.4625073
.2783811
.0959365
47
.6189623
.4290835
.2409516
.0545438
48
.5895786
.3956598
.2035281
.0131511
49
.5601948
.3622360
.1661016
"3. 9717534
60
.5308110
.3288122
.1286751
.9303657,
dbyVjUU^lC
DigitiZ'
106 TABLE VHL
L^ariikm of Um Pftient VaIim of £1, tlue at tli0 ffid of maf nonber of Yean^
Yean.
S per cent
2i per cent.
3 per cent
S^pereeat.
61
T. 6613912
' T.4530828
r.3453016
r.2360422
62
.5527910
.4423590
.3324644
.2231018
53
.5441909
.4316351
.3196271
.2081615
54
.5355907
.4209112
.3067899
.1932211
5S
.5269905
.4101874
.2939527
.1782808
56
.5183904
.3994635
.2811155
.1633404
57
.5097902
.3887396
.2682782
.1484001
5^
.5011900
.3780158
.2564410
.1334697
59
.4925898
.3672919
.2426038
.1185194
60
.4339897
.356)681
.2297666
.1035790
61
.475389:>
.3458442
.2169293
.08863^7
62
.4667893
.3351J03
.2040921
.0736963
63
.4581892
.324396r>
.1912549
.0687580
64
.4495890
.3136726
.1784177
.0438176
65
.4409d88
.3029487
.1655804
.0288773
66
.4323887
.2922249
.1527432
_. 0139369
67
.423788r>
.2815010
.1399060
2.9989966
68
.4151883
.2707771
.1270688
.9840562
69
.4065882
.2600533
,1142315
.9691169
70
.3979880
.2493294 .
.1013943
.9541756
71
.3893878
.2386055
.0885571
.9392362
72
.3807876
.2278817
.0757199
.9242948
73
.3721874
.2171578
.0628826
.9093545
74
.3635872
.2064339
.0500454
.8944141
75
.3549870
.1957101
.0372082
•8794738
76
.3463869
.1849862
.0243710
77
.3377867
.1742623
.0115337
.8495931
7S
.3291865
.1635385
2.9986965
.8346527
79
.3205S64
.1528146
.9858593
.8197124
80
.3119363
.1420908
.9730221
.8047720
81
.3033861
.1313669
.9601848
.789831?
82
.2947859
.1206430
.9473476
.7748913
83
.2861858
.1099192
.9345104
.7699610
84
.2775856
.0991953
.9216732
.7450106
85
.2689854
. .0884714
.9088359
.7300703
86
.2603853
.0777476
.8959987
.7151299
87
.2517851
.0670237
.8831615
.7001896
88
.2431850
.0562998
.8703243
.6852492
89
.2345848
.0455760
.8574870
.6703089
90
.2259846
.0348521
.8446498
.65.^3685
91
.2173644
.0241282
.8318126
.6404282
92
.2087843
,0134044
.8189754
.6254878
93
.2001841
.0026805
.8061381
.6105475
94
.1915839
2.9919.)67
.7933009
.5956071
95
.1829838
.9812328
.7804637
.5806668
96
.1743836
.970)090
.7676265
.5557265
97
.1657834
.9:)9785l
.7547892
.5507861
98
.1571832
.9490612
.7419520
.5358458
99
.1485^31
.9383374
.7291148
.5209064
100
. 1399829
.9276135
.7162775
.5059660
o
TABU Vm. lOf
of Um PftMiit V«liM«f £1, do* M tlu Md •£ any numbtt of Te«i«
T«m
4-pereenL
4ip«rceBt
6 per cent
6 per cent
51
T. 1313000
T.0250692
2.9193459
2.7094007
62
.1142667
_. 0059529
.8981566
.6840949
63
.0972333
2.9868366
.8769673
.6587890
54
.0802000
.9677203
.8567780
.6381831
66
•0681667
.9486040
•8345887
.6081773
56
.0461333
.9294877
.8133994
.5828714
57
.0291000
.9103714
.7922101
.5575655
58
.0120667
.8912551
.7710208
.5322597
59
"2.9960333
.8721388
.7493315
.5069538
60
.9780000
.8530226
.7286422
.4816479
61
.9609667
.8339063
.7074529
.4563421
62
.9489333
.8147900
.6862636
.4310362
63
.9269000
.7956737
.6650743
.4057303
64
.909S667
.7765574
.6438850
.3804245
-65
.8928333
.7574411
.6226957
.3551186
66
.8758000
.7383248
•6015064
.3298127
67
.8587667
.7192085
.5803171
.3045069
68
.8417333
.7000922
.5591278
.2792010
69
.8247000
.6809759
.5379385
.2538951
70
•8076667
.6618596
.5167492
.2285893
71
.7906333
.6427433
.4955599
.2032834
72
.7786000
.6236271
.4743706
.1779775
73
.7565667
.6045108
.4531813
.1526717
74
.7395333
.5853945 '
.4319920
.1273658
75
. .7225000
.5662782
.4108027
.1020599
76
.7054667
.5471619
.3896134
.0767541
77
.6884333
.5280456
.3684241
.0514482
78
.6714000
.5089293
.3472348
.0261423
79
.6543667
•4898130
.3260455
..0008365
80
.6373333
.4706968
.3048562
3.9755306
61
.6203000
.4515805
.2836669
.9502247
82
.6032667
.4324642
.2624776
.9249189
83
.5862333
.4133479
.2412883
.8996130
84
.5692000
.3942316
.2200990
.8743071
65
.5521667
.3751153
.1989097
.8490013
86
.5351333
.3559990
.1777204
.8236954
87
.5161000
.3368827
.1565311
.7983895
88
.5010667
.3177664
.1353418
.7730837
89
.4840333
.2986501
.1141525
.7477778
90
.4670000 .
.2795339
.0929632
.7224719
01
.4499667
.2604176
.0717739
.6971661
92
.4329333
.2413013
.0505846
.6718602
93
.4159000
.2221850
.0293953
.6465543
94
.3988667
.2030687
.0082060
.6212486
95
.3818333
. 1839524
3.9870167
.5959426
96
.3648000
.1649361
.9658274
.5706367
97
.3477667
.1457198
.9446381
.5453309
98
.3307333
.1266035
.9234488
.5200250
99
.3137000
.1074872
.9022595
.4947191
100
.2966667
.0883710
.8810702
.4694133
^^H Kwl. -.1 II lU 1
Digitized by ^^UUVJ
le
106 TABLK VIII.
Logarithm of the PreMnt Vftloe of £1, due at tiM erd of macf number of Teen.
Yrtn.
7|«'ce»L
8 per eent
9p«rcmt.
lOprremt
51
2.5014272
2.2953884
2.0912486
3.8889731
52
.4720434
.2619646
.0538221
.8475804
53
.4426)97
.2285409
.0163956
.8061877
54
.4132759
.1951171
3.9780691
.7647950
55
.3838921
•1616934
.9415426
.7234023
56
.3>4:>083
.1282696
.9041161
.6820096
57
.3251245
.0948459
.8666896
.6406169
58
.2957408
.0614221
.8292631
.5992243
59
.2663570
.0279984
.7918366
.557&316
60
.2369732
3.9945746
.7544101
.5164389
61
.2075894
.9611509
.7169836
.4750462
62
.1782057
.9277271
.6795571
.4336535
63
.148^219
.8943033
.6421306
.3922608
64
.1194381
.8608796
.6047041
.3508681
65
.0900543
.8274558
.5672776
.3094755
66
.0606705
.7940321
.5298511
.2680828
67
.0312868
.7606083
.4924246
.2266901
. 68
_. 001 9030
.7271846
.4549981
.1852974
69
3.9725192
.6937608
.4175716
.1439047
70
.9431354
.6603371
.3801451
.1025120
71
.9137516
.6269133
.3427186
.0611194
72
.8843679
.5934896
.3052922
_. 0197267
73
' .85'I9841
.5600658 '
.2678657
4.9783340
74
.8256003
.5266421
.2304392
.9369413
75
.7962105
.4932183
.1930127
.8955486
76
.7668327
.4597946
.1555862
.8541559
77
.7374490
.4263708
.1181597
.8127632
76
.7080652
.3929470
.0807332
.7713706
79
.6786814
.3595232
.0433067
.7299779
80
.6492976
.3*260995
.0058802
.6885852
81
.6199138
.2926757
4.9684537
.6471925
82
.5905301
.2592520
.9310272
.6057998
83
.5611463
.2258282
.8936007
.,5644071
84
.5317625
.1924045
.8561742
.5230144
85
.5023787
.1589807
.8187477
.4816218
86
.4729949
.1255570
.7813212
.4402291
87
.4436112
.0921332
.7438947
.3983364
88
.4142274
.0587095
.7064682
.3574437
89
.3848436
^.0252857
.6690417
.3160510
90
.355J59S
4.9918G20
.6316152
.2746583
91
.3260761
.9583382
.5941887
.2332656
92
.2966923
.9249144
.5567622
.1918730
93
.2673085
.J^914907
.5193357
.1504803
94
.2379247
.8580669
.4819092
. 1090876
95
.2085409
.8246432
.4444827
.0676949
96
.1791572
.7912194
.40705^2
..0263022
97
.1497734
.7577957
.3696297
5.9849095
98
.1203S96
.7243719
.3322032
.9435169
99
.0910058
.6909482
.2947767
.9021242
100
.0616221
.6575244
.2573502
.8607315
PART ir.
LIFE ANNUITIES.
102. A society consists of 100 persons, 20 of whom are to go out by
lot every year; each member, at the commencement, is to contribute an
equal sum to form a fund for the payment of «£l at the end of every year
to each who remains ; what is the amount to be contributed by each
when the interest of money is 4 per cent ?
At the end of the first year there will be 80 members, each of whom
is to receive £l ; at the end of the second year the number left will be
60, at the end of the third year 40, at the end of the fourth 20, and at
the end of the fifth there will be none left ; by Art. 33,
60 Xl.04-'=60x. 924556=55. 41336 ditto 2nd ditto,
40xl.04-»=:40x.888996=i35. 55984 ditto 3rd ditto,
20 X1>04~*=20X. 854804= 17. 09608 ditto 4th ditto,
their sum =185.05232 = the total amount to be con-
tributed to form the requisite fund, which, divided by 100 (the number
of contributors), gives 1.850 = £l 11 0, the sum to be contributed
by each.
103. In the Carlisle Rate of Mortelity (Table 1), of 10,000 persons
bom, 8461 survive one year, T779 survive 2 years, 7274 survive 3 years,
and so on till they all become extinct. If, when the interest of money
is 3 per cent, it were required to provide at the time of birth £l for each
of the 10,000 who survive one year, it appears that £8461 would be
paid amongst them at the end of a year, the present value of which,
8461 X 1.03~*, is the sum which will provide for the payment of £l
1.. 1. ^. .J J !_ ,^«^^ . 8461 X 1.03"'
to each survivor, which, divided by 10,000, gives TT^n
the sum to be contributed on behalf of each ; if £l is to be provided at
the time of birth for each child who survives 2 years, 7779 x 1 .03~" is
the sum to be set apart for the payment of the 7779 who survive that
7779 X 1 . 03"* *
period, and ,-^ ' is the sum to be contributed on behalf
of each. ^ , ,
Digitized by
Google
no LIFE ANNUITIES.
At the age of [14, the numher who survive is 6335, of whom 6047
attain the age of 21 : the sum which must he paid at the age of 14, to
provide £l to each of these individuals on attaining the age of 21, is
6047 X 1«03'^ and the sum to be contributed on behalf of each is
6047 X 1.03-^
6335
This sum is less than 1.03^^, which any individual would have
paid to secure an absolute right to ^^1 at the end of 7 years: the
di£ference arises from there being some chance of (he individual not
surviving the term which would entitle him to the sum ; and it is but
equitable that he should pay that fraction only of the present value which
expresses the chance of his receiving it. In the present case of 6335
persons living at the age of 14, only 6047 reach the age of 21, and, as we
may suppose every individual has the same chance of being one of these
survivors, and 6047 is the number of chances divided amongst 6335
individuals, the chance of each individual is g^rr. (Probebility,
Art. 4.)
104. The dijQference between 6335 and 6041 is 288, the number who
die between the ages of 14 and 21 yean, out of 6335 persons; and, as
each has the same chance of being one of the 288, the chance at the
age of 14 of an individual dying before he attains the age of 21 is
288
6335*
If we make r* == present value of .£1 due at the end of n years,
Pa.. => probability of a life aged m living n years,
do. of the joint existence of any num-
PCm.*! iMg »«£.)*» *— '
her of lives aged respectively m, mi,
^n &c., years, continuing n years,
do. of the joint existence of the last
(M,iii2 . m^ , Ac.)^ — \y survivors,
/m = number living at the age m according to the Tables,
the probability of a life aged irt living n years is
p =*a=!
Rule, The probability of an individual surviving any number of
years is found by dividing the number living in the Tables at the ad-
vanced age, by the number living at the present age.
Example. What is the probability of a male aged 36 completing the
age of 53, according to the rate of mortality at Chester ? (Probability,
Table 2.)
n = 53 - 36 = 17
/« 3396 ■ ^
^ Digitized by VjOOQ iC
Lira ANNUITIES. ill
105. The present ralue of a sum («) to be received at the end of any
number of years (n), in the event of an individual aged m surviving that
term, is found by multiplying the present value of that sum receivable
at the end of the given term by the probability of the individual surviving
that term.
Example, A father wishes to provide for his daughter, aged 14, the
sum of ,6850 on her attaining the age of 21 : what sura should he pa
to secure it, supposing the interest of money 3 per cent, and the rate of
mortality the same as at Carlisle? (Table 1.)
r* = 1 .03-^ l^ = /„ = 6335 I,, =r 6041 5 = 850
Table4, Pa^tI.;
1.03-'= .81309151
058 a: # inverted
650413208
40654576
691.127184 by logarithms,
7406=/t|tp^erted log 1 .03-^= 1 .9101395
4146166104 log J =2.9294189
21645111 log^« =3.1815400
4831894 log /u = 4.1982534
A^=:6335)4119249.109(659.108 2.8193518 £659.708
38010 =-£659 14 2
31824
31615
61499
51015
44847
44345|
50209
106. If the money be receivable in the event of two persons both
amriving the term, the present value of the sum due at the expiration of
the term must be multiplied by the two fractions which express the
probability of each surviving the term separately. (Probability, Art. 15.)
In the preceding example, if the receipt of the money at the end o
the seven years depended not only on a life aged 14^ surviving that term,
but also on another aged 16 surviving the same period, the value would
evidently be diminished ; and the result obtained on the suppodtion of
the receipt of the money depending on the happening of the first event
only, must be multiplied by the fraction which expresses the chance of
the happening of the other event.
Digitized by VjVJiJ
gle
112 LIFE ANNUITIES.
«'PaM..,=^. 'j.«'=|gx^x850x .81309151 =628.308
6041
(by logarithms) log^— ^X850x . 81309151 =2. 81 93518 by u-ex.«pi.
® log /;,=: J. 7154648
--log A, = 4.2033563
2. 7981729 £628.308=
^628 6 2
107. Whatever may be the number of UveS| ifthe receipt of the money
depend on aU of them surviving a given period, the present value of the
sum must be multiplied by the continued product of the fractions which
express the chance of each surviving separately.
^ P(m,m^,m^,^Lc),n = ^T* . y" • — 7 .—7 , &C.
108. As certainty is expressed by unity (Prob. Art. 6), the pro-
bability of a life dying before the end of a given time is found by
subtracting from unity the probability of the life surviving that time, it
being evident that one or other of the events must happen.
» The same rule is obtained by dividing the number of deaths that take
place in the given time by the iiumber living at the present age.
_^_i-__i-p^.
109. If there be two or more lives, the probability of their joint
existence failing in n years is
11 I
1 -"P(«ii.«l.m,,Ac.).» = 1 r~'~/ '"7 * *^*
110. The probability of any number of lives all dying in a given term
is obtained by finding the product of the chances of each separate indi-
vidual dying in that term.
If we call the respective ages of the lives m^ mi, m^ &c., then
&c. (Art. 107), is the chance that the lives aged m, mi, fii<, &c., will all
die in n years.
111. Since it is certain that the lives will either all fail, or that one or
more will survive the term, the probability that at the end of the term
they will not all have died, that is, that one of them at least will
be in existence, is
^ Digitized by VjOOQ IC
LIFE ANNUITIES. 113
wben there are two UveSy aged m and mi yean, the expresaion becomes
pi ...
when there are three lives, aged m, «t|, ^, it becomes
(M, «|, Ma),
:. =1-0 -y-..) (i-p...-.)a-p-...) =
Pm»+jP«i,,i,+P,«,.«—P(«,.«j ),»—/? <«,iij)m— PCmj.in^ ),•+?(«, «i.«,)>«
phesknt values of life a^jnuities,
112. To find the present value of an annuity payable at the end of
every year during the existence of a single life.
Let the annuity be ^^1*, and m the age of the individual during whose
life it is to continue : then the present value of the first year's payment
of the annuity is found by multiplying the present value of .£1 due at
the end of one year by the chance of the life living one y^ar (Art. 103),
the present value of the second payment by multiplying the present value
of £l due at the end of two years by the chance of the life living two
years, and finding in the same manner the present value of each year's
payment to the extremity of life ; the sum is the present value of the
annuity.
Let
m^,m^i
*<-).l
Until".
,Ac.).
{denote the present value of an annuity of ^1
during a life aged m years,
r the present value of an annuity of ^1 during
< the joint existence of the lives aged m, mj, ntf
i &c., years.
present value of an annuity of £l until the
failure of the joint existence of the last v sur-
vivors of lives aged respectively m, m^, m^ &c.,
years.
{present value of an annuity of £l for the next
n years, depending on the existence of a life
aged m years,
f present value of an annuity of £1 for n years,
< depending on the joint existence of the lives
i aged m, mi, nit, &c., years.
* The fonmila in all cases are given on the supposition that the annuity it £1 ;
from which the pieient value of an annuity of any other amount may be found by
multiplying the present value of £1 per annum by the yearly income of which the
Talue is required. t
Digitized by^UUS^lC
(■m»4 »wj»*«0
'(•">1,.
i.*«)i,
114 LIPS ANNUITIES.
present value of an annuity of £l for the tiext
71 years, depending on the joint existence of
the last t; survivorB of the lives aged m, mi, ^
&c., years.
( present value of an annuity of £ 1, to be entered
j upon at the expiration of n years, and then
^ to continue during the existeiice of a life now
aged m years,
present value of an annuity of .Cl, to be entered
upon at the expiration of n years, and then
to continue during the joint existence of the
lives now aged m, m^, m^, &c., years.
' present value of an annuity of £l, to be entered
upon at the expiration of 7i years, and then
to continue until the failure of the joint exist-
ence of the last v survivors of the lives aged
m, fTti, fi7|y &c., years.
if we call z the difference between the age m and the oldest age com-
pleted by any life according to the Table,
. a« = pm^i-r + pn^^.t* + p«,,.r* + p^^.r* + + ^^,V
writing for Pm^u Pnhwt &c., their values -y^*, -j^", &c, (Art. 104.)
(m, Ml, iii«.^Ac.)i,
(1)
If the numerator and denominator of this fraction be multiplied by
r"* (which will not affect the value of the expression), the formula
becomes
0* =
U. ^^' +/,.^. r"^* + U^ y"^' + L^ r^^'+... .U. r"^'
/..r^
(2)
Rule. Multiply the number of living at each year of age by the
present value of .£1 due at the end of the same number of years as the
age ; then the present value of the annuity at any age is found by dividing
the sum of the products at all the ages above that on which the annuity
depends by the product at that age.
113. The advantage of the last form of the fraction over the other may
be seen by taking as examples the separate ages of 96 and 95 in the
Carlisle Table of Mortality.
Ow =■
ffM =
Inf^ + l^ 7^ + Lr"" + l^r'' + Ur'^ +...,+ Ur''
Digitized by LjOOQ IC
LIFB ANNlrtTIBS. 115
On comparing the expressions for these two values, we observe that in
finding the value at the age of 95 every term is introduced which was
employed in finding the value at the age of 96 ; so that it costs very
little more trouhle to find the value at hoth the ages than to find the
value at one of them only ; hut, had the first expression for a^ heeu usedi
the operation employed in finding the value at the age of 96 would not
have afPorded direct assistance in finding the value at the age of 95 ; the
method which has heen adopted has also other important advantages^
the preparatory operations being of great use in abridging the labour of
finding the values of Temporary and Deferred Annuities and Assurances*
The following example, in numbers, of the values of annuities at
4 per cent, by the Carlisle Rate of Mortality (Table 1), will show the
process of forming a table of the values of annuities on single lives.
/j^r»»*:= IX. 01692512= .01692512 _.01692512_
/,„ r»«:= 3x .01760212= .05280636 '***"" .05280636^ ^ ^
N,«= .06913148 _.06973148_
Ur'^= 5X. 01830625= .09153125 **^. 091 53125"^ ''^^^"^
Nioi= .16126213 _.16126273_
l^^ r\«= 7X .01903850= .13326950 ^*''*'^ .133269507" ^'^^^^
N|«>= .29453223 _. 29453223 _
/i«ri«»s= 9x. 01980004= .17820036 ^''"".17820036'^ 1.66282
N«= .47273259 _.47273259_
/« r^a= 11 X. 02059204= .2265124 ^"".2265124 "" ^*^^^^
N„= .6992450 _. 6992450 _ ^
/«, f* =14X .02141572= .2998201 ^ "" .2998201 " 2.33222
N,^= .9990651 _. 9990651 _
/^ 7*f =18x .02227235= .4009028 ^ "" .4009023 "" ^'^^^^^
N«, =1.3999674 _ 1.3999674 _
4. r^ =23X .02316325= . 5327548 ^^ .5327548 ~ ^'^^TIS
N.5 = 1 . 9327222 "^ _1. 9327222 _
U r« =30x. 02408978= .7226934 ^ .7226934 *" ^-^^^^S
1 14. In forming a table of annuities great care must be taken that
the products of the present value of £l and the number of living at each
age are accurately obtained, since an error at any one age will evidently
affect the results at all the younger ages. A good method of guarding
ftgainst inaccuracy is to have the products computed, either by two
different methods or by two different individuals, and the results care-
fully compared: this being done, we find the sum of all the products
above each age, and check them by finding the sums for every five or
ten years, or any other convenient interval ; if they agree we may
assume the intermediate sums to be correct*, and then proceed to the
divisions.
* A balance of errors may possibly exist.
Digitized lyCoOgle
116 LIFB ANNUmEgi
To check the additions in the last example
/,04r^^= .01692512
/,^r'»= .05280636
/j^r^«= .09153125
/ioif^'= .13326950
l,^r'^s= .H820036
.47273259 = sum of the products abore the age of 99|
/m f** = .2265124 agreeing with the result obtained before.
/» f* = .2998201
/^ 1^ = .4009023
/„ »^ = .5327548
1 .9327222 = sum of products above the age of 95, asbefore«
115. Mr. Griffith Davies was the first who computed tables of the
values of annuities on the above plan, some of which he has published
in a tract, in which are given formulae for computing various cases of
Annuities and Assurances on Single Lives.
116. Tables have been inserted at the end to show the application of
some of these formulee, the notation varying but slightly fit>m Mr. Da-
vies's. The number in column D opposite any age is the product obtained
by multiplying the number living opposite that age in Table 1. by tlie
present value of £l due the same number of years as the age ; thus, at
the age qf 30 the number living by Table 1, is 5642, and the present value
of £l due at the end of 30 years is by Table 4, Part I. =: .30831867.
The product of these two numbers =1739.53393, which is the number
in Table 13, under column D, opposite the age of 30. Having found in
this manner the numbers in column D stall ages from birth to the extre-
mity of life, those in column N are found by beginning at the oldest
age, and taking the successive sums of the numbers in column D, as in
Art. 113, the number in column N at any age being the sum of the
numbers in column D at all the ages above the given one. Column M
is formed by multiplying the decrements opposite each age in Table 1
by the present value of £l due the same numbers of years as the age
increased by unity, and taking the successive sums from the extremity
of life, as in the formation of column N from the numbers in column D.
Column S is the sum of the number at any given age, and at all ages
above in column N ; and column R is the sum of all the numbers in
column M at any given age and above.
Dm, N.,, M,., S.,, Rm9 represent the numbers opposite any age m
in the respective columns so marked.
D-i-M N«-i» M«.i, S^_i, R^«i, opposite an age one year younger
than m.
D»+< • N«+i , M«+, , S^^ R,+, , . . t years older than m.
D(w-i5+o N(„.|)+o M(«_i)+/, S(«_,)^, R(««,)^,, t years older than a
life one year younger than m.
Digitized by LjOOQ iC
LIFE ANNUITIES.
117
117. Mr. Davies's formula is an improved modification of that of
Barrett, which first pointed out the principle of making the preparatory
lahour directly available for finding the values of temporary and deferred
annuities, &c. Messrs. Baily and Babbage, at the end of their respec-
tive works, treat on the application of Barrett's formula, which is thus
obtained :
In the expression (1) for a„ in Art. 112, writing for r its value
(1 +t)7', and call x the oldest age in the table, we have
Cm = '
L
which, by multiplying numerator and denominator by (1+0*
becomes
/^,.(l-hO'-^"+^>-i-C^.(l-i-fr-^"+'>+L^.(l-hO^-"^'^+ -f/>-i(l-t-i)+/,
Wi+0'-
which expresses the following rule :
Let the number of living at each year of age be multiplied by the
amount of £i at the end of as many years as are equal to the difference
between the age and the oldest in the table, then the sum of all the
products above any given age divided by the product at the given age
will give the value of an annuity on a life of tl\at age. The following
illustration is from the Carlisle 3 per cent ; the number in column A
opposite to any age being the product at that age, and the number in
column B the sum of the numbers in column A at that age and all
ages above: the value of £l per annum at any age is therefore the
number in column B^ at an age one year older than the given one
divided by the number in column A at the given age.
/,04 Xl.04'=lXl = 1.000000
/i« Xl.04*=3xl.04 = 3.12
/,„ X1.04«=5X 1.0816
4.120000
5.408000
9 • 528000
U X 1 . 04»=: 7X1. 124864s 7.874048
17.402048
/,co X 1 .04*=9 X 1 . 169859^10.528731
27.930779
Age
A
B
104
103
102
101
100
1.000000
3.120000
5.408000
7.874048
10.528731
1.000000
4.120000
9.528000
17.402048
27.930779
Digitized by LjOOQ IC
118
COMMON METHOD OF FORMING TABLES OF ANNUITIES.
118. The following mode of computing tables of annuities was, until
very recently, adopted by most authors on this subject : —
Art. 112. ,,:.W.'-+/-^>-+y+U.»-+&c.
and ff._, = =
\ ' + L ; Lir
(1 + a„) p^^i , iVy from which expression it appears that
the value of an annuity at any age may be found, when the value is
given at the age one year older.
If we* commence at the oldest age in the table, at which the value of
the annuity is 0, and proceed through all the other ages to the time of
birth, a table will be formed of the values of annuities ; the rule expressed
in words is to " increase the value of an annuity at any age by unity,
multiply the sum by the chance of a life one year younger completing
that age, and by the present value of £l due at the end of one year ;
the result is the value of an annuity on a life one year younger than the
given age."
119. As an example, let us fmd the values at 3 per cent by the rate
of mortality among males at Chester, as given in Table 2 of Probability.
«f„ = -f. r (1 + a,„) =:^X .910814 X (1 +0.) = .7443
1 30
flr«. = -/? r (1 + fl„) = ^ X .970874 x 1 .7443 = 1 .3731
ff^ = ^-r (1 +««) =: ^ X. 970874 X 2.3731 = 1.9375
which results are found to agree with the values given in Table 3 (Pro-
bability), computed by the method described in Art. 113.
It is scarcely necessary to state that the mode given in Art. 113
is the more advantageous of the two, not only from the utility of the
preparatory calculation*, but also from its being a more expeditious plan
of obtaining the values, as the trial of a f»w examples by each method
will prove.
Digitized by VjOOQ iC
LIFE ANNUITIES.; 119
To find the Value of an AnnxUiy* ^
"Ruh, Multiply the number of years' purchase found by the tables,
by the yearly sum of which the value is required *.
Example, What is the value of an annuity of .£364 to continue
during the life of a person aged 36, assuming 4 per cent as the interest
of money, and the rate of mortality the same as at Northampton ?
Table 1, 03.= 13.8815
364
555260
' 832890
416445
5052,8660 =-£5052 17 4
A man holds an estate producing «£56 2 6 per annum during the
life of his wife aged 36 ; what is the value thereof, interest being 5 per
cent, and the rate of mortality as at Chester ? (Probability Table 3.)
£56 2 6 = -£56.125
Oae = 13.8345
521.65
691725
83007
1383
277
69
776.461 = ^776 9 3.
120. To find the Annuity which a Sum of Dfoncy will "purchase,
RuU, Divide the sum by the number of years' purchase the annuity
is worth, according to the tables.
Example, What annuity receivable during the life of a female aged
36 may be purchased for £776 9 3 at 5 per cent interest, Chester rate
of mortality ? (Probability Table 3.)
(Prob. Table 3,) o« = 13.8345 £776 9 3 = £776.4625
13.8345)776.4625(56. 125=£56 2 6
691725
.847375
830070
17305
3470
2767
.703
* When the annuiiy is payable half-yearly, add- , and when payable «* timet
m — 1
a-year add —-: — , to the tabular value of the annuity ; in the' present example
(13.8615+.25)X364 is the present value when payable half-yearly, and (I3.881d.
-)-.375)X364 is the present value when payable quarterly. (.Fide Boily & Milne.)
Digitized by ^^UUV IC
120 LIFE ANNUITIES.
121. If money produced no interest, the formula in Art. 112 would
become
_ ,
this expression shows the average number of years that each individual
completes,
122. The number of years expectation of life of an individual whose
prospect of longevity is the same with that of individuals of the same
age, at any particular place where observations of the rate of mortality
have been made, is usually taken as the average number of years
enjoyed by each individual at that place, as shown in the tables.
Let us suppose those who complete their mth year, but die before
completing their (m + l)th year, to die at equal intervals therein, so
that, for every one who dies before the expiration of a half of the year,
some other will survive so much more than the half-year ; each individual
who dies in the year survives therefore upon an average one-half of that
year.
Of /» persons who complete the mth year of their age, t, — 4^+, die
in their (m + l)th year, and ^«+i survive their (m + l)th year;
4-U.
2
the number of years enjoyed by all those who die in the (m+ l)th year,
added to the C+i years enjoyed by those who complete their (m+l)th
year, gives -I^-— ■^+/^i= "* ""^"^ the number of years that will
be enjoyed in the first year by these l^ persons or the survivors.
And in the same manner may be shown that
•«i+l + 'iw+t *m+«+ »iii+8 ••1+8+ 'm+4
, &C.
is the number of years that will be enjoyed in the 2nd, 3rd, 4th9 &c.,
years by these /^ persons or the survivors.
If we continue these values to the oldest age in the table, and sum
them together (making z as before the difference between the age m and
the oldest in the table), we obtain the total number of years enjoyed by
these l^ persons until they all cease to exist : viz.,
Im 4" Iw+l j^ *iii+l "T lm+% j^ ^w-H "4" lm+% , 'm+» "f lm-i-4 _i
2 ■*" 2 ^ 2 + 2 +
2 "T" 2 "•"*'* + '-.+t +*«+• + '-i+4
+ Im+z^i + L+M ; this expression divided by /^, the number of indivi-
duals amongst whom this quantity of existence is divided, gives the
share of each, or in other words, the expectation of life of an individual
aged m, which will be expressed by the symbol e^ i
-Digitized by VjOOQIC
METHOD OF FORMING TABLB8 OF EXPECTATION OF LIFE. 121
_ 1 , //,^.f ^
iw-t-1 4* ^w-H "I" »ii»-H "^
•4-/m-fi-l 4-/,»4-/
)•
hence the following rule for finding the expectation of life :
** Divide the sum of the number who complete each age above the
given one, by the number living at the given age, and to the quotient
add half unity."
123. In forming a table of expectations for every age, we b^n with
the living at the oldest, adding thereto the living at the oldest but one,
then to this sum the living at the oldest but two, and to this sum again
the living at the oldest age but three; proceeding in this manner with
each age throughout the table, we have the requisite dividends and
divisors for finding the expectations.
The following calculations by the Northampton Rate of Mortality
show the mode of forming a table of expectations :
t=l i+.5= .^5=..
/„= 9 9
+ .5=r 1.05=:f„
AddttiMsclttcked.
1
4
9
16
24
34
88 =
sum of living
above 90.
124. The present expectation of life after t years is
,^.|4- /»»4<-H I C4<-fl"l"/iii.K+l , C+<4« 4- C-H^-» ,
. I »iii-^i-l + Ht4-» ,
but y^ = P>m> the probability of a life aged m living / years, and
the remaining part of the expression is the expectation of life at the age
of (m + 0 yc*" > *^^ expression may therefore be written e^^.p^ ^
125. Hence the duration of life that a person has the present expeo-
Digitized by VjUUvIC
122 LIFX ANNUITIES.
ti^tion of enjoying after a given period ib found by multiplying the ex-
pectation at the advanced age hy the chance the individual has of
attaining that age. &
How many years has a male aged 50 the expectation of enjoying afler
the expiration of 10 years hy the Chester rate?
(Table 2.) ^,^, ^ = e« X ^ = 13.96 X ^ = 10. 55.
tm iiO 3075
126. Since the expectation for the whole of life is made up of the
expectation during the next t yeara, and of the expectation after that
term, " the expectation for the next ( years only is evidently equal to the
difference between the expectation for the whole term of Ufe find the
expectation deferred for i years."
Example, How many years has a male aged 50 the expectation of
enjoying during the'next 10 years by the Chester rate ?
_^ ^« — .
^m . X «B,+i —
7 '2*7*78
^5a—-^ X <?«= 19.32 - ri^ X 13.96= 19.32 — 10.55 r= 8.77.
lio 3675
127. Many persons who have but an imperfect knowledge of the
subject, erroneously suppose that the vcdue of an annuity payable during
the life of an individual is found by calculating the value of an annuity
certain for a number of years equal to the expectation of life of the
individual.
By Art. 112 it appears, that if the probability of an individual sur-
viving I, 2, 3, &c. years to the extremity of life, be respectively mul-
tiplied by the present value of £l due 1, 2, 3, &c. years, the sum
of the several values thus found will be the value of an annuity on the
life of that individual.
The expectation shows the number of payments received on an ave-
rage by every person of the same age ; if an annuity certain be calcu-
lated therefore for a term equal to the expectation, the longest period of
discount introduced in the calculation will be the number of years'
expectation ; but in valuing a life annuity at the same age, although
each individual receives on an average the same number of payments as
are made upon an annuity certain, yet some of the probabilities are
discounted for a lopger term than i^ represented by the expectation ; at
the age of -30, for instance, the expectation is 30.80, which is the term
for which the last payment of the annuity certain is discounted, while,
in finding the true value of a life annuity, the probability of completing
each y^ar is dispo^nted for every year fi life may complete according to
^Digitized by^^UUVlC '
ANNUIiniS ON JOINT LIVES. 123
the tables ; in vhkh case the chance of receiving the 'payment at the
i^e of 70 is discounted for 40 years, and for a greater period at every
age above 10.
The present value of an annuity certain for the term of years that
^n individual has the expectation oif enjoyipg is greater therefore than
the value of the same annuity to cease on the failure of that individual's
existence. At the age of .45| Chester rate of mortality amongst males.
Table 2, the expectation is 22 years, for which term at 3 per cent the
value of an annuity certain is 15 •937» and the value of the life annuity
lit that age is 14.382. (Prob. Table 3.)
ANNUITIES ON JOINT LIVES. ^
128. When an annuity depends on the joint existence of any number
of lives aged reapectively m, mi , nit , fte., years, the present value of the
annuity is represented by the symbol a«, «,, ^t, ac.
By Art. 106, the present value of the expectation of receiving the
annuity at the end of the first year whenHhere are two lives aged m and
fill ia "•*•' ' "iii f^ the present value of the expectation of receiving
the second year's payment of the annuity is ""^** *''*'* r* ; and if the
value of the expectation of receiving each year's payment be found to
the greatest age in the tabl^, and the several values be summed to-
gether, the tot^l will be the present value of the annuity.
multiplying the numerator and denominator by r* we have
hence the foUovnng rule :
Multiply the number living opposite each age in the table by the
present value of J^l fine the same number of years as the oldest age,
then again each of these products by the number living at the corre-
sponding age of the other life ; thus, in finding the values of annuities
on ^two joint lives when the difierence of age is 5 years, the correspond-
ing ages of the lives at one period of existence will be 36 and 41, in
which case we find the product pf the number of living given in the
tables at the age of 41, and the present value of £1 due at the end of
41 yearsi and multiply this result by the number Uving at 36.
Having found the products at dl the ages qf a given difference from
birth to the extremity of life, we begin at the oldest ages and find suc-
cessively the sum^ of all the product^ i^bov^ each eqmbinatipn.
Then the v^ue of an aiinui^ fluring the joint existence of two Uvea
Digitized by KjUU vlC
124 LIFE ANNUITIES.
at any ages of the same difference as that for which the various products
have heen found may he obtained by dividing the sum of the products
above the ages, by the products opposite to them.
129. If, previous to calculating the values of annuities on joint lives,
calculations have been made of the values on single lives, the products
opposite each age in the D column for the single lives will form part of
the operation in finding the products for the joint lives.
130. When one life is a male and the other a female, and the rate of
mortality distinguishes the sexes, the number of living at the age of the
male must be taken from the table of mortality amongst males, and the
living at the age of the female from the table of mortality amongst
females.
Or, when there is no difference of sex> but it is thought proper to
use different rates of mortality for the two lives, the number of living at
the age of each of the individuals must be taken, in forming the products,
from the corresponding rate of mortality.
131. The following calculation of the value of an annuity during the
joint existence of a male aged 85 and a female aged 90, will illustrate
what has been said, and show the methods by which the values in
Table 23 were calculated (Chester 5 per cent) :
Mal«. rmHiic.
r'^'x/iooXftttri. 00760049 X 23x126= 22.03782
r^ Xto X /»4==. 0079847 1 X 30x158= 37.84753
r" x/» X/m=. 00838395 X 37x190= 58.93918
r*' X^X/«=:. 0088031 5 X 44x221= 85.60183
r* X /tKi X /^i= .00924331 X 51x252= 118.79502
323.22138
r^ x/mX/„=, 00970547 X 68x283= 186.77208
r** x/h xA»=. 0101 9074 X 92x313= 293.45255
r" x/» X/8.= . 01 070028X116X343= 425.7426
f^ X/m x/w=. 01 123530x146x384= 629.8959
f»» X/„ X /c«= .01 179706 X 176 X 436= 905.2590
2764.3435
r^ X/,0 XZ85=. 01238691x205x510=1295. 0517.
_ 323.22138 , _,
''••••'" 186.77208^^-^^^
• 2764.-3435 ^ ,,.
^~-= 1295:0517 =^-^^"'
132. The principle laid down for calculating annuities on two joint
lives applies to finding the values on any number of joint lives : if the
values were calculated on three lives when the differences of the ages
are 5 and 1, the number in the D column opposite the ages 16, 21, and
22, would be equal to the product of the number of living at 21 and 22
Digitized by VjUUV IC
. TEMPORARY ANNUITIES. l25
multiplied by the present value of £l due 22 years [hence, multiplied
by the living at 16.
What is the present value of an annuity of £45 5 0 payable durbg
the joint lives of two males aged 30 and 35, by the Chester Rate of
Mortality Table, when the interest of money is 3 per cent?
Table 23, £/„.» = 13 . 544 £Ab 5s. sz £^S . 25
45^
61720
21088
61120
• 54116
612.86600 zs£6l2 11 4.
What is the present value of an annuity of £50 payable during the
joint exUtence of a male aged 30 and a female aged 40, Chester Rate
of mortality, 5 per cent ?
Table 23, fl«,.« = 11.109
50
555.45 =: £555 9 0.
What is the annuity that may be purchased for £800 on the joint
lives of two females aged 45 and 50, Chester 3 per cent?
Table 23, a^.w = 11.549
Art. 120. -TT^ = 69.261 = £69 5 3 *
11.549
DEFERRED AND TEMPORARY ANNUITIES.
133. Let the value of an annuity deferred n years on a life aged m,
and then to continue during the remainder of life, be denoted by 0(«.) >
then the present value of the first payment of the annuity, which is to be
received at the end of (n+1) years provided the life shall continue to
exist until that time, is found by multiplying the present value of £1
due at the end of (n+ 1) years by the chance of the life surviving that
period > and the present value of any other of the payments is found by
multiplying the present value of £l due in the number of years that
must lapse from the present time, until the payment becomes due, by
the chance the life has at present of surviving that term.
Digitized by LjOOQ IC
126 Ltn ANtmiTIBS.
134. In this fonnula, -^y — , ii the present Yilue of £l due at
•■I
the end of n years, multiplied by the chance of the life living n years,
and the remaining part of the expression is the present value of an
annuity on a life aged tn+n years ; hence the following
Rule* Find the value of an annuity on a life older by the number
of years the annuity is to be deferred, than the present age ; multiply it
by the present value of £l due at the end ^ that term, and by the
chance of the life surviving that term.
135. If the numerator and denominator of the expression be multi-
plied by r* , its value remains unaltered, and becomes
This formula, when we have tables calculated of the description men-
tioned in Art. 115, points out a very short method of cal(mlating the
values of deferred annuities ; for the number in column N, opposite the
age (m+n) at which the annuity is to be entered upon, is the nume-
rator of the fraction, and the number in column D, opposite the present
age (m) is the denominator of the fraction | the formula by Davies's
method is therefore
1 36. Rule, Divide the number in column N, opposite the age at which
the annuity will be enteied upon, by the number in column D opposite
the present age.
When the annuity depends on the joint existence of any number of
lives respectively aged m, mi , 9n, , &c., the probability of their jointly
surviving the term must evidently be substituted for the probability of
one life surviving, t.e.
TEMPORARY ANNUmSS.
137. Let the present value of an annuity to continue the next n years
provided any number of lives aged m, fiii, fii«, &c., continue jointly to
exist during that term, be denoted by £!(«, .^ m, » ao^ • ^^ the value
of an annuity to continue for the next n years, together with the value
of an annuity which is to be entered upon at the expiration of n years,
and then continue during the remaining time of joint existence, is evi-
dentiy equal to the value of the annuity on the lives for the whole period
of joint existence, to be entered on immediately, we have the equation j
Digitized by ^^UUV IC
T£MtK)ltART ANNUITIES. \it
Oim, w^. w, , Ac.) + ^im, m^f «,, Ac.) =2 ff^, ^^, ^^, 4^.
by tran«po8ition,|fl(«,.^,^,ae.)-=«i«.i«^.«,.fto.- «(«. -j. ..j. «c.) .
Rule. From the value of an annuity for tlie whole term of life, 8ub«
tract the value of an annuity deferred for the number of years which
the temporary annuity has to eontinue; the difference will be the
required value of the temporary imnuity.
138. By Davies'8 method
Ruie. From the number in column N opposite the present age,
subtract the number iu column N opposite the agt at which the annuity
will cease, and divide the difference by the number in column D oppo-
site the present age.
139. The present value of an annuity for n years, payable at the
beginning of each year, will be unity added to the present value of an
annuity for (n — 1) years, payable at the end of each year, i. e.
^ + ^^->.-|-^ + — d: — d: d;;; —
the quantity D» + N» being, by the construction of the tables, equal to
Similarly, the present value of £l paid down, and of an annuity of £l
for n years payable at the end of each year, will be
1+ac^) = =r
140. To find what annual premium should be paid in lieu of a gross
sum to secure a deferred annuity.
When a- reversionary annuity is secured by an annual premium the
first payment is usually made immediately, and the subsequent payments
at the end of each year until the reversion is entered upon.
As the present value of an ann\)ity of £l for the term increased by
one year's purchase, is to £1, so is the present value of any other sum
to the equivalent annual premium.
1 +fl(-^ :
1
• •
• •
a
'"!-:
N._,-N,^.
•
•
1
• •
• •
N.+;
D,
D-.
1 +a« 1+0^— a (^)
ori^^=::2^— "ii=.: 1 :: i^fts . _^_ - annual pre^^^
Digitized by VjOOQ IC
198 LIFE ANNUITIES.
141. We have just supposed n + 1 annual payments to be made to
secure the deferred annuity: if we suppose only n payments we shall
have
l+a(«) :l ::ac«j: >-
or
Examples.
1. Required the present value of an annuity of £30» to be entered
upon at the expiration of nine years, and then to continue during the life
of an individual aged 36. (Carlisle 4 per cent)
a
cm —
r*««
1.04-»=:
: .702587
o„= 14.1046
f
Table 21.
6401.413
; Ott inrerted
702587
281035
7026
281
42
9.90971
SO
•
297.29130
7274 =
= /« inverted (Table 1)
118916520
20810391
594583
208104
TaWc 1, /„ = 5301)1405295.98(264.800 = ^264 16 0
10614
34389
31842
25475
21228
42419
42456
Digitized by LjOOQ IC
TEMPORARY ANNUITIES.
Or thus :
N«+. = N«+, = N« = 11414.218
30
Dm = 1293.150)342426.54 (264. 8 = ^264 16 0
" 2586300
8319654
'J758900
620754
517260
103494
103452
42
2. What is the present value of an annuity of £40, to be entered
upon at the expiration of 15 years, and then continue during the joint
existence of two males now respectively aged 25 and 30 years? (Chester
3 per cent)
.15
— '40 • MS • *"
log.a<ft») = log./4o + log./^j + log r" — log /„ - log./^ + loga^a,4.
Table 23, log a4«.«=log 10.977=1.0404837
Table2,Prob.l<^/40 =log 4516=3.6547539
do. log/« =log 4116=3.6144754
(Table8,Pt.l)logr" =:log 1.03""= 1.8074417
Table 2, Prob. -log ;»= — log 5459=4. 2628869
— log /«= - log 5127=4.2901367
0.6701783 £4.67928=fl(ij ^.
40 ' i»»
187.1712=£187 3 5
3. What is the present value of an annuity of £30 for the next nine
years, dependent on the existence of a life aged 36 ? (Chester 3 per
cent.)
Om = 15.8558
30
475.6740
264.800 = value of the deferred annuity, Ex. 1.
210.874 = £210 17 6
By Davies's method,—
Digied by Google
lao un ANNurriEa
Nm s 20503.891
N4> = 11414.218
9089.613 *
30
0i,= 1293.l5O)2'7269O.19(21O.813 = £2lO 19 6
2586300
1406019
1293150
112869
103452
9417
9052
365
4. What is the present vfdue of an annuity of jf90 for the next 10
years, to depend on the joint existence of a male aged 50, and a female
aged 55 ? (Chester 3 per cent, Table 23.)
Prob.Tab.2, log./« =:log2178 =3.4437322
do, log /„ t=:log2956 =3.4707044
do. ar. CO log l^ss ar. co log 3675 =4 . 4347427
do. ar. CO log /„ = ar. co log 3934 = 4 . 405 1656
Table 8, Part 1, log 1 • 03 ■'»= 1.87 16278
Table 23, log a». „=log 6 . 624 =0.8211203
0.4470930 = 2. 800=a(», „,
9.423=as^» !'•
6.623=a^«j
90 '^
596.070=596 1 5
5. An annuity of £30 during the life of a person now aged 36
is to be entered upon at the end of nine years : what annual pre-
mium should be required, supposing the first payment made imme-
diately, and the subsequent payments .at the end of each year during the
next nine years, subject to the existence of the life ? (Carlisle 4 per
cent.)
Table 21, 0*5=14. 10460, Table 1, ^=5307, ^45=4727,
Table 4, Part 1, r*=. 702587.
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TElfPORART ANNUrms. 131
14. 10460 X 4127 X . 102587 46843. 189 ^ ^^^^^
ac^= ^^ = -5307~ = ^-®^^^^
1 + at^=l+fl„- a^ii^ = 1 + 15.85577 - 8.82668 = 8.02909
8.82668
o /m/vf^^ = 1 .09934 = annual premium for a deferred annuity of * 1
8,02V09 30
32.98020 = 32 19 7, required annual premium.
By Davies's method, —
Art.140, N- N« 11414.2176
N^-i — N«+. "" N„ — Ntt " 21797 .0406-11414.2176^
11414.2176 _
10382.8230 ^ "^
32.98020 = £32 19 7, as before.
6. What annual premium, the first to be paid down, and the rt-
maioder at the end of each year for the next ten years, ahould be paid
to secure an annuity of £90, to be entered upon at the expiration of 10
yean, and then to continue during the joint existence of a male now aged
50 and a female now aged 55 ? (Chester 3 per cent. Table 23.)
By Example 4, page 129, a^^ „> = 2.800
I'' 90
1 + a^M, „) c= 7.623)252,000(33.058 =s ^£33 1 2
>•! ••22869
23310
22869
.44100
38115
• 5985
1 A party proposes to lay out £400 in the purchase of an annuity,
to be entered on at the expiration of nine years, to continue so long as a
life now aged 36 shall survive that time : what sum per annum will he
be entitled to ? (Carlisle 4 per cent.)
By Example b, page 129, a(U)= 8.82668
400
8.82668 : 1 :: 400 : r-~r = 45,317 = £45 6 4
8.820t>o
8. A person now aged 36 wishes to pay £lO down, 'and a further
annual premium of £lO at the end of each year for the next nine years,
to secure an annuity, to be entered upon at the expiration of that term,
for the remainder of bis life : what ram per annum should he obtain ?
(Carlia]e^4 per cent.)
Digitized by LjOOQ IC
192 LIFE ANNUITIES.
By Example 5, page 130, 10(l+a(a«)) =r80.2909
! Ditto a(M)= 8.82668
I T
I QQ OQOQ
j 8.82668 : 1 :: 80.2909 : ?-i~^= 9.096 = £9 I 11
ENDOWaiENTS.
142. From the above expressions we may find the annual premium re-
quired to secure a sum upon an individual attaining any particular year.
By Art 105, the present value of £i to be received at the end of n
If we suppose n payments, the first paid immediately, the annual
premium wiU be ^X n - n . =-W~N '
P»^ ^ __2719^99 271999^ _ ^
N«-Nm 75523.846-52960.516 22563. 33 ^ *-^-"^^ -
annual premium to secure £lOO at the end of 7 years to a child aged
14. (Northampton 3 per cent.)
143. ^To find the value of an annuity granted on the longest of any
number of lives.
Let there be any number of lives aged m, nii m^ &c., respectively,
then, by Art. Ill, the probability of some one or more of these lives
being in existence at the end of any year from the present time, as the
nth, on which the receipt of the payment of the annuity at the end of
that year depends, is 1 — (1 — ;»«,,) (1 - JP«,.«) (I — p«.,,«), &c.:
if n be made equal to unity the expression will give the probability of one
or more of the lives being in existence at the end of the first year, which,
multiplied by the present value of £l due at the end of one year, will
show the present value of the payment to be received at the end of the
first year ; if n be 2, and the value of the expression in this case be
multiplied by the present value of £l due at the end of two years, the
result will be the present value of the payment to be received at the end
of the second year ; and the sum of the present values of each payment
for every age to the end of the Table will evidently be the present value
of the annuity.
&C. &C. &C.
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Google
ENDOWMENTS. I33
If we add these quantities perpendicularly, the sum of those in the
first colmnn (by Art. 112) will be the present value of an annuity on a
life aged m ; those in the second, of an annuity on a life aged mi ; in the
third on a life aged ms, &c. ; — ^the total value of these expressions is
therefore
a^+a^^ +««,+ &c. -a«.,j -««,«,, -o^^.m, ~&c.+ff^«^,^ &c.
144. When there are three lives, it becomes
Rule. Find the value of the annuity on each of the single lives ; to
their sum add the value of an annuity on the three joint lives, and sub-
tract the sum of the values on each pair of joint hves.
Example, What is the present value of an annuity of £50 payablo
until the death of the last survivor of three lives respectively, aged 18,
27, and 36 years? (Northampton, 3 per cent.)
145. As there are no tables of annuities on three lives, we approxi-
mate by the following rule, which is given by Mr. Baily in his Trea-
tise on Life Annuities : — ^Take the value of an annuity on the joint
lives of the two oldest, and find the age of a single life of the same
value. Then find the value of an annuity on the joint lives of the one
just found aud the remaining life of the three, which diminished by . 05^
will give very nearly the true value.
a„ =19.0131 a,8.«7= 13.7363 Table 8.
a„ =17.4674 ai8.ai= 12.7635 do.
a^ = 15.7288 o^.,, s 12.2295= Om do.
«w.i7.«= 10.3887 = aie.5i - .05 38 . 7293
62.5980
38.7293
23.8687 X 50 = 1193.435=£ll93 8 9.
146. When the annuity is on the longest of two lives, the formula
becomes
ffm + a„^ — ««, m^ •
Rule, From the sum of the values on each of the single lives, sub-
tract the value of the annuity on the joint lives.
What is the present value of an annuity of £30 on the longest of
two lives aged 39 and 43 ? (Northampton 3 per cent.)
Table 7,
On =: 15.0750
do. '
aa = 14.1626
29.2376
Tables,
a^M^ 10.5485
18.6891
30
560.673 = £560 13 5.
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134 LIFE AmnnriEs.
What ift the preaent value of an annuity of £50 on the longest of
two lives; one a mate aged 35, the other a fienuJe aged 40 ? (Chester
5 per cent.)
(Tables. Prob.)fl» =13.1892
do. a4o = 13,3287
26. 5119
Table 23- a^,^ = 10.6690
15.8489
m
793.445 SB £792 8 11.
147. To find the present value of a deferred annuity on the long^
of any number of lives.
If the annuity be deferred n yean, the first payment will have to be
received at the end of n+ 1 years ; the present value of which is found
by multiplying the present value of £l due at the end of n+ 1 years
by the probability of the existence of the survivor at the end of that
term ; and the present value of any other payment is found in like
manner by multiplying the probability of the event on which the pay-
ment depends taking place, by the present value of £l due the num-
ber of years that must lapse before the payment will be due ; the several
terms of the series in Art. 143 represent these values ; and the sum of
them all after the first n terms will be the value of the deferred annuity ;
the sum of these terms in the first perpendicular column is
whidi, by Art. 133, is the present value of an annuity deferred n years
on a life aged m, and the sums in the other columns also evidently re-
present vslues <tf deferred annuities ; if therefore, in the formula obtained
for the value of an annuity to be continued for the whole term of life,
we substitute the present values of deferred annuities for the present
values of immediate annuities for the term of each life, the expression
for the required value of the deferred annuity will be obtained.
148. When there are three lives the formula is
149. And for the longest of two lives the expresnon it
150. If the annuity depend on the joint existence of the lives during
the n years that the annuity is deferred, the formula will be
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INBOWMSNn. )||
What 18 the present value of an annuity of £50 deferred 10 years,
and then to continue until the death of the surrifor of two males, no^
aged 35 and 40 yean? (Cheater 3 per cent.)
loga«= log. 14.3812 = 1.1511951
log /«= log 4116 = 3.6144154
ar.colag.4»=ar,colDg 4849 = 4.3143418
log r»*= log 1 .03-** = 1.8116218
0.9582461 9.083
logiiM= log 13.0950 = 1.1161055
log 4,= log 3615 = 3.5652513
ar. CO log l^t^^ ar. co log 4516 =: 4.3452461
logr"= log l.Ol-'* = 1.8116218
0.8982361 1.911
laga«j»= log 9.823 = 0.9922441
log ^45 -• log. t5+logr»*= 1.8004510
log 4e — log l^ = 1.9105034
0.1031985^5.049
9.083= a(»)^^^
1.911= fl(40
110
16.994
5.049 = a(iu,4g^
110
11.945
50
591.25 =£591 5 0.
What is the present value of £bO per annum, to he entered upon at
the end of 10 years, provided two males, now aged 35 and 40, shall
jointly survive that period, and then to continue until the death of the
Ust survivor ? (Cheater 3 per cent.)
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13^ LIFE ANNUITIES.
hi • •40
fl«. =14.3812
a„ =13f.0950
27.4762
g4>.ao= 9.823
log 17.6532 = 1.2468234
log. /«— log. /»+log r" = 1 .8004510 as in last example,
log /ao- log U = 1.9105034 do.
0.9577778 =9.0736
50^
453. 680 = £453 13 7.
151. To find the value of a temporary annutfy on any number of
Hfes.
Rule. Find the value of the annuity for the whole term of life, and
of the annuity deferred as many years as the temporary annuity is to
continue ; the difference between them will be the value of the tempo-
rary annuity. (Art. 137.)
Example. What is the present value of an annuity of £50 for the
next 10 years, depending on the existence of the joint lives or of the
survivor of two mades aged 35 and 40 ? (Chester 3 per cent.)
a» = 16.9758
a^ = 15.6537
32.6295
a^M = 12.2160
20.4135
By the last example but one the value of 1 , . g . .
the deferred annuity is . • • • J *
8.4685
50
423.425 =£423 8 6.
DEFERRED TEMPORART ANNUITIES.
152. Suppose A entitled to an annuity to be entered upon at the
expiration of d years, and then to continue during the existence of a
life now aged m, and B to enter upon a similar annuity at the expiration
of d + n years, the difference between the two ydW be the value of an
annuity to be entered upon at the expiration of d years, and then to
continue n years, subject to the existence of a life now aged m, viz, :
Ite value i. /^V.i,,+,-i=^.,*+-.a,,^.
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DEFERRED TEUPORART ANNUITIES. 137
By DaTic8*8 fohnals —
The present value of £l paid down, and of an annuity of a?l for
d years, subject to the existence of a life aged m, is (Art, 139)
153. If the total number of payments be d, the first of which is paid
down, the present value will be
154. To find the annual premium necessary to secure an annuity for
n years, to be entered upon at the expiration of d years, we must divide
the present value of the deferred annuity by unity added to the present
value of an annuity for d years, which gives
(Art 139)
155. When the total number of annual payments is cf, we divide the
present value of the deferred annuity by unity added to the present
value of an annuity for d— 1 years, which gives
D. N«-t-N.^, N_, -N^.» •
Ejrample, Required the single premium to secure an annuity' of £50
for 7 years, to be entered upon at the expiration of 9 years, subject to
the existence of a life now aged 40. (Carlisle 4 per cent.)
7+9=16
l^.f* 4458 X. 702587x13. 15312
-'^^^IT^-" 5075 =8.11769
/„.r" 4000X -533908X10.96607
^<^5-(7^= 5075 =4^
3.50302
50
£175 3 0 175.1510
Also,
N4»4^— N^m^ _N^-N,< _ 8580 . 9492 - 4878 . 0207 _ 3702 .9285
Dm ^ I>4», "" 1057.0669 ^1057.0669"^
3.50302
50
175.1510 =£175 3 0 '^
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138
LIFE ANNUITIES.
156. To find the value of an annuity payable ao long as two oat of
three lives shall jointly be in existence.
If the annuity be on three lives, A, B, and C, respectively aged m,
m, , Hit years, the chance of its being received at the end of any par-
ticular year depends on either of the following events : 1^, that the three
lives. A, B, C, be oZ/ in existence ; 2^, that A and B be alive, and C
dead ; 3^, that A and C be alive and B dead ; 4^ that B and C be both
alive and A dead : the following table shows the chance of each sepa-
rate event happening in the nth year, the sum of which shows the pro-
bability of the Tith year's payment of the annuity being received :
That
there;
wUlbe
AUve.
Dead.
The probability is
I
ABC
None
P(«, «,.«,),«
2
AB
C
Pirn, «j ). • (1— P«, » n) = Pcm », ), m
— P(«,«ij .«,),■
3
AC
B
Pim,m^).n (1 ""I'-i .-) ==!'(«. m,), ••
"■P(«.«l,«^),«
4
BC
A
P(«l.«,).» (1— P-H«) =P(»i.«4).«
— P(», .J, ■,,).«
their sum, l>(«s«i)i + P(«,«,),. + Pc,^.«,),.-2p(,,«^,^),. ,
multiplied by r*, gives the present value of the nth year's payment of
the annuity. If n be made equal to 1, 2, 3, 4, &c., and the correspond-
ing values of the expression be found, they will show the present value
of the payments of Uie annuity in the 1st, 2nd, 3rd, 4th, &c., years, and
the sum of these values for every year in which, by the tables, the
annuity can be received, will be the present value of the required
annuity : this sum (Art* 142) will be
a^m^ + «iH«, + «»j ,«, - 2 flfi..
•,f^«
151. When the value of any expression is found for the successive
values of n when made equal to 1, 2, 3, 4, &c., years, the sum of these
values continued for the whole term of existence may be denoted by
prefixing the symbol 2 to the expression ; when the sum is to be found
only for a limited number of years, as /, it may be denoted by the
character Si^.
Example. What is the present value of £80 per annum, to ceaae on
the failure of the joint existence of the last two survivors of three lives
aged 23, 25, and 30 ? (Northampton 3 per cent)
Digitized by LjOOQ iC
BXVBBfllONS/
199
ab.»
=
13.5308
Om,u.m^Ou.m,
'^
•05
B5 10.7184
On,m
=
13.0978
9
^.»
12.9661 =
39.5947
21.4368
18.1579
80
Otf
21.4368
1452.632 = £1452 12 8
REVERSIONS.
ISe. To find the Talue of an annuity on a life A aged n^ after the
extinction of another P aged mt.
The chance of the life A receiving the annuity in any year, as the nth
from the present time, depends on his being alive at the end of that
time, the life P haying failed previously, the probability of which is
P«,.0— I'lm. .) *=;'«,• — F(«,«]}.»
andZr* (p..,— ;?(im«^),,) = a., — o^.,^ , the value of the reversion.
Rule. From the value of the annuity on the life in expectation sub-
tract the value of the annuity on the two joint lives.
Example, What sum should be paid to seciure an annuity of £55 to
ft male aged 35, during his life, after the death of a female aged 40 ?
(Chester 5 per cent.)
Ou = 13.1892
Okm = 10.6690
2.5202
55
126010
12601
138.611 8s £138 12 3
159. If the reversion be secured by an annual premium the whole
ftfflount of payments will consist of the premium paid down at the
present time, and of an annuity during the joint existence of the two
lives; the annua] premium will therefore be found by dividing the single
premium by unity added to the present value of an annuity of £l during
the joint lives.
The annual premium for the above reversion will be
l^:61L==]^l = „.8,9 = £lin7.
l + flMpiO 11.669
Digitized by VjOOQ IC
m
140 ,UPK ANNUITIEa
160. If the animity cease at the expiration of t years from the preaent
time the preaent value will he
161. To find the value of the annuity payahle during the joint lives of
A and B respectively, aged m and mi, and also during t years after the
death of B, provided A shall live so long.
The value of the annuity during the two joint lives is Om, «!•
The remaining part consists of two portions, one during the next
/ years, the value of which, by the last Article, is a,, — <*(«.«, ) » and
the other after t years ; the value of any payment ^of which, as the nth,
will be the present value of £l, due at Uie end of n years, multiplied by
the chance of A surviving that period, and of B having died within t
years of that time, viz. —
which o « — ^ ^!!*l2zf-./^^" ^^!±i:i^ f=cL— P<=tiri>:?.
the expression therefore becomes r» ( ^^''''"*^'^'* — P(«,«^ » ),
the successive values of which, being found for every year after the <th,
will give for their sum
adding to which the value of the other portions, we obtain for the total
value required
By Daviea's Tablet,— -
"'v — d:: —
When m is greater than mi— ^,
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IUSVBB9I0N& 141
When fUt — < ifl greater than m,
162. To find the value of an annuity on a life A, aged m^ after the
failure of the yom< existence of two other lives, P and Q, aged irii and
flit yean.
The chance of receiring the annuity in the nth year is
the value of the reyersion is therefore
and the annual premium =?=.^^-- .
163. If A does not enter on possession until after the death of the
survivor of P and Q, the chance of receiving the annuity in the nth
year is
is the present value of the reversion.
Tlie annual premium, which is payable so long as A is in existence,
with either P or Q, is found by dividing the single premium by
1+2 r^Pm.* (Pmi,n + Pm^^n - P(,mi,mt>, n) =
164. The value of an annuity on the joint lives of A and B^ aged m
AiMlm,, after the death of P, aged m^ is
the annual premium which is payable during the joint existence of A,
Bj and P, is found by dividing by 1 + a^, ^^ ,„, •
165. The present value of an annuity on the survivor of two lives, A
uid B, aged tn and mi, after the death of P, aged mi, is
2 r" ( 1 — 1?^ ,) (p«, ,+Pmu • — JP(m,«o,«) =
S nP-m + Pmun - P(^mi\n — P(,m,m^,m - P(mi,«n),« + Po«.«„«i,),«}=2
Digitized by OOOQ IC
149 LiFB AnNurms.
The divisor for the annual premium which ia payable ao long u P ia
in existence with either of the lives A or B, ia
1 + S r* (Pm.n+Pm-n -P(-..«,).« ) Pm^ n
Examples,
166. Required the preaent value of an annuity of £40 during the joint
exutence of two livea» A and B, respectively aged 66 and 33, and seven
years after the death of B, provided A shall live so long. (Northampton
3 per cent.)
Art. 158. «c,) + 2-
a^^ =a*- |2..,J.a,,-7,9947-J??X. 813092X6. 7938=
7.9941-^5^^^= 1.9941-3.0111=4.9836
^.7t
992 «,«^^^ , ^^,^ 4222.7691 „ „„^
frrxX. 813092X5.2354= — -— l =2.7209
1552 1552
4.9836+2.7209=7.7045
40
308. 1800 =£308 3 7
(By Davies*s Tables). Here m is greater than mj — f .
= 4.9836
Kti-Ny.^ 1763.756-664.293
D„ 220.615
N,+,.«, Nt..^ 2497112 ^ ^^^^
"D^^"^ = D^^'^ 9ir35ar=' ^'^^Q^
l^-,«, lJ-.» ym58 ^ .^^^^ x40=308.180 aa before.
What is the present value of an annuity of £40, to he entered
upon after the failure of the joint existence of two lives, aged 29 and 30,
and then to continue during the life of a person now aged 18? (North-
ampton 3 per cent.)
«!• - ai8.».8o (Art. 162.)
Oit = 19.0131
aitn.M = 10.7472 = ai,.4i — .05 (Art 145)
8.2659
40
330.636 = £330 12 9
What is the present value of an annuity of iS40, to revert to a person
Digitized by VjUUVIC
fiSVKRSIONS. 143
now aged 18 after {he death of the suiviyor of two IWeSi aged 29 and
30 ? (NorthamptOQ 3 per cent.)
<»ii— «».• "-<»i».8o + ai8.«.to (Art. 163.)
Om sz 19.0131 Ott.. Bs 13. 6452
a^j^M = lO^WW a„.» =13^4448
29.7603 26.9900
26.9900
2.1703
40
110.812 3s £110 16 3
What IB the present value of a,n annuity of i^40, to revert from the
present possessor, at the death of a person aged 30, to another individual
during the joint lives of two persons, aged 18 and 29 ? (Northampton
3 per cent.)
(ks.n - ai,.».» (Art. 164.)
«,,.» = 13.5452
«i8.tt.» = 10.7472
2.7960
40
111.920 = £111 18 5
167. Those prohlems in survivorships which involve several of the
preceding cases are next to be considered.
Example. An annuity of £20 is granted on the life of the survivor
of A and B, aged 15 and 20 years, to be divided equally between them
while they are both living, and after the death of either of them the
survivor is to receive the whole of the annuity for the remainder of his
life : what is the value of A's share therein ? (Northampton 3 per cent.)
A's share consists of two separate parts ; one entitling him to half
the annuity during the joint existence of himself and B, the other
entitling him to the annuity during the remainder of his life after the
decease of B.
The value of the Ist part is . . ^ a^g, »
of the 2nd . . flis — ^is.w (Art. 158.)
the sum of the two . . . aj^ — J a^.to is the formula for finding
the value of A's share.
By substituting the value of the annuity on the life of B for that on
the life of A, we have the value of B's share, o^ — i a^.^ »
a„ =19.6577 fl» =18.6385
J a,,,^ = 7.3299 J a^s.a = 7.3299
12.3278 11.3086
20 20
246.556 r=£246 11 1 226.172 = £226 3 5
A's share B's share.
Digitized by
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144
LIFfi ANI9UITIKS.
168. An annuity of J^SO is granted on the longest of three lives, A,
B, and C, respectively aged 16, 21^ and 26 years, which is to be
equally divided between tliem whilst they are all living, and on the
decease of either of them it is to be equally divided between the sur-
vivors during their joint lives, and then to belong entirely to the last
survivor during his life. Required the value of A's interest therein.
(Northampton 3 per cent.)
A's interest consists, 1°, of one-third of the annuity on the joint
lives ( ^aie.u.cfl) ; 2°, of one-half the annuity during the joint existence
of A and B after the death of C ; 3°, of one-half of the annuity during
the joint existence of A and C after the death of B ; 4^, of the entire
annuity during the remainder of his life after the death of the other two.
The following table shows the separate values, the sum of which is
the value of A's interest therein :
Alive.
Dead.
Value of the Annuity to be received.
ABC
none
1- ^uM.m
•
AB
C
4 (<3fM.ii— tfi«.ii.n)
Art.164.
AC
B
i(^w.tt — aie.fi.«)
Ao.
A
B C
^W^^UM — Oi«,«+ ^«.ti.aB
Art. 163.
the sum a^ -* J ^w.ti '
— i <h$.u + i «x«.ii.n = value of A's interest
7.2285 =:ia,.,„
3)1 1.5641 = fl„.,i„=:a„.« -
,05
7.0149 =:iaj..a,
3.8547 =icr,,.„.«
14.2434
19.4358 = a„
23.2905
14.2434
9.0471
30
271.413 = ^^271 8 3= value of A's
interest.
169. An annuity of «£30 on the longest of three lives, A, B, and C,
aged respectively 18, 28, and 33 years, is to be divided equally between
A and B during their joint lives, but on the decease of either of them to
be divided equally between the two remaining lives, and afterwards to
be wholly enjoyed by the survivor. Required the value of A's share
therein. (Northampton 3 per cent.)
The following table shows the different parts of which A*8 interest is
composed, and the conesponding values :
Digitized by LjOOQ iC
REVERSIONS.
m:
AUve.
Dead.
Value of the Annuity to be received.
AB
AC
A
• •
B
BC
^w— «i8.«— ai8.»t+ ais.^n.tt
Art. 164.
Art. 163.
tbc sum, tf „ — J a„M— i aia 88+i a^Mn = value of A'a interest.
2)10.5668 = atM,9,m = a^u^-- .05 6.8212 = Ja„.»
6.5609 = ia„.»
5.2834
19.0131 =aM
24.2965
13.3821
13.3821
JO. 9144
30
327.432 = £327 8 8;=value of A*b interest.
By proceeding in a similar manner we obtain the expression for the
value of B's interest —
fl«8 — i a,s.m — i OtB.n + i ai8.».88 .
170. An annuity of £50 on the longest of three lives, respectively aged
18, 28, and 33 years, is to be divided equally between A and B during
their joint lives ; if A dies first, B and C are to enjoy it equally during
their joint lives, and the survivor of them is to have the whole; but if
B dies first, A is to enjoy the whole during his life, and after his decease
the whole annuity goes to G.
Required the value of their respective shares.
The formula for A's proportion, which is of the same description as
in Art. 167, is aw — i aie.«.
To find B's share :
AUtc.
Dead.
Annuity to be received.
AandB
BandC
B
• •
A
AandC
a|8-«18.»- ff«.88+ ai8.S8.a8
Art. 164.
Art. 163.
the sum = a. -r i a„.»— i a«8.88 + 4 au.g
C's share :
B's share.
Alive. '
Dead.
Annnity to be received.
B And C
C
A
AandB
iai8.«8— iai8.M.ia
Art 164.
Art.l63«
the sum =flr» - a,,,.,— • Jom.„ -f- ia^.^M = C's shace.
Digitized by Google
146
UFX ANMUITIB&
2)10.5668 =aia.a.«
6.8212 B 4a,g.,
5.2834
6.2371 =
h<hu.
17.2890 =
Om
13.0583
22.5724
13.0583
9.5141
50
475.7050 :
= £475 14 1
B'l
ithaie.
13.1218
5.2834 =
h^iUMM
= ai«.»
16.3432 =^
<hM
6.2811
= *«..*
21.6266
19.3589
19.3589
2.2677
50
113. 385 £= ^6113 7 9 C's share.
17L An annuity of i^40 on the longest of three lives, A, B, and C,
respectively aged 18, 23, 28, is to be enjoyed by A during his life, and
after his decease is to be divided equally between B and C during their
joint lives, and the survivor of them is to have the whole ; what is thfe
value of B's interest therein ? Northampton 3 per cent.
Art 164.
Art. 163.
the sum s= tf^ — <<ia.ft - i o^.n + i di8.».tB = B's share.
Interchanging B aUd C in the expression for B's share we have the
formula for the Value of G'§ interest therein.
AUve.
Dead.
Value of the Annuity to be leceived.
BandC
B....
A ....
AC ..
2)11,0984 =:a„.,j.
= <»i».«—
.05
14.0822 = ^00..
5.5492
6.6402 s: ioiui
18.1486 =<M
aQ.l2a4
23.6918
20.7224
2.9754
40
119. 016 sll9 9 4B'sahaie.
Digitized by VjOOQ IC
BIYlftSaOillEL 147
5.5492 £2iaM...„ 13.6424 = a,,.»
17>289() s= 0,8 6.6402 = ^0,,^
22.8382 20.2826
20.2826 - : .
2.5556
40
102.2340 ss .6102 4 6 C'b share
172. An annuity certain of £50 for the term of 15 years is to he
enjoyed hy P and his heurs during the jobt existence of two lives, A
and By aged 14 and 19 years, and if that joint existence fail hefore the
expiration of 8 years the annuity is to go to Q and his heirs for the
remainder of the term of 15 years. To determine the value of Q's in-
terest in the annuity. Northampton 3 per cent.
Q's interest may he divided into two parts :
Ist. The chance of enjoying the annuity during the first 8 years.
2nd. The chance of enjoying it after the expiration of that term.
The amount of the interests of P and Q together for the first 8 years
is evidently equal to the present value of an annuity certain for that
1— f*
term, the expression for which hy Art, 49 is : — , and the value
of P's interest for the same term is the present value of a temporary
annuity for 8 years on the lives of A and B ; the expression fox which,
by Art. 136 and 137, is
•WW
if this be subtracted from the vidue of the ftilnuity eertikin, it will leave
the value of Q's interest for the term ; i. e.
- ■" **U.I» T J 1 .
• *14«*W
Q's interest after the expiration of 8 years will be the present value
of an annuity for 7 years after the expiration of 8 years, provided the
joint existence of A find B shall have failed within that time, the chance
of which is by Art 109, 1 — 7- x ^ ; the present value of the second
»u »«
|Mirt of Q's interest is therefore
this, added to the value of Q's interest for the first 8 years, will give the
value of his interest in the annuity ; viz.,
Digitize^-b^GoOgle
148 LIFK ANNUmBS.
■[..^^(..^xgc-r-)]-^.
J 4iX/n_^ 4985X4610_^
_ 22980650
" iiA X /» ^ *•"" 5473 X 5199 ^ ^ * 28454121
= 1-. 807646= -192354
1—»^=:1- .789409=. 210591
i..f7^»^ /.y _ 13.4336 X .789409 X .807646
8.5648. r"= -789409
r*»= .641862
•147547
453291.
147547
132792
2951
443
74
6
(l ^ ^1^\ 0'-r») = -0283813
l—r* =.210591
.03). 238972
?D-*'+0-fe^>''-'-"O= '•''''
^^//"^ = 8.5648
16.5305
0,^.1, =14.8708
1.6597
50
82.985=82 19 8
173. The probability of the existence of any two liyes that may be
proposed, both failing at the same instant of time, is less than any
that can be assigned.
For the number of instants in the possible duration of either of them
is greater than any that can be assigned; and as the failure of both the
lives at exactly the same time can take place at only one of those instants^
the fraction showing the probability will have unity for the numerator^
Digitized by VjOOQ iC
RSVERSIONS. 149
and for the denominator a number greater than any that can be as-
signed.
174. Two lives, A and B, being proposed, if both tbe lives fail
before the expiration of an assigned small portion of time, it is equally
probable that one of them in particular^ as A, will die before or after
the other.
Let X be the number of persons of the same age, constitution, state of
health, &c., as A that die within the same time, and let them die at
X equal intervals therein, which may be assumed for small portions of
time.
And let y be the number of lives of the same age, &c. with B, that
die within the same time, and let them die at y equal intervals therein.
Suppose B to be the mth in order of the y lives that hUX during the
XftL
term, and since y\x\\m\ — the number of such lives as A that wilt
y
have failed previously, the probability that A shall have been one is — «
Suppose B to be the mth in order from the end of the term, then the
number of such lives as A that fail between the death of B and the end
of the term is — , and that A will be one of them the probability
; m
IS .
y
The two suppositions of the order in which B's life may fail are
equally probable, for some one must die the mth in order from the end
of the term, and some other the mth in order from the beginning ; and
B or any other is as likely to fail at any one of the y periods of failure
as at another.
So that for every way whereby the life of A may fail before that of B,
there is another way equally probable for its failing after B.
115. And the probability of any one of three lives in particular, A, B.
C, dying first, as A is - .
o
For if z be the number of lives of the same age, &c. as C that die
within the term, and we suppose as before, B to be the with in order of
the y persons that fail therein, the probability of the life A failing pre*
viously is — ; and in the same manner may be shown that — is the
probability of the life C failing previously ; and the probability of A and
C both failing previously is — x — . Art. 101.
And it may be demonstrated in a similar way that if B die the
filth in order from the end of the term the probability of A and C failing
after B is — X -— ; therefore it is equally probable that the life of B
will ikil the 6rst or the last of the proposed lives. _ ,
Digitized by VjOOQ iC
m LI7B ANKUmES.
If A or C die firtt, it if equally probable that in the reouwto of th^
tenn B will die either second or last of the three.
If A or 0 die last, it is equally probable that B will die first or second
of the three.
We have shown that if A or G die fiist of the three it will be equally
probable that B will die second or last, and if A or C die last it is
equally probable that B will die first or second; and we hate also piored
that the probability of B failing first is the same as of his failing last;
whence it is evident that for every way in which the life of B can fail
second there is another way, equally probable, in which it can fail firsti
and a third way, equally probable, in which it can fail last
And since it is certain that B must die first, second, or third, the sum
of these three probabilities is unity, and as each event is equally pro-
bable, the fraction f is the probability of any one of them happening.
176. The probability of the three lives failing in any particular order,
as C, A, B, is 4- > for the probability of the life of C failing first is j^ as
juat shown, and the probability of A dying before B is J; therefore
^ X i s= i is the probability of the particular order of survivorship
taking place.
17*7. To find the probability of a life failing in any particular year.
' The probability of any life or lives failing in any particular yesr will
be expressed by using the letter g, in the same manner as we have used
the letter p to denote the chance of living.
Let the probability required be that a life aged m will die in the nth
year from the present time. The number now aged m, who, by the
Tables, survive n — 1 years, or, which is the same thing, enter
upon their (m + n)th year, is /«+».!« and the number who complete
their (m+n)th year is l^^, ; the difference between these is the number
who die in the nth year, which, divided by the number living at the age
of m years, gives the present chance of an individual aged m dying in
the n<h year from this time.
9^. = ^"-'r^^ = p...-. - P... . (Art. 104.)
If there be any number of lives, and we call x the probability of the
last V survivors jointly entering upon nth year, y the probability of their
jointly surviving it, and z the probability of their fiiiiling in that year,
then, since it is certain that they must either die before the nth year, the
probability of which is (1 -*-<r), in the nth year, or after it
1— » + y + «=i,
by transposition, j» s= j^ - y ; hence the following general rule. The
probability of the joint eziatence of the last v survivors of any number of
lives failing in the nth year is equal to the excess of the probability of
their jointly entering upon it above the probability of their jointly
surviving it.
Digitized by VjOOQ iC
WWBZIOVB.
in
(Art. 104.)
yrbtn ther^ are more lives .than one it may be similarly shown that
J'Cm-l.mi-l.iiir-O. I
178. To determine the probability that one, in particular, of two
given lives, A and B, aged m aad mi, shall die before the other.
This event happening in any year, as the nth, must take place from
one or other of these two events, either by A dying in that year and B
surviving it, or by both dying in the nth year, A having died first.
That tbero will die
the probability it
inthenth
year
after it
A
AandB,
A having
died first
B
r
neither
Kpi.. n^i-p^.) (Pf^,f^i-Pm^\) Art. 174.
their sun
UPrnf^l -?«.«) (Pmi. ..1 + Pt.O
is the probability of A dying before B in the ftth year, which we write
thus : —
9(w, mi), • > and 2g(«, wj), , ,
is the total probability of A dying before B in any year during the pos-
sible term of their joint existence.
179. To find 2^(«.«,).o when 2^(„h-i.-i+i).« " »▼«».
0) C)
If A and B at the ages m, mi , were certain of jointly surviving one
year, tbe probability of A dying befere B would then be Z?(i»fi;iii4+o,. ;
' 0)
but the probability of A and B jointly surviving one year is p^m, m{i,\9
therefore |?(^«,). I ?^(iM-i.^rf». • ^ ^^« probability of A dying
0)
before B after the first year, and 'the probability of his dying before
B in the first year is 4(1— p«,i)(l+l'«p i) ; the sum of the probabili-
ties of 4 djii^S before B in the fynl year, and A dying before B after
^e first year, is the total probability required.
I^(«,«»l).ii=i(l -"Pm,l) (1 +P»,. \)+Pim,mO,l X ^^o-f |, ^,44), n •
(0 0)
When the age of the older of the two lives is the oldest age in the Tablet^
Digifized by VjUU VlC
1&9 LIFE ANNUITIES.
Tg(«x«.«j4.i),» Xp(«,«^),i=^0, and the remaining part of the ezpreBsion
is easily computecl. .
180. By means of this formula a table may be formed of the pro*
bability of one life failing before another at any ages ; for, if we com-
mence with finding the probability of the event happening at the oldest,
ages they jointly complete, we can, by means of the result, find the
probability for lives ^each one year younger ; and this new probability
again enables us to find the probability on lives each one year younger
than these last ; continuing in the same manner, the probabilities can
be found for all the ages these two lives can jointly complete.
181. The probability of the failure of the joint existence of the two
lives in the next t years is 1 — />(m,i«i).o &ncl as this event must happen
either by A dying before B, or by B dying before A,
n (I) n (i)
by transposing 2 ^(«i.«), « = l-p(«.«n)i«-2 9c,«|).» •
n {») n 0)
When t is greater than the di£ference between the age of the older
life and the extreme age in the table, it becomes
(0 (')
182. The probability of the life of A failing in the next f years is
l~p«,M&Qd this event must take pkce by A dying either first, or
second of the two lives A and B :
2 7(«.«i).»+2 9(iii,«i),«=l— p«,ii
n (.) n (i)
by transposition, 2. g(«. «j)„= 1— p«., - 2 9(«.«.i).-»
n (.) n (I)
the probability of A dying second in the next t years!
When t is greater than the difference between the age of A and the
extreme age in the table it becomes
O C)
183. The probabiUty of both the lives failing in the next I yean is
(1 —!?«,<) O'^Pmi^t) I "which probability is the sura of the chances of
A dying after B in the term, and of B dying after A in the term.
2 a(«.,wi).«+2 9(,j,»),« = (l—pm^t) (I— p-i.*),
n (.) n (.)
n («) n («)
184. To find the present value of an annuity on the life of A aged
m, after the failure of the joint existence of two other lives, B and C,
aged mi and »i, , provided that event take place by the death of B,
The present value of the nth year's payment of the annuity ia
1 (0 Digitized by LiOOgle
BSVXRfllOKS. lis
and ibe value of £ 9(«i.«t,) .being variable during the possible term, of
•1 (I)
the joint existence of B and C, tbere is no other general and certain
method of calculating the present values of the annual payments during
that period, than to calculate the value of each year's payment sepa-
rately, and add the whole together.
Let the niunber of years between the age of the older of the hves B
and C, and the limiting age in the table be denoted by z, then the pre-
sent value of the annual payments to be received after that period will be
(0 T
The payment of the annuity during any of the first x yean, as the
nth, depends on the following events ; first, that A and C shall be
living, and B dead, the probability of which is P(»,«4),»— P(im«i,«,).. ;
second, that A shall be living, and B and C both dead^ B having died
first. Let y be assumed as the constant probability during the first
2 years, that provided B and C be both dead, B shall have died first
of the two, then the probability of the second event ia
y(i-p«i..) (1 —?-,.«) p«h»==y(p».---P(«,«,%«--P(«.«.,>,ii+F(ii.. »,.«.».■ )»
adding to this the probability of the first event, we have
P(«. «^. • — ^(•.■n* iiit)»»+y(P«. • ""F("»i*i).»""P(«.«»i)*« +P(«,«n.««i)»»)*
185. If the annual decrement be supposed to be constant during the
term for each of the lives, then y will become i, and the expression
will become
therefore the value of the annuity for the first z years is
i (^ — «(«/«ii) + »(«mi4) "• <*<". "i. •4) , )»
n *i '1 *i
to which if wc add 2g(«,, «^, , X flw « we have the total value,
(0 1'
•1 *1 *1 ■! (i) V
Digitized by VjOOQ IC
114 LiFB Smmras.
ASSUSANCXS ON LIVES.
186. When tn engagement is entered into to aecnre the payment of
a anm on the death of an individual, in consideration of a stipulated
single or ajunual payment, such transaction is denominated an Asmrancc
on the life of that indiyidual.
The object of the present part of this Treatise is to inyestigate rules
for determining the proper premiums, single or annual, that shoiild be
charged in difierent cases of life Awiurances.
In the yaluation of annuities the money was supposed payable at the
end of any year, in the event of the life being in existence at the end
of the year ; so, in determining the values of assurances, it is assumed
in making th(s calculations, that the money is payable, not at the exact
time of the failure of existence, but at the erid of the year in which the
failure of the particular life or lives shall take place.
The formula wiU also assume the sum assured to be ^1, from which
the value of an aasorance of any other sum may evidently be found by
multiplying by that sum.
The same letter of the alphabet will be used as the characteristic for
denoting the present value of an assurance as was used to denote the
present value of an annuity; the italic capital {A) rqprasenting the
assurance, and the small italic (a) the annuity*
18*7. To determine -^^^^^^^^^^^ » the present value of an assur-
ance on the faili^ of the joint existence of the last v survivors of any
number of lives aged m, mi, m^ &c. respectively.
The present value of the expectation of receiving the sum at the end
of the nth year is found by multiplying the probability of the event
taking place in the nth year by the present value of £l due at the end
of n years, which gives (Art. 177)
^\p
(«• Ml > Mil A«.)» n-of rimy
and if there be found the present value of the expectation of recdving
the sum at the end of each particular year during the whole time which
they may exist, the sum of these values will be the present value of £\
to be received at the end of the year in which the failure of the joint
existence shall take place, whenever that event may happen.
bat s(i+,y«p^-__^^ = ^im^m^n^L).
Digitized by VjOOQ IC
ASSUIUNCX8 ON LIVES.' )fS
uid Xd+O-Psnqr^i^.^. =(1+0- {p^.
» Pi, Mt» Ao*)! «
+;''(,H.i,^4cLa+o-'4-y(.,.,^I).«a+o^
+&c.|
but p — ^ ^y the probability of the joint existence of the last v
BurviTors at the end of 0 years, that is, of their being alive at the pre-<
sent moment is unity, and the remainbg part of the expression is
^ ' ' r(M,Ml, Mh teO»»< («b Mil «» *0.)
/.2(l+0- i»5c=^,,... =(l+0-{l + a,^^.^.j:,}
"^ 1+i
The formula
i "^tt^Cw, mi. ma, to.)
r-(l-r)g,^,,,,^^.), or
1+i
may be used with equal convenience for finding the present value, or if
the calculation be made by both methods, one will verify the other.
The first of these formula is the one employed by Mr, Milne, the
latter by Mr. Baily^ in their valuable works on the subject
188. When there is only one life the formula becomes
l-fo.
r— (1— r)a«, or
l+».
189. By Davies's method —
The present value of the nth yearns payment is found by mul-
tiplying the present value of £l due at the end of n years by the frac-
tion which has for its numerator the number who die in the nth year
from this time, and for the denominator the number living at the pre-
sent age. Let us call d^^ the number who, according to the tables, die
in the mth year of their age ; then
rdL4.i+ >^><^«+«+ r».d^+^+ .r^.d.^+ &c, &c>
Digitized by LjOOQ iC
156 LITE ANmjrriBs.
Multiplying numentor and denominator by r" :
f*^'.dL+.+r"+'. rf.t.+r"^-'.«i,+.+ &c.+&c. ,
In Tables 11 to 16, the numerator of tbit fraction is given for every
age in column M, and the denominator in column D :
190. Whea columns D and N are given witbout tbe column M, the
value of the assurance may be found by means of them alone, without
previously calculating the value of the annuity, thus :
Art. 187. i<w=r+ra«,— a«, adding and subtracting unity which
does not alter the value, it becomes
^«=l-l+r+ra„-tf«=l-(l-r)(l + a«);
and since
«,= ^, therefore ^«=l-(l-r)(l + N:^=i-(i-r)(5-+i?-).
n of the Ubles D,
but by the construction of the tables D^+N«=:N».„
Dm
191. To find the annual premium.
The first payment is usually made at the time of effecting the insur-
ance, and the subsequent premiums paid at the end of every year during
the term of the assurance ; the single premium, which is equivalent to
the payment of an annual premium of £l, is evidently
1 + a L .
(IN, mu mS, Ac.)
The following simple rule of proportion determines the annual premium :
"As unity added to the j^rcsait value of £l per annum on the given
life or lives, is to £l, so is the single premium required, to its equiva-
lent annual premium ;" or, in other words, divide the single premium
required to insure the given sum by the present value of £l per annum
on the given life or lives increased by unity :
l-(l-r)(l+fl„,,..^;^)_ 1
HM '- ~ i+fT — ^^~^^*
* («•, «i, iw^ Ao.) * (m, wt n^ ae-)
when there is only one life it becomes
By Davies's method
1 1 _ D, _ D.
1+?W "", ; Nj "^ D.+N. - N^ »
Digitized by VjOOQ IC
ASSURANCES ON LIVES. 15/
D M '
tbe innual premium is therefore =^-^ — (I-*Of '^ unce -=r^ is the
tingle premium^ this quantity divided by (l+O is
wluch is also the formula.
D« ^ l+^« ~D« ^ N^.--N^/
Rule (1). The single premium is found by adding one to the present
Tslue of .the annuity on the given life or lives, multiplying the sum by
the difference between unity and the present value of ^1 due at the end
of one year, and subtracting the product from uni^.
Or, (2) Multiply the annuity by the annual ioterest.of •?!» subtract
the pvoduet from unity, and divide by the amount of ^1 in one year.
By Davies's method :
(3) Divide the number opposite the age in column M by the number
opposite the age in column D.
Or, (4) Divide the number in column N opposite the age one year
jouDger than the given life by the number in column D opposite the
given age, multiply the quotient by the difference between unity and the
present value of ^1 due in one year, and subtract the product from
unity.
To find the annual premium :
(1) Divide the single premium by the annuity on the given life or
lives increased by unity.
Or, (2) Divide unity by the present value of the annuity increased
by unity, and from the quotient subtract the difference between unity
and the present value of £l due in coie year.
By Davies's method :
(3) Divide the number opposite the age in eolumn M by the number
opposite the age one year younger in column N.
Or, (4) Divide the number opposite the age in column D by that
opposite the age one year younger in column N, and from the quotient
subtract the difference between unity and the present value of £l due
in one year.
192, Construction of column M, Carlisle 4 per cent.
rfi«r^=A.«.r»rr* = 1 X .01980004 X .8219271 1=. 01 62141 90= Mjo*
diBy^lm-lu^r'^'i^ 2 X .01980004 X .854804 19 =.0338 503 12
• 050124502 rrMic
^'wr^^tfui-Uy^rti 2 X .01980004 X .88899636=^35204326
.085328828=M**,
(/^/•^(/Mtt-Wr'^r^ 2 X .01980004 X .92455621 = .036612500
.I21941328=Mwi
Digitized by LjOOQ iC
118
LIFE AKKUnUR
If we widi to obtain tbe tbgle and annual premium at the age of 101^
we have
M« _Mm_ .121941
s= . 414011 =amiual premium^
I N«-. Nioo .294532
193. The present value of an awurance of £l on two joint liirea i%
m heing supposed the older age.
Assume m=85, and mj=:80| the expression by the Northampton
Table will become
The expression points out a mode of constructing a table for two
joint lives similar to the coliunn M for single lives, since, by finding the
value of C«/«| for every successive combination, and taking the suc-
cessive differences between each of these products, we have a table <^
mortality for joint lives similar to that for single lives ; then multiplying
the decrements at each combination by the present value of £l due at
the end of as many years as the age of the older, we obtain the ele-
ments for forming the table the same as in single lives. The following
is an illofitrationi the rate of interest being 3 per cent : —
CombiD*tlou
ofLMat.
i;».4.=469Xl86=8'J234
28364
/;,. ^=406x145=58870
20464
/..Air=346x 111=38406
14419
L.lm=269x 83=23987
9479
/m.4>=234x 62=14508
5952
J«.?„=l86x 46= 8556
3626
/».^,= 145x 34= 4930
2266
lv.ln~nix 24= 2664
1336
Im.lm^ 83 X 16s 1328
770
Im.lH— 62 X 9= 558
374
lm.U= 46 X 4= 184
150
tu.in= 34X 1= 34
84
^.^r= 0
Digitized by VjOOQ IC
ASSURANCES ON LIVES.
159 *
160X1*2=
374Xf*ȣ=
7TOX^s=
1336 Xf*=
2266 Xr"=
166.61327
149.36031
315.97358
3686xr^*= 246.17295
562.14653
5952 X »*= 416.21020
978.35673
9479 X r^=: 682,73085
1661.08758
14419 X y*g= 1069 ,6935
2730.7811
20464 Xf^s 1563.6947
4294.4758
28364 X r*=r 2232 . 3698
8.784513
10.717674 =M„.,o
22.559799
33.277473 =Mh.*
41.840046
81,117519 =Mg,.«
85.49575
£=M»i.ai
= Mbs.m
6526.8456
The D and N columns may be constructed as in Art. 131, then from
the N and M columns may be obtained the columns S and R, Art. 116.
Age..
D
N
S
M
R
85.80
7071.661
11633.796
27374.656
6526.8456
17363.3260
86.81
4633.321
7000.475
15740.860
4294.4758
10836.4804
87.82
2934.678
4005.7974
8740.3846
2730.7811
6542.0046
88.83
1779.5088
2286.2886
4674.5872
1661.08758
3811.223!)
89.84
1044.9475
1241.3411
2388.2986
978.36673
2150.1359
90.85
598.3020
643.0391
1146.9575
562.14653
1171.7792
91.86
334.7029
308.3362
503.9184
315.97358
609.6325
92.87
175.6939
132.74237
195.58222
166.61327
293.6591
93.88
84.98378
47.758699
62.839851
81.117519
127.0458
94.89
34.668503
13.090096
15.081252
33.277473
45.92830
95.90
11.098940
1.991156
1.991156
10.^17674
12.65084
96.91
1.991156
1.9331615
1.93316
194. The £^wing example la calculated by all the rules in page
157, to enable any one at a glance to see the application of each par-
ticular rule :
Example. What single premium would be required to secure the
payment of £700 at the end of the year in whicb the existence of a
person now i^ed 85 shall fail, Carlisle 4 per cent ?
Digitized by VjOOQ IC
160 LIFE ANNUrriSS.
lat Method. 2nd Method.
1.000000 16.04123=0^
.961538-^-^ .6416492.
. 038462= 1 - r 1.0000000
2140.71= (hi+l inverted i . 04) . 3583508) . 34456
38462 312 007
26923
154
4
1
.65544
1.
.34456=if«
007
241.192
3rd Method.
M»=468.2037 and D,, = 1358.8131
1358.8137)468.2037( .34456
•••• 4076441 007
605596 241.192
543525
62071
54352
1119
6194
925
4ih Method.
N,4 = 23155. 8543 D„ = 1358.8137
1358.8131)23155.8543 (11.0412
13588131
9561.1113 (1-1.04-')= .038462
95116959 2140.11 -
560214 38462
543525 26923
16689 154
13588 4
8101 I
.65544
.34456
700
241.192
8 £241 3 10.
Digitized by LjOOQ iC
ASSURANCS9 ON UVSa I0|
What annual premium would be required to Becure the tame f
1st method,
An
1+0.
a»+l= If .0412)241.192(14. 153
•••• 110412
10780
68165
2615
1704
911
852
59
2Bd method,
n.04I2) 1.000000 (.058681
•*• 852060 .038462= \^r
147940 .020219
136330 700
11610 14.153
10225
1385
1363
22
3rd method,
lUltlS, M»= 468.2037 N^ = 23155.8543
23155.85)468.2037 ( .020219
• •• 46311 70 700
50867 14.153
46311
4556
2316
2240
4th method,
BiHe 13, ^ - (1-r) = ^ -(1 - 1.04-*)=s
IQCQ Q1Q7
^^V. Jl - -038462=3 .058681-038462= .030219
23155.85
fljcn .020219 X700=£14.153=£14 3 1.
195. It sometimes happens that persons effecting an insurance for
the ivhole term of life, wish to pay a limited number of annual pre-
miums ; the formula for finding what the premium should be (accord-
ing tX) what has been said in Art. 140), is eride^tly
Di^fized by Google
Ml Un AflBUKUIOlS.
■"(«, mi, m9» Jte.)
1+fl:
(«, «4, «» **♦)
n denoting the number of premiuma to be paid, die fint being paid at
the time of effecting the inaurance, and the remaining n — 1 at the end
of each year for n— 1 yean.
When there ia only one life we have
/?tt/(?. Divide the aingle premium by unity added to the present
value of a temporary annuity for one year less than the number of pre-
miums which are to be paid.
Example. Suppose the insurance in the last example was to be
secured by payment of 7 annual premiums, of which the first is paid
at the time of effecting the insurance, what should be the amount of
each premium ?
J^ = — 21iil^— = cr-bu. 1 «„i la)
241.192
5009 — — — — ^— — .^
(1 + 16.0412)- ——X .190315X14.8831
5oo2
241.192 241.193 ^^^ ^^^ «^^ ,^ ,,
£=£39.845=:i£39 16 11.
17.0412-10.0880 6.0532
"^^ v^"m = ^^^^^^''^^L^i^ A>t x70O-.056922x700= 39.845.
Ng«— N41 23155 . 85 — 14930 . 64
What single and annual premiums would be required to secure £250
on the death of the survivor of two lives aged 36 and 41, Northampton
3 per cent ?
1— »(fl«t-fq4i— flmi)
l+<
am =15.7288
Oti =14.6196
30.3484
aM4i=ll£213
19.3271
.03
.579813
LOS ). 420187 ( .40795
412 052
818 81590
721 20398
977 101.983 £101 19 9 aingle praniiim*
927
50 Digitized by ^^UU V WC
TEMPORAST ASSURANCES. M9
l+a«+ati—aai.4i=20.3271)101. 988(5. on=£5 0 4 annual prem.
• 1016355
3525
2033
1492
196. If at the time of effecting the insurance, a certain sum should
be paid with a view of diminishing the annual premiums to he paid
during the term of life, this sum suhtracted from the single premium
that irould be required, is the amount for which an equivalent annual
premium is to be paid ; and as the first annual premium in this case is
paid at the end of the year^ we must divide the amount by the annuity
on the life or lives.
A person aged 26 wishes to effect an insurance of ^500 payable at
lits decease, by paying an immediate sum of J^IOO, and afterwards an
annual premium during his life. What must be the amount of that
premium, Carlisle 4 per cent ?
.289005= A,
005
144.5025
100.
If .4869) 44.S025 (3.545s=£2 10 II
349118
95307
87430
1817
6994
883.
TBUFCHIART ASSURANCm
191. To find the single premium to secure a sum-payable at tht
end of the year in which the given life or joint lives shall fail, provided
that event happen within t years.
The value of the expectation of receiving the simi at the end of Hm
year IS (P^ ^^^ ,^ ^^^^^ ..i "P^^^ «^, «^ *,.), •/
in which we have
Dig ifea^y Google
U4 tl^B ASSURANCES.
«»* ^-''-y, J...-«5
fl -^(m. Ml. iiifl, *«.>• • («, Ml, M» Afcijj
and since tbe yalue of an annuity for f— 1 yeara is the same as the
value of an annuity for t years, diminished by the value of the tth. pay*
ment» which in this case is r^.p- --^. , , we obtain
when there is only one life this formula becomes
198. By Davies's method—
The single premium for a temporary assurance is found by sum*
ming the first t terms in the numerator of Art. 189, and dividing them
by the denominator /...r". The sum of the first / terms is (from the
construction of column M) evidently equal to the difference between the
number in column M opposite the present age of the life and the
number in the same column opposite the age t years older :
••'*%- d;; •
199. When columns D and N only are given, the value may be
found without previously calculating the value ot the annuity, thus!
in which
l+«o.) -^""^7,^"^'" (Art. 189);
. J _r(N.-.-N,^-. )>(N.-N.^.)
.. -««, g-
2OO. To find the aunuttl premium.
Digitized byCjOOQlC
TEMFORaRY ASSURANCES. |«9
The number of annual payments will be i, consisting of an imme-r
diate payment and of a temporary annuity for <— 1 years ; the single
premium must therefore be divided by
Art. 191. ^sr^jrro. ^^{^-^Po^,-::^^., }-( W)*
adding and subtracting l^r^.p——^^^^^ we have
-(i-r)a.
which divided by the quantity
1— r'o L + a !L •
gives for the annual premium
V^*^^-' . (l-r)>
1— r'p ^ +o
* 0", «^ «•»» A«Ot « 0»» wi* "^ ••.)
when there is only one life it becomes
By Davies's method —
The diviaor 1 + a^^^ = ^""'"T^""*"'"' • (Art. 139) 5 the formula fqr
the annual premium is therefore (Art. 198) ,
or, (Art. 199)
KN^-t-N^^„ ) - (N,-N^) D^ N^-N^
201. Rule. To find the single premium.
Multiply the present value of £1, due at the end of the given period
Digitized by KjUU vlC
\H LIPK ASBURAKOESL
of inBuiftnce, by the cliance of the given liib or livefl surviving that tenn,
then multiply the difference between the product thus found and unity^
by the present value of £l due at the end of one year ; from this result
subtract the product obtained by multiplying the present value of a tem-
porary .annuity for the some term as the assurance by the difference
between unity and the present value of £l due at the end of a year.
By Davies's method —
(2) From the number opposite the given age in column M subtract
the number in the same column opposite the age as many years older
as the insurance has to continue, and divide the difference by the num-
ber in column D opposite the age of the party at the present tune.
Or thus (3) : From the number in column N opposite the age one
year younger than the given life, subtract the number in the same
column opposite the age one year younger than the life will be at the
expiration of the term of the insurance ; multiply the difference by the
piresent value of £l due at the end of one year ; from this product sub-
traot the difference between the number in column N opposite the
present age and the number in the same column opposite the present
age increased by the number of years the insurance is to continue, and
divide by the number in column D opposite the present age.
202. To find the annual premium.
Eule, When the single premium is known^ add unity to the present
value of an annuity for the term of the assurance diminished by the
present value of the last payment of this annuity, and divide the single
premium by the result.
When the single premium is not known divide by the same result
the difference between unity and the present value of £l to be received
at the expiration of the term of the assurance, provided the given life
or lives survive that temi, and from the quotient subtract the difference
'between imity and the present value of £l due at the end of a year.
By Davies's method—
203. From the number in column M opposite the present age, sub-
tract the number in the same column opposite the age increased by the
number of years for which the insurance is effected, and divide the
result by the di£terence between the number in column N opposite the
age one year younger than the present, and the number in the same
column opposite the present age increased by one less than the niunber
of years for which the insurance is made ; or,
204. Find the difference between the number in column N oppo.
site the present age and the number in the same column opposite the
age i^jcreased by the number of years for which the insurance is e^ted,
.and divide this quantity by the difference between the numbers in the
sane coluran^ opposite ages respectively one year less than these last,
and subtract the quotient from the present value of j£l due at the end
of one year.
Digitized by VjOOQ iC
TElfFORART ASSUSANGES. }S7
Example. What is the single premium required to insure £400
payable at the end of the year in which the existence of a life aged 48
shall fiEiil, provided that event take place within the next 1 years?
(Carlisle 4 per cent.)
L •
log f'p4a.7=logrr^X £\
log/|»= log 4013 = 3.6099144
ar.oo.log/4a=&T-co.log4521 =s 4.3441655
log r' (Table 8. Part 1.)= 1.8801666
1.8354465 • 68462= r'jp^.,
logObiS log 11<2990= l>e53068a
0.8885098 1.l359=a(<|»
13.4191=g<
5.6832=0(,
1 -.r= 1 . — . 961538= . 038463
2386.5
192310
23017
3011
115
8
.218581
1.
.68462
.31538 =1— r'p^y
835169. sr inverted
'"%
283842
18923
315
158
9
2^
.303249
.218581
.084662
400
33.8648 = £33 17 9.
2nd Method—
H^^400= !2«;^^=||:^ x400=X)8466x400=33.«4
• ss^eas 17 8
Digitized by VjUVjy
le
(
168 Lira AB8UiUirCM«
3rd Method^
1.04->(N47~N54)-(Ni«-N») .96 1586(992M1 0-5193.914)
i^; X40U^ 688.073
^(9233.338-5322.850) ^_.961 538 X 4127.496 -3910.488 ^ ^^
688.073 XWU-- 688.073
3968.745-3910.488^, ^_ 68.257_
= 688:073 ^ • "" 688:073 ^ *^"^
£33.864=£33 17 3.
(2) What u the present value of an insurance of ^6400 on a life
aged 38, for the term of 7 years, Carlisle 4 per cent?
Kl -r'pm,j)'a-r)a^^^ a^m>^ =am- ^^^
log./^= log 4727 =3f. 6745856
ar. CO. log /»=ar. co. log 5194 =4.2844981
log f' (Tables. Parti.) =1.8807666
r. 8398503 .691593=r' PatT
log a4,= log 14.1046 =1.1493608.
0.9892111 9.7546=a(«>^
15.4713=0,
5.7167=00^
Kl-r'p*. 7)= .961538(1-. 691593)=. 961538X .308407
^. ^ 296544
(l—r)a^«)^=(l-. 961538) 5.7167=
.038462x5.7167 = .219875
• 296544- .219875= ♦076669
400
30.667&=£30 la 4.
(3) What is the present value of an insurance of £^00 payable at the
end of the year in "which the joint existence of two lives aged 38 and 48
shall fail, provided that event happen within the next 7 years ? (Car-
lisle 4 per cent.)
r(l -r'p(^.4g),7) — (1 -r) a^.m)^ fl(w.«)^=ai8.4i — JT'T •^^a*
log./M= bg4073 =3.6099144
log./«= log 4727 =3.6745856
ar.co.log /«• =Br.co.log 4521=4.3447655
ar.co.log /h =ar.CQ.log 5194=4.2844981
log i^(Table 8. Part l.)=l .8807666
r. 7945302 .623061
I«g Otue =s log 9 . 583 =0.9815015 Mihie,, Table 22.
0.7760317 5.9708=a(«.«)^
a„.« =11.3880 Milne, Table 22.
§i54l3^-^<«pi»^it»
TEMpORAttT A9i»UllAl|CES. 169
f(l-''p<»B.M),7) =.961538(1. -.623061)=. 362440
(l-r)tf(^,4^ =.03S462 X 5.4112 =.208357
'^ .154083 •
400
61.6332=^61 12 8.
(4) What is the present value of an insurance of «f 400* payable on
the death of the survivor of two lives aged 38 and 48, provided tha^
event take place within the next 7 years ? (Carlisle 4 per cent.)
By Example 2, r'pBs,/ =-..69159 a^ =5.7167
» 1. r^pAB^j =.68462, a^ =5.6832
1.37621 11.3999
3, y^P(39.40,y=. 62306 a<».^ =5.4172
.75315 ^ 5.9827
=6.646=£5 12 11
1-. 75315=. 24685
r{l—r^(Pm,7+P4B,7-Pc^4M)j)} =. 961538X .24685:=:. 237355
(l-r)(a^ii) +a(4io-«(»»«« ) =.038462x 5.9827=. 230107
fi f\ . f\ —
.007248
400.
Answer £2 17 0. 2.8992
(5.) What annual premium would be required for the insurance in,
lat example t
33.8648 _ 33 8648 _ 33.8648
l-^f'«.7+a(4«)"*' 1 - .68462+5.6832"" 5.9986
n
or thus : —
f^7^^^^s^-.038462V400=.014n5x400S5r.646=r£5 12 11
V 5.9986 J . .
2nd Rule.
^""^^"XIOO- 30e-'t'?95- 248.2218 014115x400-
N,-K ^^~9Mr.4104-5193.9145 ^ 400_. 01411 5X400-
5.646s:£5 12 11.
3rd Bole.
™ / N«-N„\ ,„„ / „,^„„ 9233.3.38-5322.850>v
"^""K- n;zn;;-=-^Q>^(-^^^^ - 9921.410-5^93.915)
=400.(.961538— .94'1423)=400x .0141 15=*s£5. 646.
The annual premium for the insurance in the fourth example would
be
[r--,, ^-*'Cp».>+p^.,-P(«.4^.,) (l-r)lx400 =
n n n
400>,^^-^^^^^^■ -,.03846^^^-1^^.03846 =
• A. 24685 + 5 . 9827 / 6 . 22955
(.03962— .03846) X400=. 00116 x400=£.464=iCftcflyCoOgIe
DKFBRRED ASSURANCES.
205. To find the value of a deferred assurance. '
The present value of an assurance for the first t years added to the
present value of an assurance deferred t years, is evidently equal to the
value of an assurance to be entered upon inunediately for the whole
term of life ; it therefore follows that the value of the assurance of a sum
to be received at the end of the year in which the life or lives shall fail,
provided that event take place after t years, is equal to the difference
between the value of the assurance of that sum for the whole term of
life, and of the assurance for the first t years only.
Art. 187, A. 3^ =r- (l-Oo^ ^^ .
Art. 197,^7^ i- =ir-r'*'p. -i, . -(1 -r)a. i_
the difference gives
but a- rV"" ^7 r-% = <*/ r-z the value of an an-
nuity deferred f years.
.A
(<m|,f)i^Ae.7 '— ^ Pim,mi,ni^»c),i ^ ' i«miii,iiis>Aab) ""
•'^(iii,iiiipiiis.Ac.)i< ^ ' **^(w,«n,«i^Ac.),« (M+l> iHi-M, ni+l, Ac.)
'^ (m, 111^. IRS. Ac.), t \ ^ ' 4*fK iiii+«,iiii+<, Ae.) J ""*
"^(m,«i,«8.Ac.), * C«-Kmi+l,iiia+r,Ac.)' "^^ ^^'^
206. The annual premium is found (if i premiiimB only be payable)
by dividing the single premium by
1-p !L f^+a 5L ,
' (m, m^, m^ Ac.) 1 (m, M|. ni^ Ae.)
n
or bv 1+a ^, if premium continue till the elaim.
201. By Davies's method the formula for the single premium ia
evidently -^^t being the difference between the assurance for die
whole term of Ufe, and for the first t years only ; and according to
Art. 139, the annual premium is
if the anmxal premium be payable until the time of claim, the formula
will be
"*" D«, Digitized by VjUUvIC*
DSFSEBBD AlMURAKCES. 171
To find the tingle premium.
208. (1) Multiply the pnesent value of £l due at the end of one more
than the number of years for which the insurance is deferred, by the
chance of the life or lives surviving the number of years deferred, and
subtract from this the product found by multiplying the value of a
deferred annuity for the same term, by the difference between unity and
the present value of £l due at the end of a year.
209. (2) Divide the number in column M opposite the age the life
will attain when the assurance commences, by the number in column
D opposite the present age.
210. (3) Find the value of an assurance for the whole period of exist-
ence on lives as many years older than the given lives as the assurance
is deferred, multiply it by the present value ef £l due the number of
years deferred and by the probability of the lives surviving that period.
211. To find the annual premium.
When the premium is payable only during the term the assurance
is deferred, the divisor is the same as for a temporary assurance ; but
if the premium be payable during the whole term of life^ the divisor is
the value of the annuity on the life increased by unity.
212. By Davies's Tables.
When tibe premium is payable during the term of defennent, divide
the number in column M opposite the present age increased by the
number of years deferred, by the difference between the number in
column N opposite the age one year younger than the present, and the
number in the same column opposite the present age increased by one
less than the number of years the insurance is deferred.
When the premium is payable during the whole term of life, divide
the same quantity by the number in column N opposite the age one
year younger than the present.
Example. What single and annual premium should be paid to
lecure the payment of £400 on the death of a person aged 48, provided
that event take place after the expiratbn of 1 years? (Ga;rlirie 4 per
ecnt)
7*p^yr=rXr'oaf=. 961538 X .68462=. 658288 See Ex. l.Temp.AB8«*
,038462x7. 7359=. 297531 do.
(l-r)tft«^ =.
•360751
400
144.3004 =j^l44 6
^*» A Aru^ .759918x4073 X. 526938
or thus : f'.^ -4« X 400= —- X 400
*" =.36075X400=144.300.
To find the annual premium payable until the assurance conunenees.
144. 3000 144.^ =24.056=^24 h 1. (Ex. 5. page 169.)
n Digitized by VjUUvIC
\72 LITE AS8UHA!7CB8.
To find the annual premium payable during the whole term of Hfik
144.3 144-3 ,^ ^^ ^,^ ^ „
l+fl4a 14.4191
By Daviea'a method —
M^_M„_ 248.22116
D« "" Da "^ 688.0725
248.22176 ^^ 99288.704 ,^^ «^ ^,^^ - a . i
•6l8:072r^^^'^="68O72r='^^^^ «ngleprem.
To find the annual premium.
M^ ^^_ M» 248.22176
N^.-N^.. **^^~N^-N«^*°"~9921. 4104-5793.9145 '^**"
= ^yPt— =^4.056=ie24 1 1, the annual pre-
mium payable during the term the assurance is deferred.
^x400=|H^««=^!!Jg=*,0.008=*.« 0 ,=
the annual premium payable during the whole term of life.
SURVIVORSHIP ASSURANCES.
213. To determine the present value of £l to be recaved at the end
of the year wherein a life aged m may fail, provided that life be sur-
vived by another aged mj.
By Art 178, the probability of this event happening in the nth
year is
4(p*,«-i~P«,.)(piiii.«-i+P-.i.«)=i(P(«».«i), •-! — P(*b»4),.-^P«Mi Xp«p»^
and
is the present value of the assurance.
By Art. 187, 2r" (pc,«i)»«-i— J^("».-i).«) » ^^^ present value of an
assurance payable on the failure of the joint existence of the lives
(^m.«,), and
*iii'**»i 'iif'wi *m*Si|
hm- *mi \ im+i'^mi ^«+i*^«| Wl*^«i /
and since
•iii+l***! Cfl*^m, C+1*C| /
and i=±Ll^.iL=:^,^ehaTe
2 .-.i'-,.xp^....= ff. r (1 +a^^,^,iG00gle
SURViyOSSaiP AaSUAANCES. 17$
if the present value of the insoraDce required he denoted hy i4« .^ » we
have A^^^ 1^^^. -^ r (1 + «u+..-.) + ^Xa^.,.,) .
214. This is the formula given hy Mr. Baily in his treatise on Life
Annuities : Mr. Milne's formula is
which is more convenient than the other when we have tahles showing
the probability of a single life at every age living one year, and the
reciprocal thereof, as in Table 5.
215. As the fiedlure of either of the lives will determine the event, the
divisor for the annual premium must be 14-a«,iii| •
Example. What is the present value of an assurance of £500 pay
ableoA the death of a person aged 60, provided that event take place
before the death of auoUier aged 37 ? (Northampton, 3 per cent)
^1 -to,., ^1-^^x8.1539 ^^755383^^
••* l+» 1.03 1.03
* This formula is of the flame value as the other ; for
ana 2** (yC"'» -".-!), « \ ^ ^"^«i-' . . and iu the same way it may be shown that
2**rm,%-\ XPm„« «5lLlL!!L , When the asrorance is for / years only, the
Pmr^l, I
expression will be -^ ^im^m^) + f '
Digitized by LjOOQ iC
174 UnL AWURA19CE&
(17018.909-11682.284) ^ ^11^^ = - .32550
i(.l3338+ .32550) X500s=£264.120=je264 14 5.
By the 2nd formula*^
i j^l-(l-r)(l+a^.^)+«^.^^-(i«., .^]
l"(l-r)(l+a„.aD)=l-.0291262x9.1539=:l-.26662=.l3338
0^.^ X ^ = 8.3407 X ~^= 8-67633
9.40971
4. ^ 3935
fl^j. X =- = 8.1917 X ^= 8-3&0e3
2)1.05888
.52944
500
264.720
=r£264 14 5
264.720 264.720 ^^ ^,^ ^^ ,o r *i.
l+<3^.«o 9.1539
216. The yalue ^«^ m^ of an assurance payable on the Pilule of a
life aged m, provided he die after another life aged mi is A^ — i4«,«^.
For if there be two separate insurances^ one to secure the payment
of the sum in the event of his dying first of the two, and the other in
the event of his dying second, the two together are evidently equal to
an insurance on the single life :
^*,«u +^-s «!=><«; by transposition, AJl^^^szJ^-J^
<0 W W (I)
If the annual premium be payable until the risk is determined, which
will be on the failure of the joint existence, the divisor is 1 +0^.^ ; but
if it be payable until the failiure of the life aged m, the divisor will be
l+Om.
Example 2. Let the single and annual premium be required to
secmre the sum stated in the last example on the death of the one aged
60, provided he die after the other aged 37 ? (Northampton, 3 per
cent.)
il«=l—(l-r)(l+a«)=l.-. 029126 X 10.7774= .68610
By the laat Example ^^.y=. 52944
^^ .15666
50O
'ia330=!£7a6)
Digitized by VjOOQ iC
SURVIVOWBIP AMUBAKCBS. m
78.330 78.330 ^„ ^^^ r.« ,, ^ i
n =a~TlQo = ^®*^*'— ^® ^^ ^» annual premium payable
until the mk is determined by tbe failure of one or other of the liyes.
78.330 78.330 n« ono n^ e >. I .
. =s TfTlTrii =* ^^-268 = £7 5 4, annual premium payable
until the failure of the existence of the life assured.
217. Haymg the present yaluei provided the life aged m die before
the other aged nti , we may easily obtain the present value of a sum
payable on the death of the one aged mi « provided he die before the
other aged m; for the two risks together are evidently equal to an
insurance payable on the failure of their joint existence.
-4j^«, +4mj.,=il«.«,; by transposition, A^^ =i<«,«,--^«.m, .
What single and annual premium should be paid to secure the pay-
ment of £500 on the death of a person aged 37» provided that happen
before the death of another aged 60 ? (Northampton, 3 per cent.)
AvM = .73338 see Example 1, page 173.
Jmjr — > 52944 do.
^^ .20394
500
101.970=:iPl01 19 5, single premium.
218. Whece there are more than two lives, the number of cases of
contingent assurances that may happen is very great: the limits of
this work will aot admit of such cases being investigated here, and
even when the proper formula is given for any case, the want of tables
of annuities on three or more lives is an obstacle to finding a very
correct value. For a variety of cases in three lives, formulae are given
ii the works of Messrs. Baily, Milne, and Morgan.
By Davies's Tables-r-
A^^^^l^Hn^^^^zh^, (Art. 187.)
When m— 1 is greater than m^ ,
S-'»«i N«"lt«i fszL— ^m-|,mi *m-l ^m-\,mi
Digitized by LjOOQ iC
176 LIFB ASSURANCES.
WlieD m,^ 1 is greater than tn,
330. When m— 1 ia greater than m, ,
. _l(D^,.-H<N^.-.-i-»-N.-,.^HN,...,...»W^,rH))-
1 f. I r(N,-,.,.-.+N,.u,.)-(N>^,^-.+N^^-Jl
331. When m,— I ia greater than m,
. _ljD„„+r(N....,._>-N,.„.0-N>.,...-.+N...,^\.
IJ, (N^.-.-.-N,.....)-r(N^..,...-N^,.-0^
T^e diviaor for the annual premium will be
322. When m— 1 ia greater than m,, the annual premium will there-
fore be
1 JD..-,-»-KN.-..,.-i+N^...)-(N.-..,.-.+ N^^-.)\ .
2 1 N_...^ i
223. When nii^-l is greater than m, the annual premium will be
t/D,„.+r(N^....,.-N^.._.)-N,...,.-.+N._,.^\
224. If the risk be for t years only the expression for the sini^
premium will be
and the divisor to find the annual premium,
l+a(«.s)_=l^l^(-.«0.«'^+^-i)^- By Art 199.
225. When m— 1 is greater than mj ,
Digitized by VjOOQ iC
SURVIVORSHIP ASSURANCES.
226. When mj-l is greater than »?,
'(•-». "i), "M ^-V /XT "NI
i7r
J'— 1,1
^«-i./«.r"»
/-
I>«.-i
!I±L
^->-^>n ^N,„^,>--N,^,,,4„, ^ /,,,>_ r(N^„->-N^,,^„0
P«,-M /-.C,.i^"'»"'
/.
D,
".•i
227. When m— 1 is greater than m, ,
^
+ N,
■|4<4' N,^^^ 1,^^,1
■-\
228. When Wi— 1 is greater than wi,
^(^-"n - 2 1 d;:;:;
229. The divisor for the annual premium will he
l+a(«,«i) = Hpj ;
Buhstituting, therefore^ in the denominator in each of the ahove cases,
'^m^i.mi^i-^m^^i.mru^i for D^ „, , wc liavc thc cxpression for the
annual premium.
Required the single and annual premium for the assurance of £100
payable on the decease of a person aged 60, provided another aged 20,
survive him. (Northampton, 3 per cent )
Table, p. 182,
010.99 8.81023
l+a».«= 9.59688
2621920.
191938
86371
960
192
57
2
0-
-r)(l+fl,.»)=
.279520
.720480
9.16475
9.88523
8.73941
2)
1.14582
0)
: .57291
100
Table 5, 42040.1=9^ inverted
•m
881023
35241
176
35
9.16475
a,g«=8.62683 /
50310.1 = j^ inverted
862683 "
8627
2588
43
8.78941
57.291=£57 5 10r= single premium, r^^^^i^
Digitized k^VjOOQlC
m
A.
UFB AS8TTBANCB9.
'^''^^ =.05969
l+a«o.M 9.59688 iQQ
(1)
5.969 = £5 19 5 s annual premium.
By Davies'a Tables,—
Here, m— 1 is greater than mi , the age of the life assured against.
i(
1 +
r(N,.,...-.+N,-u.H) - (N^i-.-.+N^-.--ty
N..,..,-,=N,.„=11036765.1
N..,.., =N».,= 16757653.8
33794419.5
478079.
"m,mi
N«.i,= 11036165.7
Nw.i>=: 155 14638.2
)
32551403.9
3041491155
236560937
2703553
236561
13518
32810123.24
32551403.9
DiD.»=1115240)258ll93
1.
( .14514
1115240 2) 1.14514
.51287
811953
710096
101857
88762
13095
12426
669
100
51.287 = single premium.
r(N„.„+N.,.«)-(N«.«+N«a.)=2587l9.3
0^,0=1115240.9 2
1.7036766)2033960.2 (.11938
17036166
3302836
1703677
1599159
1533308
65851
14741
05969
100
5.969 =£5 19 5
ssannual prem.
Digitized by VjOOQ IC
SURVXVOBSHIP ASSURANCES.
179
Required tbe Bingle and annual premium for the assurance of £l
])ayable on the decease of a person aged 25, provided another aged 65,
turvive him. (Northampton, 3 per cent.)
Here, mi— 1 is greater than m, the age of the life assured; the for-
mula for the single premium is therefore
40
(N«.«-N«.,) -r(N^^-N„,
»•..
0
NV^= 9520116.1
N,>.«= 8532038.2
988137.9
162420.6
1131385)825117.3
I.
(.72598
(N,
7961695 2). 27402
295478 * 13701 = single premium.
227471
68001
56869
11132
10236
896
D,„=: 1137384.9
-N,^)-r(N«.„-N«.,,)= 825717.3 2
N,4.f4= 9520176. )311667.6
2856053
260623
190403
9520176.1
9352882.9
167293.2
478079,
15056388
1171052
13383
1170
67
162420.60
(.03214
.01631 sannual prem.
10220
66641
.3579
Reipiiied the single and annual premium to insure £l payable on
tlie death of a person now aged 60, provided that event take place
vitliin 10 years, and another life aged 20, survive him. (Northamp-
ton, 3 per cent.)
(0 a 2\ 551 /?».,
'-)
(I) 5^ -itfV ' SI P»A Pl9A
101
ffl
1 _,. , ^70^80.0 , 1 232 X 4385 X. 74409391
2038x5rl32
l_4019833^5^j_^3g^3^j^_g^^g^^
10459016
Kl-P(PM*),i4i •r'0=-615659x .910874=:. 591128
JfidBzedbyCjOOgle
180 LIFE ASSURANCES.
a(««, =a^.«-r'V..05.io.a,o.«=8,59688-. 384341X6. 04334=:
fin
8.59688-2.32210 = 6.27418
(l-r)a(ao.iio =.0291262x6. 21418=:. 182743
A«o.») = • 597728- . 182743= .414985
— ^ = y-f ago.it— 7- • 7 r'^.a^M ) —
«.^«. /« «,/^oo 1312 X 4385 X . 7440931 ^ ^ ^q^q^ \ _
1.04024(8.81023 ^120x5132 ^ ^.29990 j =
1 . 04024 X 6 . 33143=: 6 . 5862 1
Pl9,l
=7-ia,t.»— — j-r .fl,g.^i —
1.01305(8.62683— 2. 33672) = !. 01305x6. 29011. =6.37219
.414985+6.58621—6.37219 ^,,^^ . , _««:.,«
= . 31450 =5 BiDgle premium.
l+fl(«.io)^ =1.27418
A«.«).ior** = .38434 ^l|iZrr -,04564= annual prem.
6.88984 6.88984
By Daviea's Method,
Here m— 1 is greater than nii , the age of the life aseured i^inst :
N,_i.«,.x=Na..«=«036766 N.+,.,.«,+,-i=Ne,.»= 4805659
N..,.«, =:Na,.^= 16757654 N^+..i.«,+i = N«.«=J714858
33794420 9520517
9520517
24273903
24273903 x .970874=23566901.2=:r{N».»t + Na^^ - N«jp - N«jo}
N.+1..1+1 =N^.«=4123360 N^,, =N.o.«= 15261525
N^^^,+,. t=N^..>=4202366 N«, ^,., =N«.„= 15514638
8325726 30776163
23566901
31892627
30776163
2)1*116464
I775241)558232(.31446=8ingle premium.
• • • ■ 582572
25660
7908
7101
807
710
9*2 . Digitized by VjOOQ IC
558232
N^.i.-N».«
PREPARATORY TABLKS.
= .04564= annual premium.
181
A Prepwalory Table for finding the Values of Annuities, &c., on Two Joint LiTCi
(Northampton 3 per Cent.)
Difference of Age 39 Years.
Ages.
D.
N.
Value.
10
49
3914694.5
43997691.3
11.23912
n
50
3664519.7
40333171.6
11.00641
12
51
3426178.9
36906992.7
10.77206
13
52
3199166.8
33707825.9
10.53644
14
53
2984184.5
30723641.4
10.29550
16
54
2780673.6
27942967.8
10.04900
16
55
2588098.3
25354869.5
9.79672
17
56
2404594.2
22950275.3
9.54435
18
57
2229077.3
20721198.0
9.29587
19
58
2061475.2
18659722.8
9.05164
20
59
1902069.0
16757653.8
8.81023
21
60
1750335.0
15007318.8
8.57397
22
61
1606805.5
13400513.3
8.33985
23
62
1472119.1
11928394.2
8.10287
24
63
134f-577.9
10581816.3
7.85830
25
64
1228933.4
9352882.9
7.61057
26
65
1119463.8
8233419.1
7.35479
27
66
1017034.6
7216384.5
7.09552
28
67
921278.4
6295106.1
6.83301
29
68
831845.3
5463260.8
6.56764
30
69
748402.4
4714858.4
6.29990
3]
70
670629.1
4044229.3
6.03050
32
71
598222.6
3446006.7
5.76041
33
72
530894.2
2915112.5
5.49095
34
73
468367.0
2446745.5
6.22399
35
74
410378.5
2036367.0
4.96217
36
75
356677.9
1679689.0
4.70926
37
76
307026.6
1372662.4
4.47083
38
77
262363.5
1110298.9
4.23191
39
7S
222672.7
887626.3
3.98624
40
79
187890.5
699735.7
3.72417
41
80
156863.9
542871.9
3.46078
42
81
128985.1
413886.8
3.20879
43
82
104331.0
309555.8
2.96706
44
83
826C6.6
226889.2
2 74463
45
84
63460.7
163428.5
2.675-7
46
85
47797.8
115630.7
2.41916
47
86
35-286.3
80344.4
2.27693
48
87
25563.9
54780.5
2.14268
49
88
18078.3
36702.2
2.03017
50
89
12758.2
23944.0
1.87675
51
90
8929.5
15014.5
1.6S145
52
91
6218.5
8795.9
1.41447
53
92
4132.0
4663.9
1.12875
54
93
2590.5
2073.5
.80043
55
94
1368.8
704.6
.51476
56
95
570.9
133.8
.23430
Digitized by LjOOQ iC
182
LIFE ASSURANCES.
A Preparatory Table for
fiadbg the Values of Annuitiet, fte^ on Two Joint lives.
(Northampton 3 per Cent.)
Di£ference of Age 40 Years*
Ages.
D.
N.
Value.
10
50
3698408.2
40847307.7
11.04457
11
51
3456918.0
37390389.7
10.81611
12
52
3228129.0
34162260.7
10.68268
13
53
3011447.3
31150813.4
10.34414
14
54
2806311.4
28344502.0
10.10027
15
55
2612182.6
26732319.4
9.86089
16
56
2428649.8
23303769.6
9.69576
17
67
2253647.2
21060122.4
9.34047
18
58
2086466.6
18963666.8
9.08894
19
59
1926901.1
17036766.7
8.84154
20
60
1776240.9
16261624.8
8.69688
21
61
1630980.2
13630644.6
8.36728
22
62
1494605.6
12136939.0
8.11983
23
63
1367466.0
10768473.0
7.87476
24
64
1248296.9
9520176.1
7.62653
25
66
1137384.9
8382791.2
7,37023
26
66
1033580.7
7349210.5
7.11044
27
67
936514.6
6412696.9
6.84741
28
63
845833.8
6666862.1
6.68151
29
69
761202.9
4806669.2
6.31326
30
70
682298.9
4123360.3
6.04334
31
71
608816.8
3614543.6
5.77274
32
72
540466.6
2974077.9
6.50281
33
73
476966.2
2497111.7
6.23641
34
74
418053.9
2079067.8
4.97318
35
75
363476.1
1716581.7
4.71993
36
76
312992.2
1402689.5
4.48123
37
n
267562.2
1135027.3
4.24211
38
78
227174.1
907853.2
3.99629
39
79
191767.2
716086.0
3.73414
40
80
1G02I3.6
556872.4
3.469S7
41
81
131837.4
424035.0
3.21636
42
82
106721.6
317313.3
2.97328
43
83
84606.3
232708.0
2.75051
44
84
64984.7
167723.3
2.58096
45
85
48973.9
118749.4
2.42476
46
86
36176.4
82673.0
2.28261
47
87
26226.5
56347.6
2.14858
48
88
18558.6
37788.9
2.03619
49
89
13111.0
24677.9
1.88223
50
90
9190.0
16487.9
1.68629
61
91
6407.8
9080.1
1.41702
52
92
4261.7
4818.3
1.13061
63
93
2674.4
2143.9
.80163
64
94
1414.7
729.22
.61546
55
95
690.7
138.66
.23469
Digitized by VjOOQ IC
PREPARATORY TABLES.
183
A Preparatoiy Table for finding the Value of Annuitiei^ kc, on Two Joint liives.
(Northampton 3 per Cent)
Difference of Age 41 Yean.
Ages.
D.
N.
Value.
10
51
3488886.7
37864025.2
10.85275
11
52
3257091.2
34606934.0
10.62510
12
53
3038710.1
31568223.9
10.38869
13
54
2831949.2
28736274.7
10.14717
14
55
2636266.9
26100007.8
9.90037
15
56
2451149.4
23648858.4
9.64807
16
57
2276098.9
21372759.5
9.39009
17
58
2109453.4
19263306.1
9.13190
18
59
1950250.7
17313055.4
8.87735
19
60
1798417.2
15514638.2
6.62683
20
61
1654187.7
13860450.5
8.37901
21
62
1517092.2
12343^)8,3
8.13619
22
63
1388353.9
10955004.4
7.89064
23
64
1267660.4
9687344.0
7.64191
24
65
1155305.8
8532038.3
7.38509
25
66
1050126.8
7481911.4
7.12477
26
67
951750.6
6530160.8
6.86121
27
68
859822.1
5670338.7
6.59478
28
69
774003.5
4896335.2
6.32599
29
70
693968.9
4202366.3
6.05556
30
71
619411.0
3582955.3
5.78455
31
72
550037.0
3032918.3
5.51403
32
73
485565.3
2547353.0
5.24616
33
74
425729.3
2121623.7
4.98350
34
75
370274.2
1751349.4
4.72987
35
76
318957.7
1432391.7
4.49085
36
77
272760.9
1159630.7
4.25145
37
78
231675.5
927955.1
4.00541
38
79
195643.9
732311.2
3.74308
89
80
163519.2
568792.0
3.47844
40
81
134652.7
434139.3
3.22414
41
82
109081.6
325057.6
2.97995
42
83
86543.9
238513.7
2.75598
43
84
66508.7
172005.0
2.58620
44
85
50149.9
121855.0
2.42981
45
86
37066.5
84788.4
2.28746
46
87
26887.0
57901.3
2.15350
47
88
19038.8
38862.4
2.04121
48
89
13459.2
25403.1
1.88741
49
90
9444.1
15959.0
1.68982
50
91
6594.8
9364.2
1.41992
51
92
4391.4
4972.7
1-13237
62
93
2758.4
2214.4
0.80277
53
94
1460.6
753.8
0.51611
54
95
610.4
143.4
0.23485
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184 LIFE ASSURANCES.
230. To find the single premium fbr the assurance of J^l payable on
the death of A, aged m, provided he die before B, aged mi, or within
t years after the death of B.
The present value of the risk during the first t years will evidently
be that of a temporary assurance for t years on the life of A, viz., A^^^
n
After the expiration of t years it wHl depend on the following events :
That A
B
The probability of which it
shall
die in
the '
nth
year
surviving it
having died within the
last t Years, including
the nth
dying in the tth year
previous to the nth ; it
being an even chance
whether they die at
such periods of the year
as shall make the in-
terval greater than t
years, or less.
(pm.n^l-Pm,n)Pm^n
►Kp«.«-i — P««.>)(p«i.ii-<-i-p-,.»-f)
their sum, i (p»i.,-/-i +;?«,.. J (jp-.«-i— /?-,«)=
will be the total probability of the event happening in any year afler
the tih ; and since
^ ^ — ^w+1-l • *W|-Hi'^"l flm^m-l '■i,+^-#-A ♦iii-l Ni|-«-l
P(w-l.m|-<-0,ii
P«-l, 1 •PfHi-.l-M+l
»■• *m| \ »m-X*»ii«|-l / *■ *mx
Pm-T, 1 'Pm^-U t
and similarly, p^. «.?«,. «-i= ^^"'"T^'"; the value of the risk in any
year after the fth will therefore h%
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SURVIVORSHIP ASSURANCES. 18S
2 lP«-i, I .p«,,_«-I,«+i Pm-I, I •P«.-«,« Piin--#-l,«+t Pin»-M f
the BuccessiTe values of which being talcen for every year after the ah,
and added to i4(«,) the value of the risk during the first t years, will give
*fl 2lp.|.i, i.Pm^^.1,I^1 P«-|.l»P«i-«,l . Pmi-f-l, <+l Pmi-t^t J
231. By Art. 161, the divisor for the annual premium will be
«(«, -ii-o^
** Pmi-t, t
232. By Davies's Tables,
233. When to— 1 is greater than 7»i-f,
^(•-1, mi-l-l) V 7 1
P»i-l,lPi»l-#-l,H-l Cl'^Mi-^-l*^"* /« '«|
*»(---% _ N,.H.,. /„-> ^ N,.H. ,. ^
the single premium is therefore
D« "^ 2D«,«,
234. When wh— < is greater than m— 1,
P»-l, I • Pai|W-i, «+l •m-I • •tiii-<-l • ^^ 'm (»i
f*t'.N,.H-..,.-.
1)-,..
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1«6 LIFE ASSURANCES.
the single premium will therefore be
SUCCESSIVE LIVES.
235. To determine the present value of a perpetuity of £l per annum
to be eptered upon after the expiration of a life aged m.
The value of £l per annum during the existence of the life, and of a
perpetual annuity of £l to be entered upon after the decease of the same
individual, are, together, evidently equal to the present value of a per-
petual annuity of £l, to be entered upon immediately. Consequently,
if from the present value of a perpetual annuity of £l to be entered
upon immediately, we subtract the present value of an annuity of £i
on a Ufe aged m, we obtain the value of the reversion. By Art. 56,
the present value of a perpetuity of £l per annum is t > the formula
will therefore be t — ^m.
i
236. The present value of a perpetuity of £i per annum being £l,
it might appear that the present value of an assurance of £l receivable
at the end of the year in which the life may fail, and the present value
of a perpetuity of £i per annum to be entered upon after the failure of
the existence of the same life, would both be of the same amount ; this,
however, is not the case, for the person entitled to the reversionary
annuity would, at the end of the year in which the life shall fail, receive
the first payment of his annuity, while the other would receive the sum
insured, which he would then have to invest ; and consequently, a year
from the investment must elapse before he would receive his first year's
dividend of £t on this sum* In order, therefore, to place him at the
time of effecting the insurance in the same situation as the other, an
insurance for the sum of £l-ft should be effected; consequently, if we
multiply the present value of the insurance of any svm by 1 + i, we
shall have the present value of the reversion of the perpetual an-
nuity which that sum would now purchase.
237. The present value of an assurance of £l (Art. 188) is - . ;
thifl multiplied by l+i, gives 1 -lo^, the present value of the rever-
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SOCCESSIVE LIVES. 187
sion of a perpetuity of £i, being the perpetuity which might be pur-
chased for £l to be entered upon immediately.
By the formula above, the present value of a reversion of a perpe-
tuity of £l is T^a^; this multiplied by t, gives l—ia^^ the value
of die reversion of £i per annum, as before.
Example. What is the present value of a perpetuity of £50 per
annum, to be entered upon after the failure of the existence of a life
aged 39 ? (Carlisle 4 per cent.)
.04)1.00
25
fl„=:15.2718
9.1282
50
486.410 s= £486 8 2.
238. An annuity is to be enjoyed during the existence of a life aged
m, and at his decease a successor is to be named who is to enjoy the
annuity during his life. Required an expression for the present value
of the annuity on the second life.
Let the value of an annuity of £l on the second life at the tune of
entering on possession be denoted by Yt , then at the end of the year in
which the existence of the present life shall cease, his successor will be
put in possession of £l^ and of an annuity whose value is Y, : the
present value of what is to be enjoyed by the second life is therefore
the present value of an insurance of (1 + Y,) pounds, payable at the end
of the year in which the existence of a life aged m shall fail, viz.,
1^(1+Y0 Art. 188.)
If to this a« be added, we have a«+ r (1+VO, the vdue of
the two succesaive lives.
239. If there be three lives, and we call the value of the annuity on
the third life at the time of entering on possession Y, , we have 1 + Y, ,
the sum of which the third life enters on possession at the end of the
year in which the second shall cease to exist. If we call the value of
the two successive lives j?, then -r — * is the present value of a per-
petuity to be entered upon at the same time. Now, when a perpetuity
and any other sum are deferred for the same time, the value of the
perpetuity at the time of entering on possession is to its present value
as the value of that sum at the time of possession is to ita present
taiue:
1+ i : 1-x :: 1+V, : ^(i+v.).
Digitized by LjOOQ IC
1S8 UFE ASSURANCES.
If j; be equal to the value of an annuity on a life aged mi , the ex-
pression will become ^ (i+V,) , which is the same thing as the
present value of an assurance of (1 + V,) pounds on a life aged m,.
From the nature of the reasoning in this article, it is evident that if
Y, be the value of an annuity on the nth life at the time of entering on
possession, and the value of the (n— 1) preceding lives be a:..!, the
present value of the nth life is ""' (1 +V0.
240. Let x^i , the present value of the (n— 1) successive lives, be
equal to an annuity certain for the term of t years, and V, be equal to
I— r*
the value of an annuity certain for ti years, then «,.i = — r-, and
the«prcMioui=Hp=:_i_[i_i + (1+0-1 = (l±^ .
and the expression 1+V,= 1H : — = : ; therefore,
i i '
the present value of the nth life in succession ; to which adding
1-r*
— r-, the present value of the (n— 1) preceding lives, we have
I |.(«+*i+0
i '
the present value of the n successive lives, which is the same as the
value of an annuity certain for ^ + /i+l years,
241. From which it appears that the effect of adding a life whose
value at the time of nomination is the same as that of an annuity certain
for the term of ^ years, is to extend the term of an annuity certain,
whose value is equivalent to that of an annuity on all the previous lives
in succession, by the term of <x+ 1 years.
242. Also, that if a., be the value of an annuity on the life in pos*
session, and V, , V, , V4 , &c., be the values of others that succeed it
at the times of their respectivie nominations, while the terms of equiva-
lent annuities certain are /, /i , ^g, t^ /, , the present value of all
the lives in succession will be the value of an annuity certain for the
term of (7+<-f <i+^+t. •..+<f) years.
243. If each of the lives which succeed that now in possession be of
the same value at the time of nomination, we shall have ^i, <» ^gj* - •+'!»
equal to each other, and the expression (g+^+^+<i+/». . . +p will
Digitized by ^^UUV IC
SUCCESSIVE LIVES. 189
become q+t+qti^^t-i-q Oi+l) ; bo that when the present value of the
life in posseBftion is the same as the present value of an annuity certain
for i years, and the value of each of the q successive lives at the times
of their respective nominations be the same as that of an annuity certain
for f| years, we shall have the present value of all the lives, the same as
that of an annuity certain for ^+ 9(^+ 1) years s that is
i
Example. What is the present value of the next presentation to a
living of the clear annual value of £500, supposing the age of the pre-
sent incumbent to be 65 years, the rate of interest 6 per cent, and that
the age of the clerk at the time of presentation will be 28 years ?
(Chester, Prob. Table 2.)
^""*^"(1+V0 t=.06 a.=a»s=1.3l51 V,=fl«=12.5987
1+t
1.3151
°« ^-Nl+V0=-^^^^^t^"-^'^^=7.58119
•442506 l + i ^ • " 1,06
1^
l-ta»= .557494 7. 681 19 x 500=3790. 595=£3790 11 11,
the value required.
PURCHASE OP ANNUITIES, &c.
244. To find the annuity to be required on a single life for a certain
amount of purchase money, so as to allow the purchaser a given rate of
interest beside the premium necessary to secure his capital by a life
sssurance:
Let s = the sum,
t = annual interest of £l,
p = annual premium for assurance of £1^
a = the annuity.
If we assume £l to be the sum advanced, and the annuity to be pay-
able at the end of the year, the last yearns interest must be assured in
addition to the principal, viz. (l + Os the annual premium for which is
p(l+>), which, subtracted from ^1, leaves
1—^^(1+0= the available principal,
l-j)(l+0 : t+p(l+t): :» : « • Tir7fZ^ = t^e annuity required.
245. If the annuity be payable until death,
1— p=the available principal,
i4-p
1—/? : t+p ::« : s —f- = the annuity.
^ Digitized by Google
190 LIFE ASSURANCES.
246. To find the principal.
If payable at the end of the year,
flss*.-; ^; ■ .^ • firom wfaidi
t+p(l+0
247. If payable until death,
^+P
248. To find (i) the rate of interest.
If payable at the end of the year,
a^ap — af)i^8i+9p+ipL
By transposition,
«{«+P(»+«)}=a-P(«+fl)f
, ^ a^p(s+a)
s+pis+a)'
249. If the annuity be payable until death.
-P
a— flp=M+^p,
a— p(»+a)
8
250. To find the annual premium,
t+p(l+0
a — ap—apizssi+sp+gpU
^ p{sil+t)+ail+i)}=a^SH
^ a—H
^^(»+a)Cl+t)-
251. If the annuity be payable until death,
a— f>
P = '
Digitized by VjOOQ iC
VALUATION OF POLICIES 191
Examples.
Required tbe sum that should be given for an annuity of £^0 payable
at the tnd of each year during the existence of a life, supposing the
purchaser to make 5 per cent interest, and to secure his capital by
effecting an assurance on the life at the rate of £2 8 per cent.
_ 1— p(l + t) _ 1-. 024 XI. 05 _ 1— .0252 _
'"* «+pCl+0 •05+.024X1.05 ^.05. + .0252^
What annuity payable at the evid ofeack year daring the existence of
a given life should be given for £648 2 9, so as to allow the purchaser
5 per cent interest, and the premium for securing his capital by an
assurance, supposing the rate £2 8 0 per cent ?
,. i±£(l+0 =648.138 .05+.024X1.05
I-p(l+l) l-.034xl.05
^^•^^^ l-.025a ='6^8-»38X-:9,48=^S0-
Required the sum that should be given for an annuity of £50 during
the existence of a given life payable vtUU the day of deaths supposing
the purchaser to make 5 per cent interest, and to secure his capital by
effiscting an assurance on the life at the rate of £2 8 0 per cent.
1-P ^ 1— .024 ^^ .916
•=«Tf?=^><:05Tl)24=^^^-:074
48 88
^^7^^=660.541=^660 10 10.
.074
Required the annuity on a given life payable until the day of decease,
that should be allowed for £660 10 10, supposing the purchaser to
obtain 5 per cent, and to secure his capital by an assurance at the rate
of £2 8 0 per cent.
.=..i±£=«0.M,x4i±^=«0.„,x^
48.88
.916
= £50.
VALUATION OF LIFE POLICIES.
252. When a policy has been in existence a certain number of years,
it frequently happens that the party possessing it is desirous of dis*
posing of his right therein, either to the office in which the assurance
was effected, or to private individuals ; the method of determining the
values of policies will therefore be shown.
Let a sum s have been assured by an individual at the time he was
Digitized by ^^UUV IC
192 LIFE ASSURANCES.
aged m years, and suppose his present age to be m+ny and that he is
desirous of disposing of his policy, on which the annual premium is just
due, but not paid ; it is required to find an expression for determining
the value.
Let us call the annual premium payable on the policy, p« ; now it is
evident that if the policy were not subject to the payment of an annual
premium, the value of it would be the single premium of assurance on
a life aged m-{-n, viz. (sA„^+^) ; but in consequence of the charge of the
annual premium on the policy the value will be reduced by a sum equal
to the present value of all the future premiums ; that is, by the present
value of an annuity of £p^ on a life aged m+n^ the first payment of
which will be made immediately : the formula will therefore be
253. If the premium has been just paid, the value of the policy will
evidently be increased by the amount of the premium, and the form
will be
»^«+«-Pm(l+a«+0+p«=«^,+«— P-.ttf .
Or the value may be faund thus :
254. If we call p«^.. the annual premium which would be charged
on the policy at the presenrt advanced age, and subtract from it p«, we
shall have the sum which the purchaser will save every year in the
payment of the premium, the present value of which will of course be
the value of the policy. When the premium is just due, and not paid,
the form is (pm+n-^Pwdi^+^m-^'^ i this expression is equal to the one
given above, for sJ^^^ = p^+, (1 +a^+,).
When the value is calculated at the same rate of interest and by the
same table of mortality as the original premium, we may obtain a form
in which the present values of the annuities are introduced, iudc-
pendent of the annual premiums ; for by Art 188, supposing the sum
assured, jf 1,
then p«+.-|j,= ^;— — ^^^. *nd (P-+.-p.)(l+a.,0=
Rule. When the premium is just due and not paid, add unity to
the present value of the annuity on the life at the time of disposing of
the policy, multiply it by the annual premium payable on the policy,
and subtract the product from the single premium which would be
charged for insuring the sum at the present age of the life in the policy.
Digitized by ^^UUV IC
VALUATION OF UFE POLICIES.* 193
Or, Take the ' di£bieiice between the premium which would be
required at the present age and the premium charged in the policy,
muhiply it by unity added to the value of the annuity at the present
age of the life in the policy.
Or, Increase by unity the value of an annuity of £l at the present
sge, and divide the sum by unity added to the present value of an
annuity of £l at the age when the policy was effected, subtract the
quotient from unity, and multiply the difference by the sum assured.
This rule applies only when the annual premium has been calcu-
lilted at the same rate per cent, and by the same table of mortality as
are used in valuing the policy.
Example. What is the value of a policy which was effected 5 years
ago at the Equitable Insurance Office for £500, on a life then aged 55,
at an annual premium of £26 113, supposing the premium just due
and not psid, and that the value is to be calculated at the same rate as
the premiums charged at that office, viz., by the Northampton, 3 per
cent.?
i.i!.+.=500{ 1 -(I— r)(l+a«)} = 500(l-. 0291262 xlO,1'774)=
500 X .686096=5343 . 048
P-(l+fff )= 26.5625x10.7114 286.273
56.775=
£b6 15 6, the value required.
Or thus : — The annual premium at 60 is £6.3661 per cent (Table 9,)
P.4,=P«= 6.3661 X 5=31 .8305
p. szp^ =26.5625
(P.+.-PJ (I +«•+.) = 5.2680X10.7774=£56.774=56 15 6.
Or thus:
1 _ l±5-=l_ 1M;41=1-.88703=.11297
l+a« 12.15
.11297 X500=:56.485=£56 9 9.
This value differs a little from the values found before, owing to the
annual premium charged on the policy not being exactly correct ac-
cording to the Northampton Table.
255. Suppose the premium, instead of being just due and not paid, to
hare been just paid, we must in that case add the amount of the pre-
miam to the value just found, to obtain the value.
£56 15 6+^26 11 3=£83 6 9.
Let us now find what will be the value of the same policy just before
the premium becomes due, when it has been in force another year ; that
ii,when it has been in force 6 years.
By Table 9,
A^, X 500= .694382 X 500=347. 191
P«(l+fl6i)=26.5625x 10.4929 =278.716
68. 475=^^68 9 6.
256. From these examples it appears that the value at the beginning
'^Digitizecflby VjUUV IC
194 Lin AflSURAMCBS.
of the yeiT immtdiately after Ae pajnent of the premimn is £83 6 9,
and that at the end of the year just before the next payment bcoomei
due, the Talue is reduced to £68 9 69 owii^ to the risk the offiee has
incurred during the interval between the two periods.
If the Talue of the poHcy were required when the poliey has been in
force 5 years and 1 months^ we must find the dindmitiott in the Talue
at the end of the year, and multiply it by that portioD of the year which
has lapsed since the payment of the premiiun, and snbtraek the itsalt
from the Tshie at the beginning of the year, thus :
'74 13 4 value at the end of 5 years 7 months.
83 6 9
83 « 9
68 9 6
8 13 5
14 17 3
74 13 4
t
104 0 9
8 13 5
INCREASINO AND DBCREASINO 8GALB8 OF PRRMIUM&
257. Suppose the annual premium to increase or decrease a certain
sum every t years, and at the end of v intervals of t years each, the
premium to continue constant during the remainder of life. What
annual premium should be required during the first t years ?
Let p=: the annual premium required,
9= the increase or decrease per £l every t years.
^ ii-> ^«-i •-» V-i-'
by transposition and division,
^ ^, T y(«cv.+«(.>^_+ac»)^.+ +«CL-.)
^ 1+a.
By substitution in the first equation,
M.__ N._, /'N«+,,.+ N,.^«,■.+N.H^,-,^^• +N.h^,>s
d;- P- -D7 ± \ BU /
from which we obtain
^m + q (N,+,.| +N,^.i,^, + W,4^i+ +N.>4^.0
«^ ""^ ■ — .
Example. What annual premium shouM be reqmred during the
first 5 years to insure Jf 100 on a life aged 31, the annual premium to
increase 4«. every 5 years, and remain constant at the end of 20 years ?
(Carlisle 4 per cent.)
<=5 «=4 9=1^ =.002
Digitized by VjOOQ iC
INCBSASING AND nCSKASIfre SCALE OF PKEHIUMS. 195
N,.+^,=xN„= aiWI-0406
N«4^i^s: N4. = 1 5933 . 8350
N«*i..i= N4s= 11414.2176
N«+4«_i=N,o= 7962.2358
57107.3290
.002
114.214658
414.0198 ^,,,„
= .01412
N^=29314.89 iqq .
1.412 =£1 8 3.
258. Instead of the praniums being reduced or increased by a fixed
ram, they may be reduced or increased arbitrari)y» prmded that in the
cue «f increasing premiums those in the first instance be sufficient to
cover the risk for the term during which they are payable ; t. e.^ not
lets than the annual premium far a temporary insurance far th^ same
term,
259. In the case of increasing premiums, the annual premit^m for
the first interval should be more than the annual premium for a risk to
be determined at the expiration of that term, as the party assured will
have the advantage over the office of continuing or discontinuing the
risk at his own option.
260. If the annual premium for the first t years be p, for the second
t years p^ , for the third p^, , &c., and the premium is to be constant
after vl years, we shall have if we call this last q,
#-*l| n^~i f|l»— 1 nw— I
iron which we obtain by transposition and division
I r=Tt fl«-i ritt-i J
1--'
a(«) denoting the value of ^an annuity for t years, to commence at the
expiration of vt years.
The expression above for A^ may be thus written^
p(N._^-N,^«,^)^^pXN>^-l-N.>^^,-,)+p,XN»f»-,-N,^■^.^)^•..■4^.N,■^.;^^
_ ,
from wnich we obtain
261. To find the value of a policy payable by increasing or decreas-
ing premtumat T^
Digi^ecJJ^yKjUUVlC
196 LITE ABSURANCn.
Let p s the premium for £l for the first t ycaw, p, for the "next i, .
years, p,y for the succeeding t^ years, &c., and call the last premium
commencing after the payment of v premiums P ; then, supposing the
last premium to have heen just paid, and t more premiums ofp each to
he payable before any variation takes place, and the age at the time of
valuation to be m, the present value of all the future premiums will be
p.«(«) + P/'«(-) + ?//.«(«)_ + +P.a(-) f
which subtracted from the single premium for the assurance at the
present age (m), will give the value of the policy, viz.,
which may he thus written :
D.
If the last premium be just due and not paid, t^., if there be (f + 1)
premiums of p each to be paid (one of them immediately), the value
will be
A^ — { ?(!+«(«) )+ p,0(«) +p,,.fl(.) + +P.0(-) },
which may be thus written :
INCREASING AND DECREASING ANNUITIES.
262. To find the value of an increasing annuity.
Let there be n perpetuities of £l per annum, the first to be entered
on immediately, the second at the end of one year, the third at the end
of two years, and so on to the nth, which is to be entered upon at the
end of n — I years. By Art* 56, the present value of the first per-
petuity is T » of the second, -r-^ , of the third, - — r-^ — , &c., and
of the nth, : ; the present value of the n perpetuities will
therefore be
l + (l + >r' + (l-ft)-'+(14-ty+..->(l+ir»~'^
i '
the numerator of this expression is unity, added to the present value of
£\ per annum forn — 1 years, (Art, 49) ; the value of the series is
therefore
1 |i^ 1-(H'0'^-^>\ _ lj(l+i)-(I+t)-t-oi ^
if from this we subtract the present value of n perpetuities, each of £l
per annum deferred n years, we shall have remaining the value of an
Digitized by ^^UUV IC
INCRBASING AND DBCREASIN6 SCALB OF PREMIUMS. 197
animity ior n yean, commencing with £l, and increasing £l each
year, viz. :
*''j\— ^^^ w(l+2)— 1= the value of an annuity for n
years, whereof the first payment is £pj the second £2pj the third -fSp,
increasing £p each payment until the expiration of the annuity.
263. If the first payment he £a, and the future payments be in-
creased by £p each year, we must add to the value just found the
present value of an annuity of a^p pounds for n years :
l-(l+»r' . »/>(! +r)-'+p{ 1 -(!+»)-<'-'>-»» (1 +{)-'}
a. : i 5 =
1-(1 + Q" . „ { (t-m) (1 +0- + 1 - (1 + 1) ( 1 + 0^}
a. . +p _ =
a. l-d + O", Jl-(l + »n)(l+0-t ,
If p be changed in sign, the decretuing annuity is
1-0 +i)-' i_(i +,„)(! +i)-
— P-
t V
Example. What is the present value of an annuity for the next
10 yean commencing at £20, and increasiDg £\0 each year, at 4 per
cent compoand interest?
1.
1.04-''= .67556417
.04
.10
.04). 32443583
m=.40
8.110896
1
02
1.4=1+1/1
162.218 .67556417
4.1
67556417
27022567
(l+trt)(l + 0-= .94578984
1— (l + tn)(l + 0"'= .05421016'
10
.04).5421016:
.04)13.55254
338.813
162. 218+338. 813=501. 031=:i501 0 a ^ .
Digitized by VjOOQ IC
196 UFB AafNuinw.
364. Let a person aged fH be entitled to n annvitiet of £l each,
payable until his decease, the first to be entered upon immediaitelj, the
second at the end of one year, the third at the e^d of two years, and so
on to the nth, which will be entered upon at the expiration of n— 1
N
yean; the present value of the first will be -=r* the present value of
N N
the second -^^ , the present value of the nth, 1^*"' ; the value of
*^m Urn
the n annuities will be
d:
Since column S, opposite each year Of age gives the sum of the
numbers in column N at each age and at all ages above — if, therefore,
from the number in column S opposite to the age m we subtract the
number in the same column opposite the age m+n, we have the sum
of the first n terms in column N ; the expression just ybtaiaed is
therefore
If all payments cease at the end of n years from this time, the
present value of each annuity will be diminished by the present value
of a life annuity to be entered upon at the expiration of n years, viz.,
-r^; subtracting ' "^^ from "I! "^^ we have
**" *^jr^ *^» ^« present valae of an
annuity for n years, the first payment being £l, and increasing by £i
annually until the end of the term.
If we multiply by p, we have
r_v_* m^ j:i2Z, the present value of an
annuity for n years, commencing at £pf and increasing £p annually.
If the first payment be iCo, and the fiiture payments be increased
annually by £p, we must add the present value of an annuity of a— p
pounds for n years, vis.,
(«--p)(N^-N,.^.)+p(S^-S^^-n.N^^)
265. If instead of p we take — p, the expression becomes
(a+p)(N„- N^)- p(S,-S,^. -».N,t.)
__ .
the present value of an annuity for n years, commencing at £a, and
• Digitized by ^^UU*^ IC
-) which ^ves
' INCRBASINO AND DICSSASINO ANNUITIES. I9f
diminishing £p asiiuilly, until die end of the term. In this case p
must not exceed r, as the annuity 'would ultimately become ne»
gttiTe.
If < be not len than the oldest age completed by any life, aocordbg
to the Tables N.^, and S.^^, each =0, and the present value of an
annuity commencing at £a and increasing £p annually to the end of
life, will be
(g — p)N,+ p.S,
If in this expression a^p we obtain ^—^ = the present value of
an annuity commencing at £p, and increasing £p annually to the end
of life.
In the expression above, if p be taken negatively we have
^-— the present value of an annuity commencing at
£a, and decreasing £p each year to the end of life.
Required the present value of an annuity for 10 years on a life aged
50, commencing at jE20, and increasing £20 annually. (Northampton
3 per cent.)
p (S«-S::^-n.N^)^.20(S^- S^-IO.N*)
D.
D»
s«=
=85391.56
61878^6
23512.70
SO
D«,=s651.102)«O25.400('721. 5'78=iei21 11 7
. i . 4561914
T«ble6,N«.s3382.I52
140626
10
130340
33821.52
10886
S«s 28057.34
;3769
61878.86
32&9
510
456
54
Required the present value of an annuity for 10 years on a life aged
30, commeneing at £50, and increasing £4 each year. (Northampton
^ ^*°^ Digitized by VjUU^Ic
9M i.mt ANcnnrm.
(a-p)(N,-N>H>4- pjS^-S^.-n.K^
(50-4) (N..-N,.) +4 (S^- S^- 10 N^)
N„=30570.053
N4,= 16545. 194
N^=: 16545.194
10
14024.859
64 = (a^p) inverted
165451.94
S^,= 209130.1
56099436
8414915
374582.04
.645143.51
S„= 446138.7
374582.0
71556.7
4
(S«-S4,-10.N4o)= 286226.8
645143.5
D,a =: 1806.562)931370.3(515.55=
9032810
=£515 11 0
280893
. 100237
90328
9909
9033
876
Required the present value of an annuity for 10 years on a life aged
30, commencing at £50, and decreasing £4 each year. (Northampton
3 per cent.)
(a+y)(N,-N^) - p (S,-S^-n.N^) _
54(N>-N^)-4(S^-S4,-10N^)
By last example, Nn— N^o^ 14024.859
45=(a+p) inverted
70124295
5609944
757342.39
By do. p(Sw-S4o-10.N^)=: 286226.8
D«=:1806.562)471115.6(260.780=£260 15 7
3613124
1098032'
1083937
14095
12646
1449
1445 Digitized by Google
INCREASING AND DBOftSASaiiO ANNUITIES.
201
Required the preflent value of an annuity on a life aged 30, com-
mencmg at £40 and increasing £5 each year until death. (NorUiamp-
ton 3 per cent)
(a-p)N,^>pS,_ (40-5)N,>^>5.S,> ;
D« ^ D,
N,= 30570.053
Sm= 446138.7
53
S
91710159
2230693.5
15285027
1069951.9
1069951.86
Dm- 1806 . 562)3300645.4 (
1806562
.14940834
14452496
488338
361312
127026
126459
567
542
25
Required the present value of an annuity on a life aged 10, com-
menciiig at £200, and decreanng £5 each year until death. (North-
ampton 3 per cent.)
(a+P)N«-^p.S,_ 205N^-5,S|,
Ny^s: 1041.824 Sj.- 6264.30
502 5
2095648 31321.50
52391
214803.9
31321.5
D,,= 155. 598) 183482.4(11 19. 209=£l 119 4 2
, 155598
21884 4
123246
1089191
14321
14003
324
811
13
Digitized by VjOOQ iC
MS Un iflBURAMOBB.
266. Tbe cohuxiM if and R being oooBtruotod for tfsmnuaceB in a
manlier omilar to N and S for annuities, if in the formiik of Art 264
we substitute M and R, for N and S we obtain
(a-p)(M,-M^,)4.p(R,-R^-n.M^)^ ^^ ^.^^^^ ^^^.^^
for an assurance on a life aged m for the term of n years, commencing
at £a and increasing £p each year during the term of the assurance.
Similarly the fmrmula of Art. 265 will become
^^ -=^= ^=-= the single prenuum
for an assurance for n years ou a life aged m, commencing at £a and
diminishing £p each year during the terra of the assurance.
If we substitute in the last two expressions N«k-i — N»4«.i for D«, in
the denominator, we shall have the expression for the annual premium.
(Art. 40.)
If n be not lest than the oldest age in the table, M„^^ and R^^ will
disappear, and the expression for an increasing assurance will become
■ * — = the single premium for an assurance on a life
aged m, commencing at £a and increanng £p each year until the
penod of decease ; and =r = the smgle premium for
an assurance on a life aged m, commencing at £a sad decxeaaing £p
each year until the time of death.
The annual premium in the last two cases will be expressed by sub-
stituting N«.i for 0M.
Required the single and annual premium to effect an assurance on a
life aged 30 for the term of 7 years, commencing at £lOQ, and increas-
ing £bO each year. (Northampton 3 per cent.)
(a-p)(M,-
-M.+.) + p (R,-R,^-n.M^)
50 (M«-
-M„) + 50 (R«-R.,- 7 M„)
Mm:=863.5541
Mw=67l.0445
192.5096
50
9625.4800
M,,=671.0445
7
4697.3115
R.r= 12994. 68
17691.99
Digitized by VjOOQ iC
INCREASING. Ara> OSCHUlSISQ ASSURANCES. 808
18439.20-11691 .99e=: H7.30 tsB^^B^^^^.M^^
50
31865.00==
9625.48
Dao= 1806. 562)46990748(26.011 =£26 0 3=
3613124 single premium
1085924
1083931
1981
1801
180
N»=32316.615
N„ =21354. 988
11021.621)46990.48(4.263=^4 5 3=
4408651 annual premium
290391
220432
69966
66130
3835
Required the single and annual premium for an assurance for 1
years on a life aged 30, commencing at £450, and decreasing £50 each
year. (Northampton 3 per cent)
(fl-fP) (M,-M^)-p (IC-IC+,-n.M^)^
500(M«»— M„)-60(R„- R^-1 .M^)
Bylart£tampl^ M^^M^s 193.9096
500
96254.80
do. 50(R«>— R,y-1>M,y)=g 31365.00
1806. 562)58889.80(32. 591=£32 11 11 =
5419686 single premium
469294
361312
101982
90328
11654
^ 16259
1395
Digitized by VjOOQ IC
204 LIFB ASSURANCES.
Nt»-NM=1102K62'I)58889.80(5.343=:if5 6 10
5510814 annual premium
378166
330649
41511
44086
3431
Required the single and annual premium to assure a life aged 60
for the whole term of existence, commencing at £l00, and increasing
£10 each year.
(a-p)M,+p.R.,_ 90]VU4-10R^
Mao= 237.3311
90
21359.853
10.R^=28022.81
D«=345. 916)49382.66 (142.759=^142 15 2
345916
1479106
1383664
95442
69183
26259
24214
2045
1730
315
NmS3728.068)49382.66(13.246=£13 4 11 =
3728068 annual premium
1210198
1118420
. 91778
74561
Required the single and annual premium to assure a life aged 60,
Digitized by ^^UUV IC
INCREASING AKD DECBSASINQ ASSURANCES. 205
commenciog at J^IOOO, and diminiahing «&20' each year until death.
(Northampton 3 per cent.)
M«= 231.3311 R^= 2802.281
0201 20
2313317 56045.62
41466
242018.3
56045.6
D«o=345. 916) 186032.1 (531. 198 =jf531 16 0= single
1129580 premium
130741"
103115
26912
24214
2158
2421
331
311
26
N«,=:3128. 068)186032.1(49. 900=rf 49 18 0 = annual prem.
1491221
369100
335525
33515
33552
23
26T. Required the annual premium to secure a sum at the end ofn
years, should a life now aged m live so long, or the return of all the
premiums in case he should die before that time.
Suppose £l the sum to be secured, and p the annual premium re-
quired; the risk in addition to that of paying the £1^ will be an assur-
ance for n years, commencing at £p and increasing £p each year, the
annual premium for which (Art. 266,) added to the annual premium
to secure £l will be
P (R^-R«»4*-^'^m^.)+D.,^, ,
and by the conditions this expression must be equal to p, viz.,
p (R,-R,.H.~«.M^) +D,^; _
N«_,-N«+,., , y^^
Digitized by VjOOQ IC
2M Lin A98URAKCM.
p(N«-i-N^.,-R^+IW.+.+nM«^^)=r D«+,
^^^
.%p^
N^-i+ R-i4-+n M^+.-N«+,.»-R. -
Example. Required the umiul prendum to secure £100 at tbe end
of 12 years to a child now aged 9» should he then be alive, the pre-
miums to be returned in the event of his dying before that time.
(Northampton 3 per cent.)
M^=:Mftfc im-460 N..,+^i=N«,= 52960.516
12^=n IC=B,= 44580.59
nM«+,= 14129. 52 97541.11
N«_,=:95813.84 = N,
R,^,!=: 1^1=27719.02
137722.38
97541.11
40181.27)271.9999 (.6769
2410876 100
309123 6.769 s=£6 15 5
281268
.27855
24109
3746
268. The annual premium for securing an annuity of Jfl to be entered
upon at the expiration of n years, and to continue during the remaining
period of existence of a life now aged m^ is rz y ■ j if, there-
fore, we substitute N„^^ for D^^. in the last formula, we shall have
N
pss — j^- ^ ~ — the annual premium to
secure an annuity of £1 on a life now aged m, t» be entered upon at the
expiration of n years, the annual premium to be reCiurned in case the
said life should fail within the n years.
Example. What annual premium should be charged to a person
now aged 40, to secure to him an annuity of £40 to be entered upon at
the expiration of 30 years, the premiums to be returned in the event
of his dying before that time?^ (Northampton 3 per cent.)
Digitized by LjOOQ IC
INCREASING AND IISOEKAftlNO ASSURANCES. dOT
M«+.=M«= 237.3317 . N^,i5=N»=: 3728.068
20 IC=R4o=n054.01
n.M«+.= 4746.634 14782.08
N«.,=:N,.= 17659.528
R^^ssR,^ 2802.281
25208.443
14782.08
10426.36 )3382.152 ( .3243
3127908 40
254244 12.972=£12 19 5
208527
45717
41705
4012
3128
.884
269. If p be the annual premium to insure £a and a return of the
premiums, the assurance is for a+P in the first instance, and an increase
of £p each year during life : we have therefore by Art. 266,
a.M^+p.IUi=p*N^t,
hy transposing, P(N«-,-R«)=a.ML,
whence, p= r^^ — - — ^— = the annual premium for the assurance of
jfa'and a return of all the annual premiums.
Requhred the annual premium fer the assurance of ^SlOO, to he paid
on the death of a person aged 40, with a return of all the premiums
paid on the policy. (Northampton 3 per cent.)
N«.i=N„=l7659.528 U^^ 599.9792
R,=R^=;1 1054.01 100
6605.52 ) 59997.92 (9. 083=^^9 1 8
5944968
54824
52844
1980
270. Suppose n payments, the first whereof is £l paid immediately,
and the remaining payments each diminished by the nth part of £l
to he paid at the end of each successive year, we shall then have for
the present value, £l the sum paid down to be added to the present
n — 1
value of an annuity for n— 1 years, commencing with £ , and
Digitized by LjOOQ iC
d08 LIFE ASSURANGSa
diminishing annually by £-; by the formula of Art. 265, this
becomes
1+ _
but + - a= 1, tlic expreuion will therefore become
n
N^.i-:i(S^-S^)
d: '
since, by the construction of the tables, Dpi + N» = N«,.i , and
SM+».i^NM.)^,.x=Sb+«; and since rr^ is the single premium for the
assurance of £1, by dividing by the expression just founds we have
— Tj — f the first premium to be required for the assur-
ance of £l on the life, supposing the subsequent payments to be suc^
cessively reduced by the nth part of the first premium, until they alto-
gether cease after n payments.
What annual premium should be chained for the assurance of £100
on a life aged 40, the premiums being successively reduced by the tenth
part of the first premium, and ceasing altogether after the tenth pay-
ment ? (Northampton 3 per cent)
S. =840=209130.1 N«-.|=N„= 17659. 528
S«+n=Sw= 85391.6
12373.85
10)123738.5
5285.68 )599.9792(. 11352=
12373.85
528568 £11 7 (
*- 714112 percent.
528568
185544
158570
26974
26428
546
Digitized by VjOOQ IC
$09
RECAPITULATION OF FORMULiE.
NOTATION.
a. =: present yalae of if I per annum on a life aged m.
A«.aii.«2.Jte. =: do. on the joint existence of the lives aged
'fit, ITOly 9II«, &C.
a- A: = do. on the joint existence of the last v survivors
■*0"* Mil at* Ac.) •*
of the lives aged m, nti , mt , &c..
a(«) 3 present value of £1 per annum for the next n years,
"^ subject to the existence of a life aged m.
A(«.«i.i"tt*e.) ^ ^^* subject to the joint existence of the lives
"^ agedm, i»i, m,, &c.
do. subject to the joint existence of the last v
"****** • -1 survivors of the lives aged m, wii , m,, &c.
a^^^ == present value of JC^I per annum to be entered upon
at the expiration of n years, and afterwards to
continue so long as a life now aged m shall sur-
vive that period.
^v>i.«i.»& Ae.) ^ do. dependent on the joint existence of the lives
now aged m, m^ , tn, , &c.
a ^-. = do. on the joint existence of the last v survivors
Cm» «1, Mi. «C.) /. 1 1. ,
^ of the lives aged m, m, , fTt, , &c.
A substituted for a in each of the above cases, denotes the present
value of an assurance of £\ for a similar term.
A^^ Ml = present value of an assurance of if 1 on the failure of
^^^ a certain life aged m^ provided another aged iR|
survive him.
-^M,*! = present value of an assurance of £l on the death of
^^ a party aged m, provided another aged nti shall
have died previously.
i4(.^M^ = present value of an assurance of £l payable at the
^'^ "^ end of the year when a life aged m shall fail, pro-
vided that event happen within the next n years,
and another life aged m^ survive him.
^(«.«i.) = do. provided the event happen after the next n
^'> '* years.
d^zs the number dying in the mth year of age. '
e«= average number of years a life aged m survives,
called the expectation.
/^=: number of living at the age m.
p^ . s —^ s probability of a life aged m living n years.
Digitized by
Google
210 LIFE ANVUITIES.
J»(...,.«,^).." = ^'X^f.'^J^'"' = *« I«tob*WUty Of any number
of lives aged m, m, , iii« , &c. jointly surviving n
yean.
p L^ = the probability of v or more of the lives aged m, w, ,
[^m, &c., aarviTing n years.
£o 'j;| s= probability of a life aged m dying before another
I aged fR|.
2fl 9m, «', = probability of a life aged m dying before another
' * ^^^ aged ftti within the next i years.
r* = the present Talue of £l due n years hence.
£ prefixed to an expression denotes tlie sum of the
values of liie variable qpiantity from the present
ages to the extseme tabular period of existence.
2^^= the sum of the first t values.
Z =5 sum of all after the first t values.
^mj N«, M^t Bmi S«9 represent the number opposite age m in the
columns so marked.
FORMULA.
Two JOINT UTBS AND THE SURViyOR (sgcd Vl^ flli).
Om+^i — o^ «i^ value of an annuity for the above period.
Thrsb LrvBS :
The value of an annuity payable so long as there shall be at least
two out of three lives in existenee aged m, frii , fnc » Ac, is
The value of an annuity payable until the death of the survivor is
TEMPORARY ANNUITIES.
The present value of an annuity for n years on a life aged m }fi
^^-^f^ — n » or a»»— -==i*.a.»+..
The present value of an annuity for n years on two joint liveM aged
m and m,, is
»(«. «l)^^— ^. wi ~ • "I ^ • 0»+-. «l+" •
, The present value of an annuity for n years on the survivor of two
lives aged m and mi is
Digitized by VjOOQ IC
211 / ,,
DBTBRBSD ANNUITIX8.
The yalue of an annuity to be entered upon at the expiration of n
years, and continued until the failure of the eziatenoe of a life now aged
m, is
The annual premium payable in n payments, the first to be made
immediately, is
^^ or • *
The single premium for an annuity on fwojaitU lives aged m and mi»
to be entered upon at the expiration of n years is
»(«, «i^ — -j — • -1 — T-.a,,,^^ „^+, ,
irhich, divided by
will give the annual premium.
The single premium for an annuity to be entered upon at the expir-
ation of n years, and then to continue until the death of the last sur^
vivor is
«(«) +0'(mi) —«(••. mi) •
In JM In
defehred temporary annuitiks.
[The single premium for an annuity to be entered upon at the expira-
tion of d years, and then to continue n years, subject to the existence of
a hfe now aged m, is
, or g- .
The annual premium payable d years at the beginning of each year, is
or it may be found by dividing the single premium by
Digitized by LjOOQ IC
212 LIFE ANNUITIES.
ENDOWMENTS.
The present value of £l to be received at the end of 71 years, pro-
vided a life now aged m, survive that term, is
the annual premium for the same, payable n years at the beginning of
each year is
L ^^ D^^n
The value of £l to be received at the end of the year in which a life
aged m shall die, provided that event happen within n years, or to be
received at the end of n years if the life survive that time is
D«
Tlie annual premium is
REVERSIONARY ANNUITIES.
On One Life afier thefaUvre of another.
The single premium for an annuity on a life aged m after the failure
of another aged mi , is
the annual premium for the same is
On One Life after the failure of the Joint Existence of two othen.
The value of an annuity on a life aged m after the failure of the joint
existence of two others aged mi and mt , is
^"•'""''"•i mi, mg >
tbe annual premium for the same is
gm-^Ow. »i. wg
On One Life after the decease of the last Survivor of two others.
f The value of an annuity on a life aged m, after the death of the last
survivor of two others aged mi and mc, is
^"'^jiiil'""^*, 1118+^, mi, ma »
the annual premium for the same is
flm — gm. mi *" Am, «!+ «». ml. m.
Digitized by LjOOQ IC
ASSURANCES. 213
On Two Joint Lives after the decease of a third.
The value of an annuity on two joint lives aged m and i?ii, after the
decease of a third aged mt , is
the annual premium for the same is
On the Survivor of two Lives after the failure of a third.
The value of an annuity on the aurvivor of two Jivea aged m and wij,
after the death of another aged mt , is
a»+a«i—a«, mi — flU. -1— «»,. .2 +0m. mi. ms i
the annual premium for the eame is
1 + «m. -,+ «-,.««— <'•^ w„ »,
ASSURANCES.
The single premium for an aasurance on a single life aged m , is
J,=r-Cl -r)flr«, orl^(l-r)(l + 0, or ^^^,
or^, orl-(l-r)-g-;
the annual premium for the same is
T+^' - 1+^ - <^ -^)' »' ic? " le - (^-'■)-
The single premium for an assurance on two joint lives aged m and
nil is
^.,;=r-(l-rK,„, or l-(l-rXl+o„..,). or ^" "'"•'•';
the annual premium for the same is
"^"•■^ ^tA — a-^)-
1+flm.m/ l+a«.mi
The single premium for an assurance on the longest of two lives
aged m and mi » is
W l-(l-0(l+«m + ami-ff«.m,),
or
J ij- * Digitized by VjOOQ IC
214 LXFX ^ASURAMCES.
the annual premium for the same is
(^.J!!!) or (!_ j,\
The single premium for an assurance on the laat v surviYors <rf aay
number of lives aged m, mi, m^ &c., is
A i- = r— (1— r)a 1- .
or i-(i-r)(l + flt;^ ^-), »r ^"'V«.i,m>>c.)
l+t
the annual premium will be
A
i
T+a 1 ' " 1 + 0 l-
(«^ «1> ■!«« Ac.) C«i «»b P» •fc)
-'-•""•^ °r,^, ' . (1-r),
TEMPORARY ASSURANCES.
The single premium for an assurance for n years on a life aged m is
^(.)^ =r.{l-^.-}-(l-r)(a«-^.'.a^). ;
____, or ;
tKe annual premium is
l-^'-+a.-^f-.«W.
or
or
-(1-r).
M„^M«
or r —
The single premium f<v an assurance ibr n years en ttoo joifU lives
aged m and m^ is
the annual premium is
A~,
111
1-
*m-|-ii 'mi+ii
or J ^ — '■ T^'^^ 2 "(l-O.
C '-i C ^wi Digitized by VjOOQ IC
DERRBSD ABSURABTCBS. £1A
The iiDgle premium for an asBorance for n years on the longest of two
lives aged m and nii is
^s^-^ *^c>., +^c-'i -^(-^ -i>; •
the annimi premimn is
A L
«1
or,
I f^m^ _|_*i|-t-« **»+> •"4+" A^i ^ I,.
-(l-r).
DEFfiRRfiD ASSURANCES.
The single premium for an assurance on a life aged m, to be entered
upon at the expiration of n years is
the annusl premium for the same payable n years at the commencement
of each year is
^ „ M,.: .
or
-1
the annual premium for the whole term of life is
or , or
The single premium for an assurance on two joint li?es aged \n and
m^, to commence at the end of 7t years is
^-•-i. =''-r'* ^'""^^"'^^ *<?''•"■*"-""'
the annual premium for the same payable n years at the commence
numt of each year is ^ r
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216 LIFE ASSURANGBS;
the annual premium payable during the whole period otjaini ewtence
(i»l-Hi
18
^(^•.,),/ '
SURVIVORSHIP ASSURANCES.
Hie single premium to assure a sum payable on the failure of a life
aged m, provided another aged nii survive him is
Am,mi = 2 1 "*"'» — -y" *■ (l+^«iH,mi)+ "1 <^m-l,iiii>»
or when ?»— 1 is greater than «ii ,'
or when nt,— 1 is greater than m.
If, (N,-,. ..-.- N^....) - r(N,...^,. -N,.„_.))
the annual premium for the same is
or when m— 1 is greater than nii ,
1 ( D,.,.+f(N,-.. .... +N„,. ,.)- (N^..„-.+N^ ,,-.))<
or when m, — 1 is greater than m,
1 ( D,.,. + r (N,-..,.-. - N.. „.. ) - N.,.. „1.+N..^ ^ ^
The single premium to assure a sum for n years to be paid on the
failure of a life aged m» provided another aged ni) survive him is,
or when m~ 1 is greater than m, ,
2 1 D....
4* N„.|.,, wn^'»4'N,,+,, w,+«-.i -^(N^ ii+N,,, wt«>i ) I ^ _
PUBCHASB OF ANNUITIBa 217
or wlien mi— 1 is greater than m»
~ 577 i'
the annual premium for the same will be
(I) 0
or by aubstitating in the denominator in the expressions for the D and
N columns, N««i,«j-i — N^+^-i.^j+.-i for D«.,„, .
FUBCHASS OF ANNUITIES, SECURING THE CAPITAL BY AN
ASSURANCE.
Let s = the sum,
i = annual interest of £l,
p z^ annual premium for assurance of «£l,
a = the annuity.
If the annuity be supposed payable at the end of each year,
l+£(l + 0
'(«+a)(H-i)'
If the annuity be supposed payable until the day of death,
I-p
s:=z a, -n — > \
1-p
a-pis-^-d)
t = ^- ,
'« + a'
VALUATION OF LIFE POLICIES.
Let s = the sum assured,
p^= the annual premium charged on a life aged m.
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218 Lin A8SUBA1ICSB.
The value of a policy that has been in ftroe n jean» ea whiok the
premium is just due but not paid, is
If the premium has just been paid the value will be
When the value of , the policy is calculated at the same rate of interest
and by the same table of mortality as the original premium was obtained
from, the value of a policy e£fected when the age of the life was m that
has been in force n years on which the premium is just due and not paid,
will be
INCaSASING AND DECREASING PREMIUMS.
If the annual premium for an assurance of £l be increased £q after
the payment of every t premiums, and remain constant after i?^ [pay-
ments, the annual pronium to be charged for the first t payments will
be
or
ic; •
If the annual premium be decreased, ijq after the payment of every
i premiums^ the annual premium for the first t payments will be
11-1 i«r~i W-i ipt-i
or
N„
If the annual premium for <— 1 for the first t years be £p, for the
second t years Pj , for the third t years p^,, &c., and the premium be
constant after vt years, this constant premium will be
where arm) > cicm) 9 &<^*t denote an annuity for t years, to be
VW-I OK-l
entered upon at the expiration of /—I years, 2^—1 years, &c.
The foUowing is also an expression for the constant premium :
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INCREASING AND DSCBEASIHG ANNUITIES. 219
If the premium for £i lor tho first t yean from the time of valuing
the policy be p, for the neit t years be p^ , for the next tj^ years p^^, &c.,
and we call the last premium which is constant after the payment of v
premiums P, and the age at the time of valuation be m, the value of
the policy, supposing the premium just paid, will be
-^«-(P-fl(m) +P/«fl(m)^ +Py/.0(».) + P.«(«) ), Or
M,~{p(N,~N^)+pXN,^.,-NV>^,>p,XN^^,^,~N^,^,^J+P.N^^,}
— _
INCREASING AND DECREASING ANNUITIES.
The value of an annuity certain for n years, commencing at £a and
increasing £p each year, is
l-(l-ht)-» I^(l-Hn)(l+0-
a. z +p 5 .
The value of a similar annuity decreasing £p each year is
^ l-a+O"" „ l~(l + i/»)(l-h»r"
The value of an annuity for n years depending on the existence of a
life aged m, commencing at £a and increasing £p each year will be
(a-p)(N^-N^)4-p(S,-S^^,^n.N^^.)
The value of a similar annuity decreasing £p each year will be
in which case p must not exceed ; , as the annuity would then ulti-
mately become ne^tive.
The value of an annuity for the whole term of life, commencing at
£a and inx)reasing £p annually, will be
(g-p)N^+p.Sw
The value of a similar annuity decreasmg annually £p will be
(a+p)N,--p.S,.
INCREASING AND DECREASING ASSURANCES.
The single premium for an assurance for n years on a life aged m,
commencing at £a and increasing £p each year, will be
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220 LIFE ASSURANCES.
The annual premium for the same will be
The single premium for a similar assurance, decreasing £p annually,
will be
_ .
The annual premium will be
(a4^p)(M,-M^)-p(R,-R»^^-n. N,^.)
\ The single premium far an assurance for the whole term of life, com-
mencing at £a and increasing £p each year will be
(a-p)M, + p.R,
D«
The annual premium will be
(a-j>)M.+j>.R,
' N^,
The single premium for a similar assurance, decreasing £p each year
will be
(a+p)M,-p.R,
The annual premium will be
n;;;:; •
ENDOWMENTS, ANNUITIES, AND ASSURANCES,
With relum of premiums in case of Death.
The annual premium to secure £ I to be received at the end of n years,
provided a life aged m survive that term, or in the event of his dying
before that time all the premiums to be returned at the end of the year
in which he shall cease to exist will be
EUj
' The annual premium to secure £l per annum to be entered upon at
the expiration of n years, subject to the existence of a life now aged m,
or in the event of his dying before that time the premiums to be re-
turned at the end of the year in which the existence shall fail, will be
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PRACTICAL RULES AND EXAMPLES. 221
N^+j;
The annual premium to assure £l and a return of all the premiums
paid will be
Suppose an assurance of £l to be provided for by payments at the
beginning of each year, the premiums being diminished at the end of
every successive year by the nth part of the first premium, so that after
n payments they shall altogether cease, the first premium will be
PRACTICAL RULES [AND EXAMPLES.
To find the value of an annuity on single and joint lives :
Find in the table the present value of -^1 per annum at the given
sge and rate per cent, and multiply by the annuity whose value is
required.
Example. What is the present value of an annuity of £10 on a life
aged 36, according to the Carlisle rate of mortality, when 6 per cent
interest is allowed ?
In Table 21, under 6 per cent opposite the age 36, we find 12.465
which, multiplied by • • • • . 70
gives 812.550s
£812 11
When tbe annuity is payable half-yearly, add .25 to the number of
years' purchase in the table; when payable quarterly, add .315.
In the above example, if the annuity be payable half-yearly, the value
will be 12.115x10 = 890.05=890 1 0; if payable quarterly, the
value will be 12. 840x10=898. 80=£898 16 0.
Example, What is the present value of an annuity of £40 payable
daring the joint existence of two lives aged 35 and 40? (Northamp-
ton 3 per cent.)
In Table 8, look for younger age 35, and opposite to 401 ., 2134
we have . . . . . . j *
which, multiplied by . . . . . 40
gives 448.536=
^448 10 9
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292 LIFE ASBtntABTCSS.
AnnuiHes on the Survivor of Two Lives.
Look in the table for the present value of jEI per annum on each
of the single lives, and subtract from the sum the value of the annuity
on the two joint lives/
Example, What is the present value of «^40 on the survivor of two
lives ag^ 35 and 40 ? (Northampton 3 per cent)
In Table 7, opposite to the age of 35 we have . • 15. 9378
ditto 40 . . 14.8416
30.1854
In Table 8, at the ages of 35 and 40 we have • . 11>2134
which, subtracted, gives • . . . .19. 51110
this, multiplied by 40 . . . . . 40
gives 182.880=
£*JS2 111, the present value of the annuity.
Annuity on Three Joint Lives.
As but few tables of the values of annuities on three joint lives have
been published, we can in general only approximate to the values by
means of the tables of values on two joint lives, which may be done in
the following manner : —
Take the present value of the annuity on the joint lives of the two
oldest, and find at what age the present value of an annuity on a single
life will be equal thereto ; the value of an annuity on the joint lives of
the youngest of the three lives and a life of the age just found will be
the value of the annuity on the three lives nearly.
In general we shall be nearer the truth if we subtract .05 from the
value just found.
What is the present value of an annuity of £M^ to cease on the
failure of the* joint existence of three lives aged 24, 36, and 56 ?
(Northampton 3 per cent.)
In Table 8, we find the value of an annuity on two joint [lives
aged 26 and 56, which by Table 1, is the value of an annuity on a
single life aged 63 nearly.
The value of an annuity on two joint lives aged 24 and 63, dimi-
nished by .05 is 1,8083
multiplied by . . , . , . 50
390.415 =£390 8 3.
Annuity on the Survivor of Three Lives.
Add together the values of the annuities on each single life, from the
sum subtract the value of the annuity on each pair of joint lives, and
add the value of the annuity on the three joint lives.
Example. What is the present value of £50 per annum so long as
any one of the three lives aged 24, 36, and 56, shall be in existence ?
(Northampton 3 per cent.)
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PRACTICAL RUL1SS AMD BSAMPLKS. 993
Value of £1 aunuity at 24 s= 17.9830
do. do. 36= 15.7288
do. do. 56= 10.8826
do. on 3 joint lives by\ _ ^ qaqq
last example ] " ^'^^^^
52.4027
30.6473
21.7554
50
1087.770 =<iei087.15 6.
Annuity at 24 and 36 s= 12.4081
do. 24 and 56= 9.3224
do. 36 and 66 = 8.9168
30.6473
Deferred Annuity,
To find the value of a deferred annuity on a lingle Hfe.
Find the value of the annuity of £l in the table opposite to the ^e
which the life will attain when the annuity is entered upon, multiply
it by the number of living in the table at the same age, and by the value
of £l due at the end of as many years as the annuity is dderred, and
divide by the living at the present age.
Or, divide the number in column N opposite the age the life will
attain when the annuity is entered upon, by the number in column D
opposite to the present age.
Example, What is the present value of £50 per annum to be
entered upon at the end of seven years, and then to continue until the
death of an individual now aged 43 ? (Carlisle 4 per cent.)
By Table 1, the number living at the age of 43 is 4869* and at
the age of 50 the number is 4397, and the present value of £1 due at
the end of seven years is . 759918, Table 4.
The present value of £l per annum at the age of 50 is 12.8690;
therefore,
4395
12. 8690 X. 75991 8 X -T^^=8.8313=valueofdeferred annuity of £l,
48 o9
and 8.8313x50=44K565=£441 11 3= value required.
Or thus :
The number in column N at the age of 50, is 7962.236
and in column D at the age of 43, is 901 . 584
7962.236
=8.8313=value of deferred annuity of ^fl,
IS before.
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901.584
8.8313X50=441. 565= £441 11 3, as before.
224 UFE ASSURANCES. :
Deferred Annuity <m Two Joint Liveg.
Multiply together the number liring at the age of each life when the
annuity ia to be entered upon by the present value of £l due aa many
yean as the annuity is to continue, and divide by the product of the
living at the present ages, and multiply the quotient by the value of the
annuity on the joint lives at their ages when entering upon the annuity.
Example. What is the present value of an annuity of £30^ to be
entered upon at the expiration of 10 years, and then to continue during
the joint existence of two lives now aged 38 and 42 ? (Northampton
3 per cent.)
Table 1, living at 38 := 3785, living at 42 = 3482, living at
48=3014, living at 52=2694. Table 4, Part 1, present value of
£l due 10 years is .744094, Table 8, the value of £l per annum on
two joint lives aged 48 and 52, is 8.6987
3014 2694 ^-^«^^ « ^^«», „ ^««», (value of deferred
■ 5Hsr-X5:JBsX-^^4094x ,8. 6981s= 3.9881=^ .^ -^i
3785 3482 l annwtyof£l,
3.9687 X30r=119.66l=£ll9 13 3 do. of £30.
Deferred AnnuUy on the Survivor of Two lAceg.
Find the value of the deferred annuity on each of the single lives,
and from the sum subtract the value of the deferred annuity on the two
joint lives.
Example. Required the present value of an annuity of £30, to be
entered upon at the expiration of 10 yeari, and then to continue until
the death of the last survivor of two lives aged 38 and 42. (North-
ampton 3 per cent.)
By Table 7, the value of £1 per annum on a life aged 48 is 12 . 9508
do. do. 52 11.9303
The number of living as in last example :
12.9508x|?i^X.744094=7.6736^^«^"* f ^^^"^.f ^"^^ °'
3785 I £1 on a life aged 38
0694
n, 9303 X^T^X. 744094=6. 8683 do. do. 42
34o^
14.5419
3.9887=1
do. by last example on the
joint lives
10.5532= do. on the survivor
30
316.5960=£316 11 ll=value rcquu-ed.
Temporary Annuities.
From the value of the life annuity to be entered upon immediately,
subtract the value of an annuity deferred the term the annuity con-
tinues.
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PRACTICAL RULBS AND EXAMPLES. 225
Or, from the number in column N opposite to the present age, sub-
tract the number in column N opposite the age at the expiration of the
annuity, and divide by the number in column D at the present age.
Example. What is the present value of an annuity of £50 for the
next seven years, subject to the existence of a life aged 43? (Carlisle
4 per cent.)
By Table 21, 14.5053= value of £l per annum on a life 43
f do. do. deferred 7 years, by
I Example m page 223,
5. 6740=: value of £l per annum for the next 7 years
50
283.7000=:i£283 14 0=r value required.
Or thus:
By Table 13, the number in column N at age 43, is 13077.739
do. do. 50, 7962.236
thedifierence 5115.503
which, diyided by 901.584, the number in colimm D at the age 43,
gives
5115.503 ^ ^^^ 1 i. «t ^ „
^, ^^^ = 5.674 svalueof £1 per annum for 7 years
901.584 50
283. 700= £283 14 0, value required as before.
ENDOWMENTS.
The present value of a sum to be received at the end of any number
of years, provided a certain party is then alive, is found by multiplying
the present value of £l due at the end of that term by the number
of living at the age the life will then attain, and dividing by the living
at the present age.
Or, by dividing the number in column D opposite the age of the
life when the money is receivable by the number in column D opposite
the present age.
A &ther wishes to provide for his son, now 10 years of age, £100
when he attains the age of 21 years ; what present sum will provide for
the same ? (Carlisle 4 per cent.)
21-10=11
By Table 4, Part 1, the present value of £l due at the end) 640501
of 11 years is • ./*
; which, multiplied by the living at 21, Table 1, . . = 6047
gives 3928.016
this result divided by 6460, the living at 10 years, gives
^^ — r=. 60805, the value of £l to be received at the age of 21
•*. • 60805 X 100=60.805=£60 16 1, value required.
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895 XIFB ANNUinSS.
Number in colmnn D opposite age 10 is 4S64.1445
do. do, 31 2653.6268
...?g3:^X 100=60. 805=£60 16 1, aa before.
4o07 • 1445
To find the annual premium :
Divide the single premium by unity added to tbe present yalue at aa
annuity on tbe life for a term one year km tban tb« number tbft muwt
lapse before the money is payable.
Or, divide tbe number in column D l>y tbe diflkrence between the
number in column N opposite the age one year younger than the pre-
sent age and the number in column N opposite t|ie age one year younger
than the age of the life when the monev is payable.
Multiplying .60805 the present value of £l to be received at the
age of 21, by 18.23196, the annuity on a life 21, we obtain 11.08594,
which BubtiBCted from
19.58339 the value of an annuity on a life aged 10,
1 8 40*745 o* 1^*^^^^ ^^ ^^ annuity of £1 for 10 years on a
^^^^ ' "" I life aged 10,
•60805= present value of the last payment thereof,
the difference 7 . 88940= value of £l per annum for 9 years on a life
aged 10,
60.805 60.805 ^ „^^ «^ ,^ ,^
1+7'.18940 = 8:88940 =^-^=^^ '^ 10, annual premmm.
D« _ 2653.62'? 265362. »?_
N.-Nw" 89828.891-51034.451 ^ ^""38794.440"" '
BBVEBSIONART ANKUITIES.
One Life on the death of another.
From the value of the annuity on the li& in expectation^ iubfract ^he
value of the annuity on tbe joint lives.
Example. What is the value of £60 per annum so long im ^ penw
aged 43 shall surviye anoflier aged 66 ? (Northampton 3 per owt,) ] i
fl^ jgi 14,1626 TaWc^
auM = 6.7124 „ a
7.4502
60
447.0120 =£447 0 3.
y To find the annual premium, divide the jsingle premium by unity
added to the value of £l per annum on the joint lives.
7.7124)477.0120(61.W0=£61 17 0
462744
142680
65556
61690
3867, Digitized by Google
PRACTICAL BULBS AVD BXAMFLES. 2Sf
On Two Joint Lives after tf^ (l^ath qfa Third.
From the value of the annuity on the two lives in expectation, sub-
tract the value of an annuity on the thcee joint lives.
Example. A and B, aged 38 and 4&, are entitled on the death of
C aged 68, to an annuity of £*10 on their joint lives : what is the value
thereof? (Northampton 3 per cent.)
Annuity on two joint lives 42 and 68= annuity on single life aged 12.
Value of £l per annum on two) ^g. hAoo
joint uves, 38 and 42 • J
do. three lives, 38, 42, and 68ss 5.3685 =anny. 38 and 12 nearly
5 •3153
70_
816.2n s£316 5 5.
Tq find the annual premium, divide by unity added to the present
value of £l per annum on the three joint lives.
6. 3685)376.271(59. 083s=£59 1 8
^ 318425
'^ 578460
573165
5295
• 5094
201
On One Life after ihefail^re qfthe joint E^tmce of Two others
. f rpin ^ pv^^nt value pf the annuity QP th# Wp in e^p^ctfttipn,
n^btr^ct tt^e aopifity op the tl^ree joint Uve§,
JS^omp/^f ^M i» the vnlue qf ftp wipwty rf iJlO oh a life »w
aged 36, after thct failure pf tha joint exiatenoe ^f \W9 Qtl^erfi ag^ 62
and 68 ? (Ijorthapaptpn 3 p^ cepti)
Table 7, annuity of £l at age 36 . . = 15 . 7288
, do. 8, annuity at 36, 62, and 68, equal 1 -_ 4 9094
annuity at 36 and 74, nearly /
10.8284
70^
757.988 = '
£757 19 9
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328 LIFE ASSURANCBS.
To find the annual premium, divide the single premium by unity
added to the value of £l per annum on the three joint liyes.
5.90936)757.968 (128.269 =
590936 £128 5 5
167052
1181872
488648
472749
15899.
11819
4080
3545
535
On One Life after the Death of the Survivor of Two others*
To the yalue of an annuity on the life A in expectation, add the value
of an annuity on the joint lives of A and the other two (P and Q,) sub-
tract the values of annuities on the joint lives of A and P, and on Uie
joint hves of A and Q.
A life aged 16 is entitled to an annuity of £40 on the death of the
survivor of two lives aged 65 and 70* What is the present value P
(Northampton 3 per cent.)
Om S19.4358 Table 7, \ aM.«=7.5613
«w.ii.7» =s 4,3541 do. 8, a„.,o=6^2378
23.7899 13.7991
13.7991
9.9908
40
399.632=:£399 12 8
The annual premium is found by adding unity to the sum of the
values of £l per annum on the joint hves of A and P, and on the
joint lives of A and Q, subtracting therefrom the annuity on the three
joint lives, and dividing the single premium by the result.
13.7991 10.4450)399.632(38. 261=£38 5 3
4.3541 313350
9.4450 86282
83560
2722
2089
633
626
7
On the Survivor of Two Lives after the Failure of a Third.
Add together the values of the annuities on each of the lives A and B
in expectation, subtract the annuity on the joint lives of A and P, the
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REVEBSIONART ANNUITIES. 229
life in poflaession, and on the joint lives of B and P, and add the
annuity on the joint lives of A, B, and C.
Example, What is the value of £50 per annum on the survivor of
two lives aged 21 and 23, after the death of another aged 58 ? (North-
ampton 3 per cent.)
annuity at 21 • =18.4*708 annuity at 21 & 58=:8.9936
do. 23 . =18.1486 do. 23 & 58=8.9514
do. 21, 23, & 58= 7.8560 17.9450
44.4754
17.9450
26.5304
50
1336.520 =^£1336 10 5.
To find the annual premium, add unity to the sum of the values of
£l per annum on the joint lives of A and P, and of B and P, subtract
the value of the annuity of £l on the three joint ^lives, and divide the
single premium by the result.
Value of £l annuity on joint lives 21 and 58=8.9936
do. 23 and 58=8.9514 ]
17.9450
7.8560
10.0890
11.0890)1336.520(120.527=^120 10 6
227620
221780
5840
5545
295
222
73
ASSUBANCESL
For the whole Term of Life {Single Premium),
Subtract from unity the present value of £l due 'at the end of one
year, and multiply the diiSerence by unity added to the present value of
£l per annum on the Ufe or lives, and subtract the result from unity,
which gives the present value of an assurance of £l.
When the assurance is on one life only, divide the number in column
M opposite the age of the life by the number in column D ; or.
Multiply the number in column N opposite to the age one year
younger than that of the given life by the difiPerence between unity and
the present value of £l due at the end of one year, divide by the number
in column D at the present age, and subtract the result from unity.
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S80 UFA ASSURANCES.
Annual Premium.
Ditide the single premium by unity iMlded to the tldue of £l per
aftmudi on the life or Hves i Or,
Divide unity by the present value of an annuity of £1 ou {he ^ven
life or lives increased by unity^ and from the quotient subtract the dif-
ference between £l and its present value at the end of one year ; the
result will be the annual premium ftr the aesurailcd of £l.
When the assurance is on a single life
Divide the number in column M opposite to the present age by the
number in column N opposite to the age one year younger ; or,
Divide the number in column D opposite to the present age by the
number in columtt N opposite to the age one year younger^ and subtract
from the quotient the difierence between unity and the present value of
£l receivable at the end of one year.
Example, What is the single premium that should be paid to secure
£200 at the end of the year in which a person now aged 46 shall cease
to exist ? (Northampton 3 per cent.)
By Table 7, the value of £l per annum at the lige of 46 increased
by unity, is 14.4498, and by Table 4, Part 1,
1— .910874 r= .029126= difference between unity and the present
value of £l to be received at the end of one year.
i-(l4. 4498 X. 029126)=!— .47085 =.57915 fi= the single
premium for an assurance of £\^ therefore
•57915X200=115. 830=£115 16 7= single premium required.
For the annual premium we have
or, JT-Tigs " •^29126 = .06921 - .02913 = .04008 = annual pre-
mium for assurance of £l ;
therefore .04008x200= 8. 016 =£8 0 4, as before.
Example 2. Required the . single and annual premium to insure
£200 on a life aged 56, Carlisle 4 per cent.
By Table 13, the tiUmber m column M opposite to the age 56 is
240.1036, tod the bumber in column D 444.8289;
therefore, by the rule, |^54S^^0=='S3977Xfi002!4107.954sS
£107 19 l=Bingle premium^
The number in column N» opposite to the age of 55 ii 5523 .IMde,
240 1086
therefore, ^^^^'^^^^x 200=. 045 11 x200=9. 022=1^9 0 5 =tha
annual ptetaiium.
Digitized by LjOOQ iC
AMURANCES. 231
Example 3. Required the single and annual premium to iniure
£250 on tlie joint Uves of two pereons aged 36 and 41. (Northampton
B per cent.)
The difference between unity and the present value of £l due at the
end of oue year 1— • 9'708740=: .029126.
Bj Table 6| the value of the annuity on the joint lives inoreased by
uaity is 13.0313.
l-(12.0213x .029126)=!- .36Oiacs*6498'7ssnn9/0 premum for
asBuranoeof £l;
iheiefore, •6498*7 X 2505=162.46123162 9 4 single premium requited.
For the annual premium we have
r^r-i-—-^,029l26a5. 083186 - .029126= .054060 = annuo/ pre-
12.0213
mium for assurance of £l.
.054060 X 250= 13. 51 5=£13 10 3.
EaampU 4. What single and annual premium should be required
to secure d^250 at the end of the year in which the survivor of two lives
Aged 43 and 45 shall cease to exist ? (Northampton 3 per cent)
Table 7| the value of £l per annum on a life aged 43 is =14. 1626
do. do. do, 45 =13.6920
27.8546
Table 8, do. on two joint lives aged 43 and 46= 9.9703
p. 222» Value of £1 per annum on the survivor of the) .^ gQ4Q
two lives . • J "^
Therefore, 1— (18.8843X .029126)=l-.55003=.44997=
single premium for £L
•44997 X. 250=^^112.492=112 9 10=single premium required.
For the annual premium we have
^ -.029126=4052954— .029126=.023828 = annual prem.
18.8843
for£l;
dierefore, .023828x250= 5 .957 =£5 19 2=annual prem. required.
JSjMfMpIs 5. Required the single and annual premium to secure
£400 on the failure of the joint etisteuc^ of three Uves aged 38, 45,
and 64. (Northampton 3 per cent.)
By Table 8| the vidue of £l annuity on two joint lives aged 45 and
64 is 7.0536, which by Table % is equal to the value of the annuity on
abingle Ufe aged 69; the value of £l per annum on two joint lives
aged 36 and 69 is 6.1608^ which, diminished by .05, gives 64 1108,
the value of £l per annum on three j<mit lives aged 38) 45, and 64
(page 222.)
1— (.029126x7. 1108) = 1— .20711=. 79289= single premium for
assurance of £l ;
flMHAfe, i79ae9x400BB8317. 156^^817 3 Osssingle prem. required.
Digitized by ^^UUV IC
232 LIFE ASSURANCES.
: For the annual premium we have
—i— --.02913==. 14063—. 02913==. 11150==annualprem.for^l J
therefore . 11150 x 400=44 •600:=:£44 12 0 = annual prem. required.
' Example. Required the single and annual premium for the insur-
ance of ^400 on the death of the Burrivor of three Uvea aged S8| 45,
and 64. (Northampton 3 per cent)
15. 2975 rvalue of £l per annum on a life aged 38, Table 1,
13.6920= do. do. do. 45,
8.6115= do. do. do. 64,
6.1108= do. by laat example on three joint lives
43 .71 18 aged 38, 45, and 64.
10 4026=1^*^'"®^^^^ ^ annum on two joint lives aged 38 and 45,
\ Table 8,
7.3152= do. do. do. 38 and 64,
7.0536= do. do. do. 45 and 64,
24.7714
43.7118^24. 7714=18. 9404=value of £l per annum on [the sur-
vivor of three lives aged 38, 45, and 64 (page 222)
l-(19.9404x .029126)=!— .58077=. 41923=single prem.for £1
. 41923x400=167. 692=£167 13 I0;:zsingle premium reqmTtd.
For the annual premium we have
i^ —.02913= .05015— .02913= •02I02sann. prem. for £],
.02102X400=8.408=^8 8 2= annual premium required.
TEMPOBART ASSUBANGES.
Find the present value of £l at the end of the term subject to the
existence of the life or lives, subtract it from unity, and multiply the
difference by the present value of £l due at the end of one year ; from
the result subtract the present value of £l per annum on the life or
lives for the term, multiplied by the difference between unity and the
present value of £l due at the end of a year.
Or, When the assurance is on a single life, divide the difierence be-
tween the numbers in column M at the present age, and at the age which
he would attain, on surviving the term of assurance by the mimber in
column D at the present age.
To find the annual premium :
Find the present value of the expectation of receiving £l at the end
of the term, subject to the existence of the lives ; subtract it from unity.
Digitized by ^^UUV IC
TEMPORARY ASSURANCES. S33
and divide the difference by the diffisrence increased by the value of j£l
per annum for the term on the given lives ; from the quotient take the
difference between imity and the present value of £l due at the end of
one year.
When there ia only one life
Divide the difEerence between the numbers in column M at the present
age, and at the age which the party would attain on surviving the term
of the assurance, by the difference between the numbers in column N
at ages respectively one year younger than taken for column M.
Example 1. What is the present value of an assurance of £200
for seven years on a life aged 36 7 (Northampton 3 per cent.)
Table 1, living at 36=:3935, living at 43=3404,
Table 4, Parti, the present value of iSl due 7 years s. 813092
do. do. I year =.970874
3404
•5—- =.865057= expectation of life surviving seven years,
. 865057 X. 813092= .703371 rvalue of expectation of receiving £1
at the end of the term,
1-. 703351 = .296649,
. 296649 X . 970874s. 2880087i
By Table 7i the value of £l per annum on a life aged 36=15.7288
do. do. 43=14.1626
: 15.7288— (14. 1626X .703371)=15. 7288— 9.9616=5.7672=
value of temporary annuity for seven years,
.2880087-(.029126x 5.7672) = .2880087- .167975s:* 120034 =
single premium for assurance of £l,
.120034x200=24.0068=^^24 0 2=single premium required.
.296649 ^„^,^ .296649 ^^,«
-.0291 3= -s-T^s— - — . 0291 3=
.296649+5.7672 6.0638
• 04892 - . 02913= .01979=annual prem. for assurance of £l,
.01979X200=3.958=^3 19 2 do. £200.
Example 2. Required the single and annual premium for an assur-
ance of j^300 for 6 years on a life aged 36. (Carlisle 4 per cent)
Number in col. Mat 36= 454.802
do. 42= 377.064
do. in col. D at 36=1293.150
454.802—377.064 77.738
Number in col. N at 35=21797.041
do. 41=14930.643
6866.398
= .06012=Bingle premium for assur-
1293.150 1293.150
ance of £l,
.06012x300= 18. 036 =£18 0 9 single premium for £300.
Digitized by ^^OOQ IC
9U
LIFE AflSURANGX&
For the aninial premiiini^ .i
'^ ^ '= .0li32:=!annual premium for aasurance of £l tot 1 ycAti,
6800 k 3 VO ^QQ
3.396=£3 7 11
do.
£300.
ASSURANCE ON ONB LIFE AGAINST ANOTHEIL
To find the single premium to seeure a sum payable oti the death ef
A» provided he die before B :
First, find the present value of an assurance of £l on the two joint
liteS} then find by the tables the Value of an atinuity of £1 on two joint
lives, one a year younger than A, the other of the age of B, alld divide
it by the probability of a life one year younger than A living one year ;
add the result to the present value oi the assuranoe of £1 on the joint
lives.
Then subtract the value of an annuity of £1 on the two joint lives,
one the age of A^ the other one year younger than B» divided by the
chance of a life one year younger than B living one year.
The difference divided by two will be the value of an assurilmce of £1
on the death of A, provided he die before B.
The annual premium is foulid by dividing the single premium by the
value of an annuity of £l on the joint lives of A and B inaeased by
unity.
Example. What smgle and annual premium should be charged to
insure £500 on the death of a person aged 38| provided another aged
43, survive him ? (Northampton 3 per cent.)
10.6349 value of annuity at 38.43,
.0(19136
9436.11
29126
2913
1747
87
12
2
.33687
•66113
10.92930
11.59043
10 « 98995
2). 60048
•30024
005
lO.inOrs do.
87.43,
10.1438= do.
38.43.
e 5, age 87, 1^019810
Table 9, age 42,
1.0122910
0717.01
8347.01
1019810
1022910
71387
71604
1020
4092
713
307
10.92930
82
10.98995
11.6349) lSO.iaO(12.908s£l2 18
^ - 116349
ana. pran. ^
33771
23270
10501
10471
.30
150il20ca£l60 2 & sitigle premium.
Digitized by VjOOQ iC
tABtS t.
935
IWe of RalM of Mortality
Dy 6. Danes, Esq.,
at Northampton, Carlisle, the Equitable Insunmce Office
and according to the Observations of Des Pardeux,
NorUumptoa
Carllcle.
Dm
Paicieox.
Bqnit-
afile.
Nortii-
«fflpton.
Carliil*.
Deg
Pareietti.
Mt
1
i
1
f
I
Ufteg.
Lhtor
1
i«s.
tag.
1
lag.
^i.
tit.
3000
^
Q
o
Age.
2612
82
4211
1
68
549
IT
1826
(
0
11650
10000
1539
53
41
1
8650
1367
8461
68^
54
2530
82
4143
70
538
12
1785
41
«
7283
502
7779
505
55
2448
82
4078
73
526
12
1744
42
3
6781
335
7274
276
1000
30
56
2366
82
4000
76
5l4
12
1702
43
4
6446
197
6998
201
970
22
57
2284
82
3924
82
502
13
1639
44
5
6i49
184
6797
121
948
18
58
2202
82
3842
93
489
13
1615
45
6
606^
140
6676
82
930
15
59
2120
82
d74d
106
476
13
1570
46
f
5925
110
6594
58
915
13
60
2038
82
3643
122
463
13
1524
46
8
5815
80
6536
43
902
12
61
1956
82
3521
126
450
13
1478
46
9
5735
60
6493
33
1890
10
62
1874
81
3395
127
437
14
1432
47
10
5675
52
6460
29
880
8
2844
11
63
1798
81
3268
125
423
14
1385
48
11
5623
50
6431
31
872
6
2883
11
64
1712
80
3143
125
499
14
1337
49
12
5573
50
6400
32
866
6
2822
12
65
1632
80
3018
124
395
15
1288
50
13
5523
50
6368
33
660
6
2810
12
66
1552
80
2894
123
380
16
1238
51
14
9473
50
6335
35
854
6
2798
13
67
1472
80
2771
123
364
17
1187
52
19
5423
50
6300
39
848
6
2785
14
68
1392
80
2648
123
347
18
1135
53
16
5373
53
6261
42
842
7
2771
15
69
1312
80
2525
124
329
19
1082
54
19
5320
58
6219
43
835
7
2756
16
70
1232
80
2401
124
310
19
1028
54
18
5262
63
6176
43
•828
7
2740
17
71
1152
80
2277
134
291
20
974
55
19
5199
67
6133
43
*82)
7
2723
18
72
1072
80
2143
146
271
20
919
55
29
5132
72
6090
43
814
8
2705
18
73
992
80
1997
156
251
20
864
56
21
5060
75
6047
42
806
8
2687
18
74
912
80
1841
166
231
20
808
56
22
4985
75
6005
42
798
8
2669
19
75
832
80
1675
160
2ll
19
752
55
23
4910
75
5963
42
790
8
^650
19
76
752
77
1515
156
192
19
697
55
24
4835
75
5921
42
782
8
2631
20
77
675
73
1359
146
173
19
642
54
25
4760
7$
5879
43
774
8
2611
20
78
602
68
1213
132
154
18
588
54
26
4685
75
5836
43
766
8
2591
21
79
634
65
1081
128
186
18
534
54
27
4619
75
5793
45
758
8
2570
22
80
469
63
953
116
118
17
480
54
28
4535
75
5748
60
760
8
2548
23
81
406
60
837
112
101
16
426
63
29
4469
75
5698
56
742
8
2525
24
82
346
57
725
102
85
14
373
52
39
4385
75
5642
57
734
8
25U1
24
83
289
55
623
94
71
12
321
50
31
4310
75
5585
57
726
8
2477
25
84
234
48
529
84
69
11
271
47
39
4235
75
5528
56
718
8
2452
26
65
186
41
445
78
48
10
224
43
33
416Q
75
5472
55
710
8
2426
26
86
145
34
367
71
38
9
181
38
34
4985
75
5417
53
702
8
2400
26
87
111
28
296
64
29
7
143
32
35
4010
75
5362
65
694
8
2374
27
88
83
21
232
51
22
6
111
26
36
3935
75
5307
56
686
8
2347
27
89
62
16
181
39
1^
5
85
20
37
3860
75
5251
57
•678
2320
28
90
46
12
142
37
ii
4
65
16
38
3785
75
5194
58
"671
2292
28
91
34
10
105
30
7
3
49
13
39
3710
75
5136
61
664
2264
28
92
24
8
75
21
4
2
36
11
49
3635
76
5075
66
657
2236
28
93
16
7
54
14
2
1
25
9
41
3559
77
5009
69
650
2208
28
94
9
5
40
10
1
1
16
7
42
3482
78
4940
71
643
2180
28
95
4
3
30
7
0
0
9
5
43
3404
78
4869
71
636
2152
29
96
1
1
23
5
4
3
44
3326
78
4798
71
629
2123
30
97
18
4
1
1
4$
3248
78
4727
70
622
2093
30
98
14
3
46
3170
78
4657
69
615
8
2063
30
99
11
2
47
3092
78
4588
67
607
8
2033
31
100
9
2
48
3014
78
4521
63
599
9
2002
32
101
7
2
49
2936
79
4458
61
590
9
1970
33
102
6
2
50
2857
81
4397
59
581
10
1937
35
103
3
2
59
2776
2694
82
82
4338
4276
62
65
571
660
11
11
1902
1865
37
39
104
Dili
izecf
ly VJ
3C
,?■•
TABLE n
Comparative View of the Ezpectatioiia of Life at different Places.
Sweden.
Age.
Cheit«r,
Cheiter,
North-
Carlisle.
Bquitoble
Malefc
Des
Govt.
Govt
Males.
Females.
amptoQ.
(Daviet).
Female.
Pavdenx.
Males.
Females.
0
34.46
39.44
26.18
38.72
60.16
65.51
1
40.80
44.52
32.74
44.68
42.95
50.13
66.59
2
43.78
45.22
37.79
47.65
44.92
50.04
55.37
3
45.52
49.17
39.65
49.82
46.11
47.71
49.80
55.05
4
46.41
50.13
40.58
50.76
46.78
48.17
49.42
64.65
5
46.45
50.57
40.84
51.26
46.79
48.27
48.93
54.23
6
46.39
50.42
41.07
61.17
46.66
48.20
48.36
53.72
7
46.17
49.96
41.03
50.80
46.43
47.98
47.71
63.15
8
45.78
49.30
40.79
50.24
46.07
47.66
47.02
52.50
9
44.89
48.59
40.36
49.57
46.61
47.30*
46.30
61.80
10
44.47
47.82
39.78
48.82
48.83
45.07
46.83
45.67
51.05
11
43.72
47.02
39.14
48.04
48.02
44.38
46.26
44.83
60.27
12
42.94
46.22
38.49
47.27
47.20
43.70
46.68
44.07
49.48
13
42.15
46.45
37.83
46.61
46.40
43.01
44.89
43.31
48.70
14
41.39
44.68
37.17
46.76
46.60
42.33
44.20
42.63
47.93
15
40.62
43.93
36.51
46.00
44.81
41.64
43.51
41.76
47.19
16
39.88
43.20
35.85
44.27
44.04
40.92
42.82
41.01
46.51
17
39.20
42.50
36.20
43.57
43.27
40.19
42.17
40.29
45.86
18
38.55
41.82
34.58
42.87
42.52
39.47
41.52
39.61
45.22
19
37.93
41.17
33.99
42.17
41.78
38.74
40.87
38.98
44.60
20
37.30
40.49
33.43
41.46
41.06
38.02
40.22
38.39
43.99
21
36.67
39.79
32.90
40.75
40.33
37.33
39.62
37.83
43.36
22
36.95
39.08
32.39
40.04
39.60
36.64
39.00
37.34
42.73
23
36.45
38.37
31.88
39.31
38.88
35.96
38.40
36.87
42.09
24
34.85
37.68
31.36
38.59
38.16
35.27
37.78
36.39
41.45
25
34.44
37.02
30.86
37.86
37.44
34.68
37.17
35.90
40.81
26
33.68
36.46
30.33
37.14
36.73
33.91
36.66
35.41
40.17
27
33.11
35.90
29.82
36.41
36.02
33.23
35.93
34.86
39.62
28
32.53
36.34
29.30
36.69
35.33
32.66
35.30
34.31
38.87
29
31.93
34.78
28.79
36.00
34.66
31.88
34.69
33.75
38.22
30
31.30
34.22
28.27
34.34
33.98
31.21
34.06
33,17
37.57
31
30.64
33.58
27.76
33.68
33.30
30.57
33.29
32.59
36.91
32
29.96
32.94
27.24
33.03
32.64
29.94
32.80
32.00
36.26
33
29.29
32.31
26.72
32.36
31.98
29.30
32.16
31.40
35.61
34
28.62
31.67
26.20
31.68
31.32
28.67
31.62
30.79
34.96
35
27.96
31.04
25.68
31.00
30.66
28.03
30.88
30.17
34.31
36
27.31
30.42
25.16
30.32
30.01
27.31
30.23
29.64
33.68
37
26.66
29.80
24.64
29.64
29.36
26.68
29.58
28.91
33.04
38
26.04
29.18
24.12
28.96
28.70
26.01
28.89
28.28
32.40
39
25.42
28.56
23.60
28.28
28.06
26.33
28.18
27.66
31.76
40
24.82
27.96
23.08
27.61
27.40
24.66
27.48
27.02
31.12
41
24.22
27.37
22.66
26.97
26.74
24.06
26.77
26.39
30.46
42
23.65
26.77
22.04
26.34
26.07
23.44
26.06
25.74
29.81
43
23.08
26.06
21.64
26.71
25.40
22.83
25.34
25.08
29.14
44
22.63
26.64
21,03
26.09
24.75
22.22
24.62
24.42
28.48
45
21.99
24.93
20.52
24.46
24.10
21.61
23.89
23.76
27.81
46
21.44
24.33
20.02
23.82
23.44
20.98
23.15
23.07
27.13
47
20.90
23.72
19.51
23.17
22.78
20.36
22.46
22.38
26.44
48
20.35
23.11
19.00
22.60
22.12
19.72
21.74
21.68
26.75
49
19.84
22.63
13.49
21.81
21.47
19.09
21.07
20.98
25.06
50
19.32
21.92
17,99
21.11
20.83
18.46
20.38
20.30
24.35
61
18.80
21.31
17:50
20.39
20.20
17.87
19.73
19.62
23.65
52
18.29
20.67
17.02
19.68
19.59
17.29
19.11
18.97
22.93
TABLE 11.
ComparatiTe View of the Expectation of Life at different Placee.
^7
Swedra,
Aft.
Gheiler.
Chetter.
North-
Carlisle.
EquiUble
0>aTleO.
M«le&
Dee
GOTt
Govt
lUln.
FcmalM.
uipton.
Female.
Poreleos.
Females.
53
17.79
20.03
16.54
18.97
19.00
16.70
18.48
18.34
22.22
54
17.27
19.38
16.06
18.28
18.43
16.12
17.85
17.73
21.50
55
16.74
18.73
15.58
17.58
17.85
15.53
17.25
17.15
20.79
56
16.17
18.06
15.10
16.89
17.28
14.95
16.64
16.57
20.08
67
15.61
17.38
14.63
16.21
16.71
14.37
16.02
16.02
19.38
56
15.04
16.70
14.15
15.55
16.15
13.79
15.44
15.47
18.69
59
14.47
16.05
13.68
14.92
15.60
13.21
14.84
14.93
18.00
60
13.96
15.40
13.21
14.34
15.06
12.63
14.25
14.39
17.32
61
13.53
14.85
12.75
13.82
14.51
12.12
13.65
13.84
16.64
62
13.21
14.41
12.28
13.31
13.96
11.62
13.04
13.28
15.96
63
12.90
13.98
11.81
12.81
13.42
11.11
12.43
12.72
15.30
64
12.61
13.56
11.35
12.30
12.88
10.61
11.86
12.17
14.64
65
12.29
13.06
10.88
11.79
12.35
10.10
11.26
11.63
14.00
66
11.87
12.47
10.42
11.27
11.83
9.62
10.69
11.10
13.37
67
10.35
11.82
9^96
10.75
11.32
9.15
10.14
10.61
12.76
68
10.76
11.17
9.50
10.23
10.82
8.67
9.61
10.14
12.16
69
10.16
10.54
9.05
9.70
10.32
8.20
9.11
9.67
11.57
70
9.63
9.98
8.60
9.18
9.84
7.72
8.64
9.22
10.99
.71
9.21
9.52
8.17
8.65
9.36
7.32
8.17
8.79
10.44
72
8.99
9.19
7.74
8.16
8.88
6.89
7.73
8,37
9.92
73
8.85
8.89
7.33
7.72
8.42
6.53
7.31
7.96
9.41
74
8.74
8.63
6.92
7.33
7.97
6.23
6.90
7.54
8.92
75
8.59
8.34
6.54
7.01
7.52
5.91
6.50
7.12
8.46
76
8.37
7.98
6.18
6.69
7.08
5.59
6.10
6.69
8.00
77
8.05
7.61
5.83
6.40
6.64
5.28
5.71
6.23
7.58
78
7.72
7.24
5.48
6.12
6.20
4.96
5.36
5.78
7.19
79
7.42
6.90
5.11
5.80
5.78
4.61
5.00
5.35
6.83
80
7.10
6.60
4.75
5.51
5.38
4.28
4.69
4.94
6.50
81
6.83
6.35
4.41
5.21
5.00
4.01
4.39
4.55
6.20
82
6.61
6.18
4.09
4.93
4.63
3.80
4.01
4.18
5.89
83
6.39
6.13
3.80
4.65
4.30
3.57
3.84
3.82
5.57
84
6.17
6.26
3.58
4.39
4.00
3.39
3.52
3.46
5.22
85
5.93
6.43
3.37
4.12
3.73
3.23
3.21
3.12
4.84
86
5.67
6.46
3.19
3.90
3.50
3.09
2.92
2.81
4.44
87
5.38
6.27
3.01
3.71
3.31
2.92
2.67
2.53
4.03
88
5.01
5.96
2.86
3.59
3.11
2.71
2.36
2.31
3.62
89
4.71
5.48
2.66
3.47
2.91
2.43
2.06
2.12
3.21
90
4.32
5.01
2.41
3.28
2.65
2.05
1.77
1.95
2.83
91
3.95
4.57
2.09
3.26
2.36
1.71
1.50
1.83
2.49
92
3.66
4.14
1.75
3.37
2.03
1.40
1.25
1.65
2.21
93
3.48
3.73
1.37
3.48
1.70
1.23
1.00
1.49
1.97
94
3.25
3.38
1.05
3.53
1.31
1.10
.50
1.34
1.75
95
3.22
3.12
.75
3.53
1.05
1.00
1.18
1.55
96
3.12
2.80
.50
3.46
.75
.97
1.32
97
2.55
2.61
3.28
.50
i
.75
1.12
96
1.94
2.10
3.07
.50
.94
99
1.26
1.35
2.77
.00
.75
100
.50
,50
'
2.28
.50
101
1.79
m
1.30
103
104
-
.83
.50
Die
tized by v_
oogle
TABU IIL
TaUM firom tlia Bip«rienee of the Amktble Coiporation.
Number who
•uceetitvely
Preaent Value
Single
Annual
oT£l per Ann.
Freniiuni
PremiuQi
Age.
attiUaeaeh
DAcremeuta,
fbrlife.
Ibr Aaaannoe.
far Aaaurance,
Year of Age.
IpprCent.
4 per Cent.
4 j»r Cent.
9
2125595
11691
13.4814
.25071
.01287
10
2113904
12895
18.3270
.25666
.01328
11
2101009
14077
18.1770
.26242
.01368
10
208^932
15234
18.0316
.26802
.01408
13
2071698
16781
17.8908
.27343
.01447
14
2054917
17673
17.7584
,27863
.01485
15
2037244
18946
17.6289
.28350
.ei5«?
16
2018208
19780
17.5062
.28822
.01557
17
1993518
20984
17.3860
.29282
.01593
IB
1977534
22139
17.2739
,29716
.01626
19
1955395
22997
17.1683
.30122
.01658
20
1932398
24027
17.0675
.30510
.30870
.01689
21
1908371
25018
16.9737
.01718
22
1883353
25957
16.8871
.31203
.01744
23
1857396
26425
16.8081
.31507
.01769
24
1830971
26325
16.7327
,31797
.01793
26
1804646
26537
16.6558
.32093
'.0W8
26
1779109
24097
16.6707
.32420
.01846
27
17^5012
22185
16.4701
.32807
.01878
28
1732827
20343 :
16.3482
.33276
.01918
28
1712484
18780
16.2041
.33830
.01966
30
1693704
17884
16.0392
.34405
.35162
.02^23
31
1675820
J7317
17576
15.8580
.02086
32
1658503
15.6653
.35903
.02154
33
1640027
17963
15.4664
.36668
.02227
34
1622964
18630
15.2631
.374^0
.02803
sp
1604334
19361
15.0579
.38239
.02381
36
1584073
19915
14.8515
.39033
.02462
37
156505^
20326
14.6421
, .39838
.02547
38
1544732
20708
14.42^2
.40601
.02636
30
1524024
20216
14.2092
.415Q3
.02729
40
1503208
212^8
13.9822
.42376
.02688
41
1482520
20723
13.7444
.43291
.02936
42
1461797
20077
13.4968
13.2411
.44243
.03P52
43
1440820
21286
.45227
.03176
' 44
1419534
21794
12.9772
.46242
.03308
46
1397740
22567
12.7067
,47282
.03460
46
1375173
23692
12.4319
.48339
.03599
4f
1351581
24888
12.1548
.494Q5
.03766
48
1326693
26542
11.8781
.50469
.03019
49
1300151
28173
11.Q054
.51518
.04087
50
1271978
29641
11.3376
.52550
.04960
61
1242337
30843
11.0718
.53570
.04438
52
1211494
31682
10.8078
.54585
.04623
58
1179812
32484
10.6420
.55608
.04818
54
1147328
33384
10,?740
.56638
.05024
Digitized by LjOOQ IC
TABLE m.
238
TablM frpm tha Szpemnci of the Amicable Cpxporatiop.
Number who
Pfesent Value
Single
Premiam
Annufl
■ueoesdyaly
ofiElperAmi.
Premium
Ag«.
atUlneach
Decrementa.
for Ufe.
for Assurance,
for A-ssurance.
Year of Age,
4 per Cent.
4 per Cent,
4 per Cent.
56
1113944
34273
10.0052
.57672
.0524Q
M
1079671
35161
9.7357
.58709
.05469
67
1044510
35996
9.4660
.59746
.05709
68
1008614
36436
9.1960
.60784
.05962
69
972029
36328
8.9229
• .61835
.06232
60
935701
36312
8.6400
.629^3
.06527
61
899399
36629
8.3484
.64044
.06851
68
862760
37203
8.0510
.66188
.07201)
63
826567
37991
7.7504
.66346
.07585
64
787666
39371
7.4492
.67503
.67981
66
748195
40666
7.1548
.68635
,08417
66
707689
41636
6.8686
• .69736
.08869
67
666003
42273
6.5888
.70812
.09331
68
6g3730
42752
6.3168
.71858
.09821
69
580978
42873
6.0529
.72874
. 1033^
,10867
70
698106
42936
6.7966
•73859
71
496169
42684
6.6611
.74803
,11416
72
452486
!, 42007
5.3178
•76701
,11983
,12567
78
4|0478
369469
41010
5.0966
.76552
74
39423
4.8888
.77351
.13135
75
380036
37376
4.6917
.78109
,13724
76
292666
3522A
4.6025
•7P837
.14327
77
257436
3282P
4.3233
.79526
.14939
78
224616
30108
4.1532
.80180
.15559
79
194612
87619
3.9878
.80816
.16203
80
166993
24854
3.8308
.81420
,16864
61
142139
2217J2
3.6806
.81996
88
1 9967
19674
3.6363
.82557
63
1 10393
16956
3.3936
.83102
84
83438
14607
3.2466
.83667
♦
85
^8931
12468
3.0869
.84281
«
66
16463
10578
2.9194
.84926
87
45885
; ^6731
9154
2.7360
.86631
88
7696
2.5646
.8P329
89
29036
|2690
6446
2.3609
.87073
90
6234
2.1560
.8f862
81
17356
12970
4386
1.9184
.88775
92
3650
1.6697
.89732
93
9320
2937
1.4167
.9P705
94
6383
2312
1.1613
95
4071
1824
.8771
96
\ 2247
1198
.6529
97
1049
649
.4549
98
400
s\t: 300
•2404
99
I 100
100
|dO
Digitized by VjVJVJ
gle
240
TABLE IV.
The Logarithm, and its Arithmetical Complement, of the Number who complete
each year of Age, according to Dr. Price'k Table of Mortality for Northampton.
Age.
I^g/«
^h
Age.
Log 4.
^i
0
4.0663259
5.9336741
48
3.4791432
4.5208568
1
3.9370161
4.0629839
49
.4677561
•5322439
2
•8623103
.1376897
50
•4559102
•5440898
3
.8312937
•1687063
51
.4434195
.5565805
4
.8092903
.1907097
52
.4303976
.5696024
5
•7958105
.2041895
53
•4169732
.5830268
6
.7828308
.2171692
54
•4031205
.5968795
7
.7726883
•2273117
55
•3888114
.6111886
8
•7645497
.2354503
56
.3740147
.6259853
9
.7585334
.2414666
57
.3586961
.6413039
10
.7539659
.2460341
58
•3428173
.6571827
11
.7499681
.2500319
59
.3263359
.6736641
12
•7460890
.2539110
60
.3092042
.6907958
13
•7421750
.2578250
61
•2913689
.7086311
14
.7382254
.2617746
62
.2727696
.7272304
15
.7342396
•2657604
63
.2535803
.7464197
16
.7302168
.2697832
64
.2335038
.7664962
17
.7259116
.2740884
65
•2127202
.7872798
18
.7211508
.2788492
66
.1908917
.8091083
19
.7159198
.2840802
67
.1679078
.8320922
20
.7102866
.2897134
68
.1436392
.8563608
21
.7041505
.2958495
69
.1179338
.8820662
22
.6976652
.3023348
70
.0906107
.9093893
23
.6910815
•3089185
71
.0614525
•9385475
24
.6843965
.3156035
72
.0301948
^.9698052
25
.6776070
.3223930
73
2.9965117
3.0034883
26
.6707096
.3292904
74
.9599948
.0400052
27
.6637009
.3362991
75
.9201233
.0798767
28
.6565773
.3434227
7S
.8762178
.1237822
29
.6493349
.3506651
77
•8293038
.1706962
30
.6419696
.3580304
78
.7795965
.2204035
31
.6344773
•3655227
79
.7275413
•2724587
32
.6268534
.3731466
80
.6711728
.3288272
33
.6190933
.3809067
81
.6085260
.3914740
34
•6111921
.3888079
82
.5390761
•4609239
35
.6031444
.3968556
83
.4608978
•5391022
36
.5949447
•4050553
84
.3692159
•6307841
37
.5865873
•4134127
85
.2695129
•7304871 -
38
•5780659
•4219341
86
.1613680
.8386320
39
.5693739
.4306261
87
.0453230
..9546770
40
•5605044
•4394956
88
1.9190761
2.0809219
41
.5513280
.4486720
89
.7923917
.2076083
42
•5418288
.4581712
90
.6627578
•3372422
43
.5319896
.4680104
91
.5314789
.4685211
44
.5219222
.4780778
92
•3802112
.6197888
45
.5116160
•4883840
93
.2041200
.7958800
46
.5010593
.4989407
94
0.9542425
1.0457575
47
.4902395
.5097605
95
.6020600
.3979400
Digitized by ^^UUV I
TABLE V.
241
Proportion that dio in each year by the Norihampion Table of Mortality, also the
Proportion that giuviTe, and its Reciprocal.
A«e.
Pioportbn
which di«.
Proportion
wluchtnrrive.
ditto.
Ag«.
Proportion
whlch'die.
Proportion
ditto.
0
.257511
.742489
1.34682
48
.025879
.974121
1.02656
I
.158035
.841965
1.18770
49
.026908
.973092
1.02765
2
.068928
.931072
1.07402
50
.028351
.971649
1.02918
3
.049403
.950597
1.05197
51
.029539
.970461
1.03044
4
.030562
.969438
1.03152
52
.030433
.969562
1.03139
. 5
.029445
.970555
1.03034
53
.031394
.968606
1.03241
6
.023084
.976916
1.02363
54
.032411
.967589
1.03350
7
.018565
.981435
1.01891
65
.033497
.966503
1.03466
8
.013757
.986243
1.01395
56
.034658
.965342
1.03590
9
.010462
.989538
1.01057
57
.035902
.964098
1.03723
10
• 009163
.990837
1.00925
58
.037239
.962761
1.03868
11
.008892
.991108
1.00897
59
.038679
,961321
1.04024
12
.008972
.991028
1.00905
60
.040235
.959765
1.04192
13
.009053
.990947
1.00914
61
.041922
.958078
1.04375
14
.009136
.990864
1.00921
62
.043223
,956777
1.04518
15
.009220
.990780
1.00930
63
•045176
.954824
1.04731
16
•009864
.990136
1.00996
64
.046729
.953271
1.04902
17
.010902
•989098
1.01102
65
.049020
.950980
1.05155
18
.011972
.988028
1.01212
66
.051546
.948454
1.05434
19
.012887
.987113
1.01305
67
.054348
.945652
1.05747
20
.014030
.985970
1.01423
68
.057471
.942529
1.06097
21
.014822
.985178
1.01505
69
.060975
.939025
1.06493
22
.015045
.984955
1.01527
70
.064935
.935065
1.06944
23
.015275
.984725
1.01551
71
.069444
.930556
1.07463
24
.015512
.984488
1.01576
72
.074627
.925373
1.08064
25
.015756
.984244
1.01601
73
.080645
.919355
1.08772
261
•016009
.983991
1.01627
74
.087719
.912281
1.09615
27
.016269
.983731
1.01654
75
.096154
.903846
1.10638 '
28
.016538
.983462
T 1.01682
76
.102393
.897607
1.11407
29
.016816
.983184
1.01710
77
.108148
.891852
1.12126
30
.017104
.982896
1.01740
78
.112957
.887043
1.12734
31
.017401
.982599
1.01771
79
.121723
.878277
1.13859
32
.017710
.982290
1.01803
80
.134328
.865672
1.15517
33
.018029
.981971
1.01836
81
.147783
.852217
1.17341
34
.018360
.981640
1.01870
82
.164740
.835260
1.19723
35
.018704
.981296
1.01906
83
.190311
.809689
1.23504
36
.019060
.980940
1.01943
84
.205128
.754872
1.25806
37
.019430
.980570
1.01981
85
.220430
.779570
1.28276
38
.019815
.980185
1.02022
86
.234483
.765517
1.30634
39
.020216
.979784
1.02063
87
.252252
.747748
1.33735
40
.020908
.979092
1.02135
88
.253012
.746988
1.33871
41
.021635
.978365
1.02211
89
.258065
.741935
1.34783
42
.022401
.977599
1.02291
90
.260869
.739131
1.35294
43
.022914
.977086
1.02345
91
.294118
.705882
1.41667
44
.023452
.976548
1.02401
92
.333333
.666667
1.50000
45
•024015
.975985
1.02461
93
.437500
.562500
1.77778
46
.024606
.975394
1.02523
94
.555556
.444444
2.25000
47
.025227
.974773
1.02588
95
.750000
.250000
4.00000
349
TABJ.E Yi
A Ftepuaioiy Table for findiog the Values of Anmuties, &c.^ by the Notthanqptpn
Table of MortaUty. (3 per Cent)
Age.
9
19
11
12
13
U
16
17
IS
II
21
22
23
24
^
26
27
28
29
30
31
32
33
36
37
^6
99
41
42
^3
^4
46
46
47
11650.000
8393.058
6864.920
6205.576
5727
5390
.4^2
5679.342
4Q17.567
4590.415
4395.400
4222.7^
4662.175
3908.790
3760.894
3618.298
348p.dl7
3348.276
3218.688
3090.870
2964.917
2841.464
2719.999
2001.634
2487.856
2378.500
2273.402
2172.410
2075,372
1932.143
1892.585
180^.562
1723.945
1644.607
1568.429
1496.293
1425.087
1357.703
1293.034
1230.981
1)71.446
1114.334
1059.258
1006.156
954.9(38
905.908
858.897
813.855
770.708
N.
142947.3^1
134549.293
127684.367
12)478.791
115751.604
110^QM61
105281.8)9
100464.252
95873.837
9)478.437
87255.705
83193.530
79284.740
75523.846
71905.548
^8424.731
65076.455
61857.767
58766.897
55801.9^0
52960.516
50240.516
47638.882
45151.026
42772.526
40499.124
.88326.714
36251.343
34269.199
32376.615
3P570.053
28846.108
27201.501
25633.072
54137.779
22712.691
21354.988
20061.954
18830.973
17659.528
16i545.194
15485.936
14479.780
13524.811
12618.903
11760.007
10946.152
10175.^4
S.
2719587.3
2576639.9
2442Q90.7
2314406.3
2192927.5
$077175.9
1966814.7
1861532.9
1761068.7
1665194.8
1573716.4
1486460.7
1403267,2
1323982.4
1248458.6
) 176553.0
1108128.3
1043051.8
981194,1
922427.2
8666,25^2
813664.7
763424.2
715785.3
670634:3
627861,7
587362.6
549035.9
512784.5
478515.3
Mem J
415568.7
386722.6
359521.1
333888. U
309750.2
287037.5
265682.5
245620.6
2267^9.6
209130.1
192584.9
177099.0
162619.2
1490^4.4
136475.5
124715. £i
1)3769.3
7147.166
4234.544
2946.015
2486.614
2188.971
2019,037
1864.940
1751.107
1664,272
1602.958
1558.313
1520.747
1485.678
1451.630
1418.574
1386,481
1355.323
1323.257
1289.188
1253.260
1216.164
1177.460
1138.318
1100.317
1063.422
1027.601
992.8241
959.0599
926.2791
894.4531
863.5541
833.5551
804.4298
776.1528
748.6994
722.0456
696.1682
671.0445
646.6525
622.9710
59.9.979^
577.3595
555.1096
533.22731
511.982^
491.3561
471.3307
451.8885
R.
70883.26
63736.09
59501.55
56555.53
5406S.02
51879.95
49860.91
47995.97
46244.87
44580.59
42977.64
41419.82
39898.58
38412.90
36961.27
35542.69
34156.21
32800.89
31477.63
30188.44
28935.18
27719.02
26541.56
25403.24
24302.93
23239.50
22211.90
9)219.08
20260.02
19333.74
18439.29
17575.73
16742. la
15937.75
15161.59
14412.90
13690.85
12994.68
123123.64
116^6.98
11054. Of
10454.03
9876.67
9321.57
8788.34
8276.36
7785.00
7313.67
Digitized by ^^UUV IC
TABLX VI. MS
A PreptratQry T»ble f^r findiag the Yaluei pf Aonulti^, &c»f by tli« NorttooplfD
Table of Mortality. (3 per Cent.)
Age.
D.
N.
S.
M.
H.
48
729.884
9448.059
103593.9
433.0126
6861.780
49
689.814
8756.245
94147.80
414.6865
6428.768
60
651.702
8104,543
85391.56
396.6660
6014.081
51
614.762
7469.762
77287.pl
878.7275
5617.415
52
579.244
6910.517
69797.^5
361.0965
5238.688
53
545.256
6365,^62
62886.73
343.9790
4877.591
54
512.756
5852.506
56521.47
327.8600
4538.612
56
481.686
5370,820
60668.97
3U.2251
4206.252
56
451.991
4918.829
45298.15
295.5601
3895.097
57
423.618
4495,211
• 40379.32
280.8512
3599.467
58
396.514
4098.697
35884.11
266.5855
3319.116
59
370.629
3728,068
31785.41
251.2498
3053.530
60
345.916
3382.152
28057.84
237.8317
2802.281
61
322.826
3059.824
24675.19
223.8190
?564.949
62
299.821
2760.004
21615.87
210.6998
2341.130
63
278.506
2481,497
18855.36
198.1180
2130.430
64
258.179
2223,317
16373.87
185.9027
1939.312
6S
238.946
1984.371
14150.55
174.1896
1746.409
66
220.615
1763.756
12166.18
162.8177
1572.2?0
67
203.149
1560.608
10402.42
151.7770
1409.402
68
186.512
1374.095
8841.81
141.0579
1257.625
69
170.673
1203.422
7467.72
130.6510
1116.567
70
155.598
1047.824
6264.80
120.5472
985.916
71
141.257
906.5667
5216.47
110.7377
865.369
72
127.619
778.9479
4309.91
101.2139
754.631
73
114.655
664.2927
3530.96
91.9675
658.417
74
102.339
561.9^40
2866.67
82.9904
561.450
75
90:6425
471.3115
2304.71
74.2748
479.460
76
79.5405
891.7710
1883.40
65.8130
404.185
77
69.3167
322.4543
1441.63
P7.90q8
338.372
78
60.0196
262.4347
1119.18
50.6277
289.466
79
51.6898
210.7454
856.^4
44.0455
229.838
80
44.0751
166.6703
646.00
37.9370
185.793
81
37.0434
129.6269
479.83
82.1889
147.856
82
30.6495
98.9774
349.70
26.9740
11^.667
83
24.8547
74.1227
250.72
21.9718
88.793
84
19.5384
54.5843
176.60
U.9795
66.891
85
16.0781
39.6062
122.01
13.4883
49.44?
86
11.4121
28.0941
82.^1
10.9614
3^.953
87
8.4817
19.6124
54.41
7.66344
25.695?
88
6.1574
13.4550
34.80
5,58622
19.099
89
4.4855
8.9895
21.35
4.07368
19.442
90
3.2166
5.7729
12.86
2.95484
8.369
91
2.3083
3.4846
6.584
2.14015
«.4U
92
1.5819
1.8627
3.100
1,49101
».274
93
1.0238
.8589
1.217
,969059
1.793
94
• 6591
.2998
,3583
,534150
,8236
95
.2413
.0585
.0585
.239548
,2894
96
.0585
.0000
.0000
.05^858
,0569
'""^■""
y;^UU>7l
344
TABLS Vn.
TU Valoa of an Anniiiiy on a nngle life aeeoiding to tko Notthampton Table
ofMortaUty.
Age.
3 per cent
4 per cant.
6 per cent.
6 per cant
7peree«t.
SperoMit.
1
16.0215
13.4663
11 .563
10.107
8.963
8.046
2
18.5995
15.6336
13.420
11.724
10.391
9.321
3
19.5758
16.4626
14.135
12.348
10.941
9.812
4
20.2109
17.0109
14.613
12.769
11.315
10.147
5
20.4735
17.2500
14.827
12.962
11.489
10.304
6
20.7275
17.4832
15.041
13.156
11.666
10.466
7
20.8537
17.6122
15.166
13.275
11.777
10.570
8
20.8857
17.6632
15.226
13.337
11.840
10.631
9
20.8123
17.6260
15.210
13.335
11.846
10.641
10
20.6633
17.5248
15.139
13.285
11.809
10.614
11
20.4800
17.3944
15.043
13.212
11.759
10.569
12
20.2838
17.2524
14.937
13.130
11.687
10.517
13
20.0814
17.1050
14.826
13.044
11.618
10.461
14
19.8728
16.9517
14.710
12.953
11.545
10.401
15
19.6577
16.7923
14.588
12.857
11.467
10.337
16
19.4358
16.6265
14.460
12.755
11.384
10.268
17
19.2183
16.4638
14.334
12.655
11.302
10.200
18
19.0131
16.3111
14.217
12.562
11.226
10.137
19
18.8208
16.1691
14.108
12.477
11.157
10.081
20
18.6385
16.0354
14.007
12.398
11.094
10.030
21
18.4708
15.9141
13.917
12.329
11.042
9.986
22
18.3112
15.7997
13.833
12.265
10.993
9.947
23
18.1486
15.6827
13.746
12.200
10.942
9.907
24
17.9830
15.5630
13.658
12.132
10.890
9.865
25
17.8144
15.4405
13.567
12.063
10.836
9.823
26
17.6425
15.3152
13.473
11.992
10.780
9.778
27
17.4674
15.1870
13.377
11.917
10.723
9.732
28
17.2890
15,0557
13.278
11.841
10.663
9.685
29
17.1070
14.9212
13.177
11.763
10.602
9.635
30
16.9217
14.7835
13.072
11.682
10.539
9.584
31
16.7326
14.6423
12.965
11.598
10.473
9.531
32
16.5398
14.4977
12.854
11.512
10.404
9.476
33
16.3432
14.3494
12.740
11.423
10.333
9.418
34
16.1425
14.1953
12.623
11.331
10.260
9.359
36
15.9378
14.0415
12.502
11.236
10.183
9.296
36
15.7288
13.8815
12.377
11.137
10.104
9.231
37
15.5154
13.7172
12.249
11.035
10.021
9.164
38
15.2976
13.5486
12.116
10.929
9.935
9.093
39
15.0750
13.3754
11.979
10.819
9.845
9.019
40
14.8476
13.1974
11.837
10.705
9.752
8.941
41
14.6196
13.0184
11.69&
10.589
9.657
8.863
42
14.3912
12.8385
11.551
10.473
9.562
8.783
43
14.1626
12.6580
11.407
10.356
9.466
8.703
44
13.9296
12.4691
11.258
10.235
9.366
8.620
45
13.6920
12.2835
11.105
10.110
9.262
8.533
46
13.4498
12.0892
10.947
9.980
9.154
8.443
47
13.2028
11.8899
10.784
9.846
9.042
8.348
TABLE VIL '
34S
TIm Value of an Annuity on » Single Life according to ihe Northampton Tiable
of Mortality.
Age.
8 per cent.
4p6reMit.
6 percent
6 per cent
7 per cent
Spereent
48
12.9508
11.6866
10.616
9.707
8.925
8.249
49
12.6937
11.4758
10.443
9.563
8.804
8.146
50
12.4360
11.2649
10.269
9.417
8.681
8.041
51
12.1828
11.0586
10.097
9.273
8.559
7.937
52
11.9303
10.8497
9.925
9.129
8.437
7.833
53
11.6740
10.6379
9.748
8.980
8.311
7.725
54
11.4138
10.4220
9.567
8.827
8.181
7.614
55
11.1500
10.2011
9.382
8.670
8.047
7.499
56
10.8826
9.9777
9.193
8.509
7.909
7.379
57
10.6115
9.7494
8.999
8.343
7.766
7.256
58
10.3369
9.5169
8.801
8.173
7.619
7.128
59
10.0588
9.2804
8.599
7.999
7.468
6.996
60
9.7774
9.0400
8.392
7.820
7.312
6.860
61
9.4929
8.7957
8.181
7.637
7.152
6.719
62
9.2055
8.5478
7.966
7.449
6.988
6.574
63
8.9100
8.2913
7.742
7.253
6.815
6.421
64
8.6115
8.0310
7.514
7.052
6.637
6.262
65
8.3047
7.7616
7.276
6.841
6.449
6.095
66
7.9948
7.4882
7.034
6.625
6.256
5.922
67
7.6821
7,2109
6.787
6.405
6.058
5.743
68
7.3673
6.9301
6.536
6.179
5.855
4.559
69
7.0510
6.6473
6.281
5.949
5.646
5.370
70
6.7342
6.3619
6.023
5.716
5.434
5.176
71
6.4179
6.0758
5.764
6.479
5.218
4.978
72
6.1037
5.7904
5.504
5.241
5.000
4.778
73
5.7939
5.5076
5.245
5.004
4.781
4.576
74
5.4912
5.2304
4.990
4.769
4.565
4.375
75
5.1997
4.9626
4.744
4.542
4.354
4.180
76
4.9254
4.7102
4.511
4.326
4.154
3.994
77
4.6520
4.4574
4.277
4.109
3.952
3.806
78
4.3725
4.1979
4.035
3.884
3.742
3.609
79
4.0772
3.9217
3.776
3.641
3.514
3.394
80
3.7815
3.6439
3.515
3.394
3.281
3.174
81
3.4994
3.3777
3.263
3.156
3.055
2.960
82
3.2294
3.1219
3.020
2.926
2.836
2.751
83
2.9823
2.8874
2.797
2.713
2.632
2.557
84
2.7938
2.7084
2.627
2.551
2.479
2.410
85
2.6202
2.5436
2.471
2.402
2.337
2.275
86
2.4619
2.3934
2.328
2.266
2.207
2.151
87
2.3124
2.2516
2.193
2.138
2.085
2.035
88
2.1852
2.1316
2.080
2.031
1.984
1.939
89
2.0131
1.9677
1.924
1.882
1.842
1.803
90
1.7948
1.7582
1.723
1.689
1.656
1.625
91
1.5010
1.4739
1.447
1.422
1.398
1.374
92
1.1903
1.1715
1.153
1.136
1.118
1.102
93
.8390
.8276
.816
.806
.795
.785
94
.5362
.5301
.524
.518
.512
.507
95
.2427
.2404
.238
.236
.234
.232
146
TABU VIII.
Value of on Annuitjr on Two joint Lives. (Korthampton 3 per Cent.)
Tounget Age One Year,
A«e.
Value.
Age.
ValQA.
Age.
V«lM.
Age.
Value.
Agft
Valtt«.
1
9.4909
21
11.4182
41
0.5231
61
6.5715
81
2.6315
8
11.0159
23
11.3423
43
9.4008
62
6.3944
83
2.4396
a
11.6027
23
11.2693
43
0.2779
63
6.2107
83
2.2623
4
11.9957
24
11.1943
44
9.1516
64
6.0239
84
2.1278
5
12.1717
25
11.1171
45
0.0314
65
5.8303
85
2.0037
6
12.3469
26
11.0378
46
8.8879
66
5.6333
86
1.8907
7
12.4493
27
10.9561
47
8.7503
67
5.4334
87
1.7844
8
12.4978
33
10.8721
48
8.6087
68
5.2307
88
1.6966
9
12.4845
29
10.7856
49
8.4628
69
5.0256
89
1.5750
10
12.4261
30
10.6966
50
8.3157
70
4.8168
90
1.4176
11
12.3468
31
10.6050
51
8.1708
71
4.6110
91
1.1986
12
12.2592
32
10.5106
53
8.0256
72
4.^033
92
.9625
la
12.1675
33
10.4135
53
7.8772
73
4.1971
93
.6872
14
12.0713
34
10.3134
54
7.7254
74
3.9945
94
.4454
15
11.9705
35
10.8102
55
7.5703
75
3.7987
95
.2044
16
11.8648
35
10.1039
56
7.4120
76
3.6145
96
.0000
17
11.7607
37
9.9944
67
7.2503
77
3.4298
18
11.6634
38
9.8813
58
7.0853
78
3.2397
19
11.5734
39
9.7648
59
6.9172
79
3.0360
20
11.4890
40
9.6444
60
6.7459
80
2.8299
Younger Age Two Years.
Age.
Value.
Age.
Value.
Age.
42
Value.
Age.
Value.
Age.
Valtttf.
2
12.7897
23
13.1722
10.9075
62
7.3909
82
2.7774
! 3
13.4736
23
13.0873
43
10.7638
63
7.1758
83
2.5731
4
13.9316
24
12.9999
44
10.6162
64
6.9571
84
2.4179
5
14.1374
25
12.9101
45
10.4642
65
6.7305
85
2.2747
6
14.3417
26
12.8176
46
10.3076
66
6.5000
86
2.1443
7
14.4612
27
12.7225
47
10.1471
67
6.2659
87
2.0215
8
14.5177
28
12.6246
48
9.9816
68
6.0288
88
1.9193
9
14.5022
29
12.5238
49
9.8111
69
5.7890
89
1.7784
10
14.4341
30
12.4200
50
9.6391
70
5.5472
90
1.5969
U
14.3418
31
12.3132
51
9.4697
71
5.3044
91
1.3463
12
14.2397
32
12.3031
52
9.3999
72
5.0618
92
1.0773
13
14.1328
33
12.0898
53
9.1262
73
4.8211
93
.7661
14
14.0208
34
11.9730
54
8.9487
74
4.5848
94
.4945
15
13.9034
35
11.8526
55
8.7673
76
4.3565
95
.2260
16
13.7802
36
11.7285
56
8.5820
76
4,1415
96
.0000
17
13.6591
37
11.6006
57
8.3928
77
3.9261
18
13.5458
38
11.4686
58
8.1998
78
3.7046
19
.13.4411
39
11.3335
59
8.0029
79
3.4679
20
13.3429
40
11.1920
60
7.8024
80
3.2288
21
13.2548
41
11.0502
61
7.5983
81
2.9991
Digitized by VjOOQ IC
TABLB Vni.
Uf
Valae of ftn Amraity on Two joint LitrM. (NorUi*iiit»ton 3 pto Ceni)
Younger Age Three Years.
Age.
Valae.
Age.
Value.
Age.
Vaiae.
Age.
Valaa.
Age.
Vaiae.
3
14.1960
23
13.7944
43
11.3429
63
7.5456
83
2.6786
4
14.6799
24
13.7024
44
1 .1868
64
7.3138
84
2.6165
5
14.8977
25
13.6078
45
11.0262
65
7.0736
85
2.3661
6
15.1139
26
13.5104
46
10.8609
66
6.8294
86
2.2280
7
15.2404
27
13.4102
47
10.6905
67
6.5814
87
2.0983
8
15.3003
28
13.3070
48
10.6158
68
6.3301
88
1.9907
9
15.2842
29
13.2008
49
10.3355
69
6.0760
89
1.8423
10
15.2127
30
13.0914
50
10.1536
70
5.8199
90
.6517
: .3900
11
15.1154
31
12.9788
51
9,9744
71
5.6628
91
12
•15.0080
32
12.8627
52
9.7947
72
5.3059
92
1.1098
13
14.8953
33
12.f431
53
9.6110
73
5.0512
93
.7874
14
14.7773
34
12.6199
54
9.4231
74
4.8011
94
.6067
15
14.6535
35
12.4928
55
9.2311
75
4.6596
95
.2307
16
14.6238
36
12.3619
56
9.0349
76
4.3320
06
.0000
17
14.3962
37
12.2268
57
8.8347
77
4.1041
18
14.2769
38
12.0875
68
8.6303
78
3.8699
19
14.1667
39
11.9437
59
8.4218
79
3.6200
20
14.0633
40
11.7953
60
8.2095
80
3.3680
21
13.9706
41
11.6455
ei
7.9933
61
3.1262
22
13.6837
42
11.4947
62
7.7735
82
2.8931
Younger Age Four Yean
i:
Age.
Value.
Age.
Value.
Age.
44
Value.
Age.
Value.
Age.
Value.
4
15.1812
24
14.1784
11.5786
64
7.6627
84
2.5845
6
15.4075
25
14.0809
45
11.4123
65
7.3132J
85
2.4290
6
15.6318
26
13.9806
46
11.2411
66
7.0595
86
2.2872
7
15.7633
27
13.8771
47
11.0650
67
6.8020
87
2.1536
8
15.8238
28
13.7706
48
10.8832
68
6.6409
88
2.0412
9
15.8096
29
13.6610
49
10.6968
69
6.2770
89
1.8875
1.6906 '
10
15.7360
30
13.5481
50
10.5084
70
6.0110
00
11
15.6358
31
13.4318
61
10.3228
7\
5.7440
91
1.4213
12
15.6250
32
13.8119
52
10.1365
72
9.4772
4.2127
92
1.(336
13
15.4088
33
13.1884
53
9.9461
73
93
.8037
14
15.2870
34
13.0610
64
9.7513
74
4.9532
94
.6169
15
15.1593
35
12.9298
55
9.5522
75
4.7024
96
.2363
16
15.0253
36
12.7944
56
9.3488
76
4.4660
06
.0000
17
14.8937
37
12.6547
57
9.1411
77
4.2293
18
14,7707
38
12.6106
68
8.9291
78
3.9862
19
14.6569
39
12.3619
69
8.7129
79
3.7271
20
14.5504
40
12.2083
60
8.4925
80
3.4660
21
14.4549
41
12.0534
61
8.2681
81
3.2157
22
14.3653
42
11.8973
62
8.0399
82
2.9747
23
14.2732
43
11.7402
63
7.8033
83
2.7530
Digitized by VjOOQ IC
948
TABLB VIII.
Valae of an Annuity on Two joint lives. (Noithampton 3 per Cent)
Younger Age Five Years.
Ag«.
. Value.
Age.
Valae.
Age.
45
Valae.
Age.
Value.
Age.
Valae.
5
15.a381
25
14.3015
11.5973
65
7.4290
85
2.4545
6
15.8666
26
14.2000
46
11.4236
66
7.1706
86
2.3104
7
16.0008
27
14.0955
47
11.2447
67
6.9082
87
2.1745
8
16.0649
28
13.9878
48
11.0605
68
6.6422
88
2.0599
9
16.0490
29
13.8769
49
10.8703
69
6.3733
89
1.9033
10
15.9748
30
13.7627
60
10.6793
70
6.1022
90
1.7030
11
15.8736
31
13.6450
61
10.4907
71
5.8301
91
1.4301
12
15.7616
32
13.5236
52
10.S015
72
5.5582
92
1.1392
13
15.6441
33
13.3985
53
10.1079
73
5.2887
93
.8067
14
15.5209
34
13.2695
54
9.9099
74
5.0242
94
.5181
15
15.3917
35
13.1365
55
9.7075
'75
4.7686
95
.2356,
16
15.2562
36
12.9993
56
9.5007
76
4.5277
96
.0000
17
15.1230
37
12.8578
57
9.2895
n
4.2863
18
14.9985
38
12.7117
58
9.0738
78
4.0384
19
14.8836
39
12.5609
59
8.'B538
79
3.7745
20
14.7759
40
12.4051
60
8.6296
80
3.5087
21
14.6794
41
12.2480
61
8.4013
81
3.2540
22
14.5889
42
12.0896
62
8.1690
82
3.0090
23
14.4959
43
11.9302
63
7.9281
83
2.7839
24
14.4001
44
11.7662
64
7.6830
84
2.6125
Younger Age Six Yean.
Age.
Valae.
Age.
26
Valae.
Age.
46
Value.
Age.
Value.
Ag*
Valae.
6
16.0993
14.4204
11.6105
66
7.2904
86
2.3414
7
16.2363
27
14.3149
47
11.4291
67
7.0234
87
2.2030
8
16.3021
28
14.2062
48
11.2422
68
6.7526
88
2.0861
9
16.2867
29
14.0942
49
11.0497
69
6.4789
89
1 .9265
10
16.2121
30
13.9788
50
10.8551
70
6.2029
90
1.7225
11
16.1100
31
13.8598
51
10.6641
71
5.9257
91
1.4452
12
15.9970
32
13.7371
52
10.4721
72
5.6489
92
1.1501
13
15.8784
33
13.6107
53
10.2756
73
5.3743
93
.8135
14
15.7540
34
13.4802
54
10.0746
74
5.1049
94
.5220
15
15.6234
35
13.3457
55
9.8691
n
4.8446
95
.2371
16
15.4864
36
13.2068
56
9.6591
76
4.5991
96
.0000
17
15.3519
37
13.0635
57
9.4446
n
4.3531
18
15.2261
38
12.9157
58
9.2255
78
4.1004
19
15.1100
39
12.7629
59
9.0020
79
3.8315
20
15.0014
40
12.6052
60
8.7742
80
3.5608
21
14.9040
41
12.4460
61
8.5421
81
3.3014
22
14.8128
42
12.2856
62
8.3060
82
3.0521
23
14.7190
43
12.1240
63
8.0610
83
2.8231
24
14.6224
44
11.9578
64
7.8118
84
2.6488
25
14.5229
45
11.7867
65
7.5533
85
2.4880
Digitized by LjOOQ IC
TABLE VIIJ.
249
Value of an Annuity on Two joint Lives. (Northampton 3 per Cent)
Younger Age Seven Yean.
Afe.
Value.
A8«.
Valae.
A«e.
Value.
Age.
Valoe.
Age.
Value.
7
16.3752
27
14.4514
47
11.5502
67
7.1043
87
2.2248
8
16.4424
28
14.3424
46
11.3619
68
6.8306
88
2.1063
9
16.4276
29
14.2300
49
11.1680
69
6.5537
89
1.9444
10
16.3532
30
14.1142
50
10.9723
70
6.2745
90
1.7377
11
16.2511
31
13.9948
51
10,7789
71
5.9941
91
1.4570
12
16.1378
32
13.8717
52
10.5858
72
5.7139
92
1.1586'
13
16.0189
33
13.7447
53
10.3877
73
5.4361
93
.8189
14
15.8941
34
13.6137
54
10.1851
74
5.1634
94
.5249
15
15.7632
35
13.4785
55
9.9779
75
4.8999
95
.2382
16
15.6257
36
13.3390
56
9.7660
76
4.6512
96
.0000
17
15.4906
37
13.1950
57
9.5496
n
4.4021
18
15.3644
38
13.0463
58
9.3286
78
4.1462
19
15.2480
39
12.8927
59
9.1030
79
3.6738
20
15.1391
40
12.7341
60
8.8731
80
3.5996
21
15.0415
41
12.5740
61
8.6388
81
3.3369
22
14.9503
42
12.4125
62
8.4003
82
3.0844
23
14.8563
43
12.2500
63
8.1529
83
2.8526
24
14.7595
44
12.0826
64
7.9011
84
2.6761
25
14.6598
45
11.9103
65
7.6400
85
2.5134
26
14.5571
46
11.7329
66
7.3742
86
2.3649
Younger Age Eight Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
8
16.5106
28
14.4173
48
11.4354
68
6.8843
88
2.1225
9
16.4967
29
14.3052
49
11.2409
69
6.6057
89
1.9592
10
16.4228
30
14.1896
50
11.0447
70
6.3246
90
1.7505
11
16.3211
31
14.0704
51
10.8512
71
6.0423
91
1.4673
12
16.2082
32
13.9474
52
10.6566
72
5.7601
92
1.1663
13
16.0897
33
13.8206
53
10.4584
73
5.4803
93
.8239
14
15.9652
34
13.6897
54
10.2551
74
5.2056
94
.5278
15
15.8345
35
13.5546
55
10.0471
75
4.9400
95
.2394
16
15.6971
36
13.4151
56
9.8345
76
4.6894
96
.0000
17
15.5623
37
13.2711
57
9.6173
n
4.4382
18
15.4363
38
13.1223
58
9.3954
78
4.1802
19
15.3201
39
12.9687
59
9.1689
79
3.9054
20
15.2115
40
12.8099
60
8.9379
80
3.6290
21
15.1143
41
12.6496
61
8.7025
81
3.3639
22
15.0234
42
12.4880
62
8.4630
82
3.1093
23
14.9297
43
12.3252
63
8.2143
83
2.8755
24
14.8333
44
12.1576
64
7.9612
84
2.6975
25
14.7339
45
11.9850
65
7.6986
85
2.5333
26
14.6315
46
11.8073
66
7.4313
86
2.3836
27
14.5260
47
11.6241
67
7.1597
87
2.2422
Digitized by LjOOQ IC
850
TABLB Vin.
Valae of an Annuity on Two joint Livei. (Northampton 3 per Cent)
Younger Age Nine Years.
Age.
Vilue.
A|».
Value.
Age.
Value.
Age.
Value.
Age.
81
Value.
9
16.4837
27
14.5293
46
12.0020
63
8.2377
3.3780
10
16.4108
28
14.4214
46
11.8248
64
7.9846
82
8.1224
11
16.3101
29
14.3102
47
1U6422
65
7.7220
83
2.8877
12
16.1982
30
14.1954
48
11.4540
66
7.4546
84
2.7090
13
16.0806
31
14.0770
49
11.2601
67
7.1828
85
2.5442
14
15.9571
32
13.9549
50
11.0643
68
6.9071
86
2.3938
li
15.8273
33
13.8289
51
10.8713
69
6.6282
87
2.2518
16
' 15.6909
34
13.6988
52
10.6776
70
6.3467
88
2.1316
17
15.5569
35
13.5645
53
10.4788
71
6.0639
89
1.9676
18
15.4319
36
13.4258
54
10.2764
72
6.7813
90
1.7578
19
15.3165
37
13.2825
55
10.0688
73
6.6009
91
1.4733
20
15.2087
38
13.1345
56
9.8566
74
6.2255
92
1.1700
21
15.1124
39
12.9816
57
9.6396
75
4.9593
93
.8270
22
15.0224
40
12.8235
58
9.4180
76
4.7080
94
.5297
23
14.9296
41
12.6639
69
9.1917
77
4.4561
95
.2408
24
14.8340
42
12.5030
60
8.9610
78
4.1972
96
«0000
25
14.7355
43
12.3409
61
8.7258
79
8.9216
26
14.6340
44
12.1739
62
8.48G3
80
3.6440
-
Younger Age Ten Years.
Age.
Value.
Age.
28
Value.
■Age.
V4lue.
Age.
Vtiue.
Age.
Valufe.
10
16.3391
14.3735
46
11.8001
64
7.9808
82
8.1259
11
16.2398
29
14.2636
47
11.6188
66
7.7185
83
2.6911
12
16.1293
30
14.1. 501
48
11.4319
66
7.4520
84
2.7123
13
16.0132
31
14.0330
49
11.2391
67
7.1811
85
2.6474
14
15.8911
32
13.9121
60
11.0446
68
6.9062
86
8.3970
15
15.7627
33
13.7874
51
10.8628
69
6.6280
87
2.2649
16
15.6277
34
13.6586
62
10.6603
70
6.3472
88
2.1346
17
15.4952
35
13.5256
63
10.4631
71
6.0650
89
1.9708
18
15.3715
36
13.3882
54
10.2608
72
6.7829
90
1.7603
19
15.2575
37
13.2463
55
10.0549
73
5.5030
91
1.4756
20
15.1510
38
13.0996
56
9.8438
74
5.2280
92
1.1726
21
15.0559
39
12.9480
57
9.6279
75
4.9622
93
.8282
22
14.9670
40
12.7912
58
9.4074
76
4.7112
94
.6304
23
14.8755
41
12.6329
59
9.1823
77
4.4595
95
.2406
24
14.7811
42
12.4733
60
8.9526
78
4.2008
96
.0000
25
14.6838
43
12.3124
61
8.7184
79
3.9252
26
14.5836
44
12.1468
62
8.4800
80
8.6476
27
14.4802
45
11.9760
63
8.2324
81
3.8816
Digitized by ^^UUV IC
TABLl VUL
tol
Value of an Amuiiiy on Tiro joint LItos. (Northampton 3 par Cent)
Younger Age Eleven Years.
Age.
Valua.
Age.
29
Value.
Age.
Value.
Age.
65
Value.
Age.
83
Value.
11
16.1420
14.1929
47
11.6760
7.7023
2.8903
19
16.0331
30
14.0809
48
11.3906
66
7.4372
84
2.7117
13
15.9186
31
13.9653
49
11.1994
67
7.1676
85
2.5471
14
15.7982
32
13.8460
60
11.0064
68
6.8940
86
2.3969
15
15.6715
33
13.7227
51
10.8161
69
6.6169
87
2.2550
16
15.5382
34
13.5955
52
10.6251
70
6.3373
88
2.1348
1.9706
17
15.4073
35
13.4640
53
10.4295
71
6.0563
89
18
15.2852
36
13.3282
54
10.2292
72
5.7752
90
1.7606
19
15.1727
37
13.1878
55
10.0236
73
9.4963
91
1.4758
20
15.0676
38
13.0427
56
9.8146
74
5.2223
92
1.1728
21
14.9739
39
12.8926
57
9.6002
75
4.9572
93
.8284
22
14.8864
40
12.7375
58
9.3812
76
4.7071
94
.5305
23
14.7963
41
12.5807
59
9.1575
77
4.4561
95
.2406
24
14.7033
42
12.4226
60
8.9292
78
4.1979
96
.0000
25
14.6074
43
12.2634
61
8.6965
79
3.9229
26
14.5086
44
12.0993
62
8.4596
80
3.6458
27
14.4066
45
11.9301
63
8.2134
81
3.3802
28
14.3014
46
11.7557
64
7.9627
82
3.1248
Younger Age Twelve Years.
Age.
Value.
Age.
Value.
Age.
Value.
Ag«.
66
Value.
Age.
Value.
19
15.9259
30
14.0021
48
11.3415
7.4172
84
2.7097
18
15.8131
31
13.8881
49
11.1521
67
7.1491
85
2.5454
14
15.6944
32
13.7704
50
10.9607
68
6.S769
86
2.3955
)5
15.5695
33
13.6487
51
10.7721
69
6.6013
87
2.2539
16
15.4380
34
13.5231
52
10.5827
70
6.3231
88
2.1340
17
15.3088
33
13.3932
53
10.3887
71
6.0434
89
1.9701
18
15.1884
36
13.2590
54
10.1901
72
5.7636
90
1.7603
19
15.0775
37
13.1203
65
9.9867
73
5.4859
91
1.4755
20
14.9740
38
12.9769
56
9.7780
74
5.2130
92
1.1727
21
14.8817
39
12.8285
57
9.5659
75
4.9490
93
.8283
22
14.;956
40
12.6750
58
9.3485
76
4.6998
94
.5305
23
14.7069
41
12.5200
59
9.1264
77
4.4498
95
.2405
24
14.6154
42
12.3635
60
8.8998
78
4.1925
96
.0000
25
14.5210
43
12.2059
61
8.6687
79
3.9182
26
14.4237
44
12.0435
62
8.4333
80
3.6418
27
14.3232
45
11.8760
63
8.1887
81
3.3768
28
14.2196
46
11.7038
64
7.9395
82
3.1220
29
14.1126
47
11.5252
65
7.6808
83
2.8879
m
JABLB Vlin
Value of an Annuity on Two joint Litoi. (Northampton 3 per Cent.)
. Younger Age Thirteen Yean.
Agi.
Valae.
Ag«.
ValiM.
Agn.
Valve.
Agt.
^ Value.
Ag«.
Value.
13
15.7021
31
13.8060
49
11.1007
67
7.1278
85
2.5431
14
16.5851
32
13.6899
50
10.9111
68
6.8572
86
2.3936
15
15.4620
33
13.5699
51
10.7241
69
6.5832
87
2.2523
16
15.3323
34
13.4459
52
10.5364
70
6.3065
88
2.1328
17
15.2049
35
13.3177
53
10.3441
71
6.0281
89
1.9692
18
15.0862
36
13.1852
54
10.1472
72
5.7498
90
1.7597
19
14.9769
37
13.0482
55
9.9455
73
5.4733
91
1.4752
20
14.8750
38
12.9065
56
9.7392
74
5.2017
92
1.1725
21
14.7842
39
12.7598
57
9.5273
75
4.9390
93
•8282
22
14.6996
40
12.6081
58
9.3123
76
4.6909
94
•5304
23
14.6124
41
12.4548
59
9.0919
77
4.4419
95
•2405
24
14.5224
42
12.3000
60
8.8670
78
4.1856
96
.0000
25
14.4295
43
12.1442
61
8.6375
79
3.9122
26
14.3337
44
11.9834
62
8.4038
80
3.6367
27
14.2347
45
11.8177
63
8.1609
81
3.3724
28
14.1327
46
11.6467
64
7.9134
82
3.1182
29
14.0273
47
11.4704
65
7.6563
83
2.8847
130
13.9184
48
11.2884
66
7.3943
84
2.7069
YooDger Age Fourteen Yeapi.
Afli.
Value.
Age.
Value.
Age.
Valne.
Age.
ValM.
Age.
86
Valee.
14
15.4700
32
13.6042
50
10.8572
68
6.8345
2.3907
15
15.3487
33
13.4859
51
10.6720
69
6.5621
87
2.2499
16
15.2209
34
13.3636
52
10.4861
70
6.2870
88
2.1309
17
15.0953
35
13.2372
53
10.2955
71
6.0102
89
1.9677
18
14.9783
36
13.1064
54
10.1003
72
5.7333
90
1.7587
19
14.8708
37
12.9711
55
9.9004
73
5.4583
91
1.4746
20
14.7704
38
12.8312
56
9.6958
74
5.1881
92
1.1722
21
14.6812
39
12.6863
57
9.4864
75
4.9266
93
.8281
22
14.5981
40
12.5363
58
9.2716
76
4.6797
94
.5304
23
14.5123
41
12.3848
59
9.0537
77
4.4319
95
.2405
24
14.4238
42
12.2319
60
8.8305
78
4.1768
96
.0000
25
14.3325
43
12.0777
61
8.6028
79
3.9045
26
14.2382
44
11.9188
62
8.3708
80
3.6300
27
14.1409
45
11.7548
63
8.1296
81
3.3666
28
14.0404
46
11.5857
64
7.8838
82
3.1132
29
13.9366
47
11.4111
65
7.6284
83
2.8803
30
13.8294
48
11.2310
66
7.3682
84
2.7031
31
13.7187
49
11.0450
67
7.1034
85
2.5397
Digitized by LjOOQ IC
TABU VIHr
S63
Value of an Annoitj on Two jcunt Livea. (Northampton 3 per Gent)
Younger Age Fifteen Years.
^9^
Value.
Ag«.
Value.
Age.
Value.
Age.
69
Value.
Age.
Value.
15
15.2292
33
13.3965
51
10.6154
6.5376
87
2.2463
16
15.1034
34
13.2760
52
10.4312
70
6.2642
88
2.1278
17
14.9797
35
13.1513
53
10.2424
71
5.9891
89
1.9653
18
14.8645
36
13.0223
54
10.0490
72
5.7138
90
1.7569
19
14.7586
37
12.8888
55
9.8509
73
6.4404
91
1.4734
90
14.6599
38
12.7506
56
9.6481
74
5.1716
92
1.1715
21
14.5723
39
12.6076
57
9.4406
75
4.9116
93
,8278 ;
22
14.4906
40
12.4595
58
9.2283
76
4.6660
94
.5303
23
14.4065
41
12.3098
59
9.0105
77
4.4195
95
•2405 '
24
14.3195
42
12.1586
60
8.7900
78
4.1656
96
.0000
25
14.2298
43
12.0063
61
8.5641
79
3.8946
26
14.1371
44
11.8492
62
8.3339
80
3.6213
27
14.0414
45
11.6871
63
8.0945
81
3.3589
28
13.9425
46
11.5198
64
7.8505
82
3.1064
29
13.8404
47
11.3471
65
7.5969
83
2.8744
•30
13.7349
48
11.1688
66
7.3386
84
2.6978
31
13.6258
49
10.9847
67
7.0755
85
2.5350
32
13.5131
50
10.7987
68
6.8083
86
2.3865
Younger Age Sixteen Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
70
Value.
Age.
Value.
16
14.9794
34
13.1825
52
10.3715
6.2378
88
2.1230
17
14.8577
35
13.0596
53
10.1845
71
5.9644
89
1.9613
18
14.7443
36
12.9324
54
9.9930
72
5.6908
90
1.7637 j
19
14.6402
37
12.8008
55
9.7967
73
5.4190
91
1.4711
20
14.5431
98
12.6645
56
9.5958
74
5.1519
92
1.1700;
21
14.4571
39
12.5233
57
9.3901
75
4.8933
93
.8269
22
14.3770
40
12.3771
58
9.1797
76
4.6492
94
•5298
23
14.2944
41
12.2293
59
8.9647
77
4.4041
95
.2403:
24
14.2090
42
12.0800
60
8.7441
78
4.1516
96
.0000
25
14.1209
43
11.9296
61
8.5210
79
3.8820
26
14.0299
44
11.7743
62
8.2927
80
3.6099
27
13.9358
45
11.6141
63
8.0551
81
3.3488
28
13.8386
46
11.4487
64
7.8130
82
3.0974
29
13.7382
47
11.2779
65
7.5613
83
2.8663
30
13.6344
48
11.1015
66
7.3047
84
2.6905
31
13.5270
49
10.9194
67
7.0436
85
2.5284
32
13.4160
50
10.7353
68
6,7783
86
2.3805
33
13.3012
51
10.5538
69
6^5094
87
2.2409
Digitized by VjOOQIC
fi54 TABM Yin.
Valae of an Annuity on Two joint Lives. (Northampton 3 per Cent.)
Younger Age Seventeen Years.
Age.
Valae.
Age.
Value.
Age.
57
Value.
Age.
Value.
17
14.7378
37
12.7145
9.3405
77
4.3881
18
14.6262
38
12.5800
58
9.1319
78
4.1369
19
14.5238
39
12.4407
59
8.9187
79
3.8687
20
14.4284
40
12.2963
60
8.7009
80
3.5979
ill
14.3439
41
12.1504
61
8.4775
81
3.3380
S2
14.2654
42
12.0030
62
8.2520
82
3.0877
£3
14.1843
43
11.8543
63
8.0162
83
2.6576
24
14.1005
44
11.7009
64
7.7759
84
2.6825
25
14.0140
45
11.5425
65
7.5260
85
2.5211
2€
13.9246
46
11.3789
66
7.2712
86
2.3739
97
18.8302
47
11.2100
67
7.0118
87
2.2349
28
13.7366
48
11.0355
68
6.7483
88
2.1176
29
13.6379
49
10.8553
69
6.4811
89
1,9566
30
13.5358
50
10.6731
70
6.2112
90
1.7499
31
13.4301
51
10.4934
n
5.9395
91
1.4682
32
13.3209
52
10.3129
72
5.6676
92
1.1680
33
13.2078
53
10.1277
r3
5.3974
93
.8256
34
13.0908
54
9.9380
74
5.1317
94
•5291
35
12.9697
55
9.7435
75
4.8746
95
.2401
36
12.8443
56
9.5444
76
4.6318
96
.0000
Younger Age Eighteen Years.
Age.
Valae.
Age
Value.
Age.
58
Value.
Age.
Valoe.
18
14.6164
38
12.5027
9.0889
78
4.1236
19
14.4156
39
12.3651
59
8.8774
79
8.8566
20
14.3218
40
12.2225
60
8.6612
80
3.5870
21
14.2389
41
12.0783
61
8.4405
81
3.3281
22
14.1618
42
11.9326
62
8.2144
82
3.0788
23
14.0822
43
11.7857
63
7.9814
83
2.8495
24
14.0000
44
11.6340
64
7.7427
84
2.6752
25
13.9150
45
11.4774
65
7.4944
85
2.5)44
26
13.8272
46
11.3156
66
7.2412
86
2.3677
27
13.7363
47
11.1484
67
6.9834
87
2.2293
28
13.6424
48
10.9757
68
6.7214
88
8.1124
29
13.5452
49
10.7972
69
6.4558
89
1.9521
30
13.4448
5Q
10.6168
70
6.1874
90
1.7461
31
13.3408
51
10.4387
71
5.9172
91
1.4654
32
13.233:i
52
10.2599
72
5.6467
92
1.1660
33
13.1218
53
10.0765
73
5.3779
98
.8244
34
13.0065
54
9.8884
74
5.1136
94
.5285 '
35
12.8871
55
9.6956
75
4.8577
95
.2398
36
12.7635
5Q
9.4981
76
4.6162
96
.0000
37
12.6354
57
9.2959
77
4.3736
Digitized by
Google
Y^Im of fm Aaniti^ wn Two joint lii? m. (If Qitl>4»»tm 3 p«F C«Mt.)
Younger Age Nineteen Yean.
m
Age.
Valua,
Ag«.
Valua.
Ag*
Valw.
A8^
V«4aa.
19
14.3164
39
12.2973
59
8.8415
79
3.8462
20
14.3242
40
12.1563
60
8.6268
80
3.5776
21
14.1427
41
12.0188
61
8.4076
81
3.3196
22
14.0671
43
11.8698
62
8.1841
83
a. 0711
23
13.9889
43
11.7248
68
7.^9508
83
8.8426
24
13.9089
44
11.5745
64
7.7141
84
2.6688
25
13.8247
45
11.4195
65
7.4673
85
3.5085
26
13.7388
46
11.25Q4
66
7.2155
86
2.3623
27
13.6401
47
11.0939
67
6.9591
87
2.2?43
28
13.&567
48
10.9228
68
6.6985
88
2.1079
29
13.4611
49
10.7459
69
6.4348
89
1.9481
30
13.3698
50
10.5671
70
6.1671
90
1.7428
31
13.2598
51
10.3907
71
5.8988
91
1.4628
32
13.1538
&2
10.2134
73
5.6289
92
1.1641
33
13.0440
58
10.0315
73
5.3613
03
.8233
34
12.9304
54
9.8450
74
5.0981
94
.5379
35
12.8126
55
9.6537
75
4.8434
95
.2396
36
12.6906
56
9.4578
76
4.6028
96
.0000
37
12.5642
57
9.2571
77
4.3612
38
12.4332
58
9.0516
78
4.1133
Younger Age Twenty Yeftra.
Ag..
VM««.
Ag*
Vidae.
Ag«.
60
Valne.
Age.
Vahi«.
20
14.)335
40
12.0963
8.5969
80.
3.5695
21
14.0534
41
11.9554
61
8.3790
81
3.3123
22
13.9798
42
11.8130
62
8.1568
82
3.0645
23
13.9025
43
11.6693
63
7.9254
83
2.8366
24
13.8231
44
11.5209
64
7.6881
84
2.6633
23
13,7411
45
11.3674
65
7,4439
85
2.5034
26
13.6563
46
11.2089
66
7.1933
86
2.3576
27
13.5685
47
11.0449
67
6.93S2
87
2.2-200
28
13.4776
48
10.8754
68
6.6788
88
2.1039
29
13.3885
49
10.7001
69
6.4157
89
1.9445
30
13.3868
50
10.5239
70
6.1497
90
1.7397
31
13.}853
51
10.3480
71
5.8819
91
1.4604
32
13.0809
52
10.1723
72
5.6137
92
1.1Q23
33
12.9728
53
9.9917
78
5.3472
93
.8221
34
12.8607
54
9.8066
74
5.0850
94
.5272
35
12.7445
55
9.6168
75
4.8311
95
.2393
36
12.6241
56
9.4223
76
4.5915
96
.0000
37
12.4993
57
9.2230
77
4.3507
38
12.3699
58
9.0190
78
4.1026
39
12.3356
59
8.8102
79
3.8373
Digitized by LjOOQ IC
856
TABLB VIII.
Valaa of on Asumiiy on Two joint Livet. (Northampton 3 per Cent)
Younger Age Twenty-One Yean.
Age.
Value.
Age.
Valiu.
rA«e.
Value.
•Age.
Value.
21
13.9747
41
11.9063
61
8.3573
81
3.3076
22
13.9018
42
11.7654
62
8.1362
82
3.0602
23
13.8265
43
11.6233
63
7.9060
83
2.8328
24
13.7486
44
11.4763
64
7.6711
84
2.6598
25
13.6679
45
11.3244
65
7.4251
85
2.5002
26
13.5845
46
11.1673
66
7.1771
86
2.3547
27
13.4982
47
11.0048
67
6.9230
87
2.2173
28
13.4088
48
10.8368
68
6.6645
88
2.1015
29
13.3162
49
10.6629
69
6.4024
89
1.9423
30
13.2203
50
10.4871
70
6.1374
90
1.7379
31
13.1210
51
10.3135
71
5.8705
91
1.4589
32
13.0181
52
10.1391
72
5.6031
92
1.1612
33
12.9114
53
9.9600
73
5.3374
93
.8213
34
12.8009
54
9.7762
74
5.0759
94
.5267
35
12.6862
55
9.5877
75
4.8228
95
.2391
36
12.5674
56
9.3945
76
4.5838
96
.0000
37
12.4441
57
9.1964
77
4.3437
38
12.3162
58
8.9936
78
4.0961
39
12.1835
59
8.7861
79
3.8315
40
12.0457
60
8.5740
80
3.5643
Younger Age Twenty-Two Years.
Aft.
Value.
Age.
Value.
Agu
Value.
Age.
Value.
22
13.8303
42
11.7233
62
8.1198
82
3.0577
23
13.7563
43
11.5826
63
7.8906
83
2.8305
24
13.6798
44
11.4371
64
7.6568
84
2.6573
25
13.6006
45
11.2866
65
7.4132
85
2.4984
26
13.5185
46
11.1309
66
7.1631
86
2.3531
27
13.4336
47
10.9699
67
6.9115
87
2.2159
28
13.3457
48
10.8032
68
6.6539
88
2.1002
29
13.2546
49
10.6308
69
6.3926
89
1.9413
30
13.1602
50
10.4563
70
6.1284
90
1.7370
31
13.0623
51
10.2841
71
5.8622
91
1.4583
32
12.9609
52
10.1110
72
6.6956
92
1.1608
33
12.8557
53
9.9332
73
5.3305
93
.8211
34
12.7467
54
9.7507
74
5.0697
94
.5266
35
12.6336
55
9.5634
75
4.8171
95
.2391
36
12.5162
56
9.3713
76
4.5786
96
.0000
37
12.3945
57
9.1745
77
4.3390
38
12.2681
58
8.9729
78
4.0920
39
12.1369
59
8.7665
79
3.8278
40
12.0006
60
8.5555
80
3.5610
41
11.8627
61
8.3399
81
3.3047
Digitized by LjOOQ IC
TABLE VIII.
257
VaIim of an Aniraiiy on Two joint Uvti. (Northampton 3 per Cent.)
Younger Age Twenty-Three Yean.
Ag«.
VftlM.
Ag..
Valae.
Age.
63
Valaa.
Ag«.
83
Value.
23
13.6837
43
11.5403
7.8748
2.8282
24
13.6086
44
11.3963
64
7.6419
84
2.6557
25
13.5308
45
11.2473
65
7.3994
85
2.4965
26
13.4502
46
11.0932
66
7.1519
86
2.3514
27
13.3668
47
10.9336
67
6.8996
87
2.2144
28
13.2803
48
10.7684
68
6.6429
88
2.0989
29
13.1907
49
10.5974
69
6.3825
89
1.9402
30
13.0978
50
10.4244
70
6.1191
90
1.7362
31
13.0015
51
10.2535
71
5.8537
91
1.4576
32
12.9016
52
10.0818
72
5.5878
92
1.1603
33
12.7980
53
9.9053
73
5.3234
93
.8208
34
12.6905
54
9.7241
74
5.0632
94
.5264
35
12.5789
55
9.5381
75
4.8113
95
.2390
36
12.4632
56
9.3474
76
4.5733
96
.0000
37
12.3429
57
9.1518
77
4.3342
38
12.2181
58
8.9514
78
4.0877
39
12.0885
59
8.7462
79
3.8240
40
11.9538
60
8.5363
80
3.5576
41
11.8174
61
8.3218
81
3.3017
42
11.6795
62
8.1029
82
3.0551
Younger Age Twenty-Four Years.
Age.
Value.
Age.
44
Value.
Age.
64
Value.
Age.
Value.
24
13.5349
11.3540
7.6265
84
2.6535
25
13.4586
45
11.2066
65
7.3851
85
2.4946 ■
26
13.3795
46
11.0539
66
7.1386
86
2.3197
27
13.2975
47
10.8959
67
6.8872
87
2.2129
28
13.2126
48
10.7322
68
6.6315
88
2.0976
29
13.1245
49
10.5628
69
6.3720
89
1.9390
30
13.0332
50
10.3912
70
6.1094
90
1.7353
31
12.9384
51
10.2218
71
5.8449
91
1.4569
32
12.8401
52
10.0514
72
5.5797
92
1.1599
33
12.7381
53
9.8763
73
5.3161
93
.8205
34
12.6322
54
9.6965
74
5.0566
94
.5263
35
12.5222
55
9.5119
75
4.8053
95
.2390
36
12.4081
56
9.3224
76
4.5679
96
.0000
37
12.2895
57
9.1281
77
4.3293
38
12.1663
58
8.9290
78
4.0833
39
12.0382
59
8.7251
79
3.8201
40
11.9052
60
8.5164
80
3.5542
41
11.7704
61
8.3031
81
3.2986
42
11.6341
62
8.0853
82
3.0524
43
11.4965
63
7.8583
83
2.8258
Digitized byi^jOOQlC
258
TABLE VIII.
Vtltto of an Anaui^ on Two joiot Livw. (NozthMnpton 3 per Cent)
Younger Age Twenty*Fiye Yean.
Ag..
V^ue.
Age.
Value,
Age.
Vtlue.
Age.
Vmlue.
25
13.3837
45
11.1642
65
7.3702
85
2.4926
26
13.3062
46
11.0131
66
7.1248
86
2.3479
27
13,2247
47
10.8567
67
6.8745
87
2.2113
28
13.1423
48
10.6946
68
6.6197
88
2.0962
29
13.0558
49
10.5267
69
6.3612
89
1.9379
30
12.9661
50
10.3566
70
6.0995
90
1.7343
31
12.8730
51
10.1888
71
5.8358
91
1.4562
32
12.7763
52
10.0199
72
5.5714
92
1.1594
33
12.6759
53
9.8462
73
5.3085
93
.8202
34
12.5716
54
9.6678
74
5.0497
94
.5261
35
12.4634
55
9.4846
75
4.7990
95
.2389
36
12.3508
56
9.2965
76
4.5622
96
.0000
37
12.2339
57
9.1036
77
4.3242
38
12.1124
58
8.9058
78
4.0787
39
11.9860
59
8.7031
79
3.8160
40
11.8546
60
8.4957
80
3.5506
41
11.7215
61
8.2836
81
3.2955
42
11.5868
62
8.0670
82
3.0496
43
11.4508
63
7.8412
83
2.8233
44
11.3100
64
7.6106
84
2.6513
Younger Ag^ Tw«nty-5ix Years,
Age.
Value.
Age.
Valae.
Age.
66
VeUe.
Ag«.
86
Value.
26
13.2301
46
10.9706
7.1104
2.3461
27
13.1513
47
10.6158
67
6.8612
87
2.2097
28
13.0695
48
10.6554
68
6.6075
68
2.0949
29
12.9S46
49
10.4891
69
6.3499
89
1.9367
30
12.8965
50
10.3207
70
6.0891
90
1.7334
31
12.8050
51
10.1543
71
5.8263
91
1.4555
32
12.7100
52
9.9870
72
5.5628
92
1.1589
33
12.6113
53
9.8148
73
5.3006
93
.8199
34
12.5087
54
9.6379
74
5.0426
94
.5260
35
12.4021
55
9.4562
75
4.7926
95
.2388
36
12.2914
56
9.2695
76
4.5564
96
.0000
37
12.1761
57
9.0780
77
4.3189
38
12.0563
58
8.8816
78
4.0740
39
11.9317
59
8.6803
79
3.8118
40
11.8020
60
8.4742
80
3.5469
41
11.6706
61
8.2634
61
3.2922
42
11.5377
62
8.0480
82
3.0467
43
11.4033
63
7.8234
83
2.8208
44
11.2642
64
7.5940
84
2.6490
45
11.1200
65
7.3548
85
2.4906
Digitized by VjOOQ IC
TABLK Vm.
Valaa of an Annaity on Two joint Iiives. (Northampton 3 per Gent
Younger Age Twenty-Seven Yeari.
259
Ag«\
Value.
Ag«.
Value.
Age.
67
Value.
Ace.
Vala
27
13.0740
47
10.7733
6.8474
87
2.2080
28
12.9939
48
10.6146
68
6.3948
88
2.0938
29
12.9106
49
10.4499
69
6.3382
89
1.9354
30
12.8242
50
10.2832
70
6.0784
90
1.7324
31
12.7344
51
10.1185
71
5.8165
91
1.4548
32
12.6411
52
9.9527
72
5.5538
92
1.1584
33
12.5441
53
9.7821
73
5.2925
93
.8196
34
12.4433
54
9.6067
74
5.0352
94
•5259
35
12.3385
55
9.4265
75
4.7859
95
.2388
36
12.2293
56
9.2414
76
4.5503
96
.0000
37
12.1160
57
9.0513
n
4.3135
-
38
11.9980
58
8.8563
78
4.0691
39
11.8752
59
8.6564
79
3.8075
40
11.7473
60
8.4517
80
3.5431
41
11.6177
61
8.2423
81
3.2888
42
11.4865
62
8.0282
82
3.0437
43
11.3539
63
7.8049
83
2.8182
44
11.2165
64
7.5767
84
2.6467
45
11.0740
65
7.3387
85
2.4885
46
10.9264
66
7.0955
86
2.3442
Younger Age Twenty-Eight Years.
Age.
Value.
Age.
48
Value.
Age.
68
Value.
Age.
Value.
28
12.9153
10.5719
6.5815
88
2.0918
29
12.8338
49
10.4091
69
6.3260
89
1.9341
30
12.7490
50
10.2440
70
6.0672
90
1.7313
31
12.6610
31
10.0810
71
5.8063
91
1.4540
32
12.3695
52
9.9168
72
5.5445
92
1.1579
33
12.4743
33
9.7479
73
5.2840
93
•8193
34
12.3753
54
9.5742
74
5.0275
94
•5256
35
12.2722
55
9.3935
75
4.7789
95
.2387
36
12.1651
36
9.2119
76
4.5440
96
.0000
37
12.0535
57
9.0234
77
4.3078
38
11.9373
58
8.8299
78
4.0640
39
11.8163
59
8.6315
79
3.8030
40
11.6903
60
8.4282
80
3. .5391
41
11.5625
61
8.2202
81
3.2853
42
11.4331
62
8,0073
82
3.0407
43
11.3023
63
7.7856
83
2.8155
44
11.1667
64
7.5586
84
2.6443
45
11.0260
65
7.3219
85
2.4863
46
10.8802
66
7.0800
86
2.3423
47
10.7289
67
6.8330
87
2.2063
DigitizecLbwS.
260
TABLE VIII.
Value of an Annuity on Two joint lives. (Northampton 3 per Cent)
Younger Age Twenty-Nine Years.
Ace.
ValM.
Age.
ValM.
Aga
Value.
A««.
ValM.
29
12.7540
49
10.3663
69
6.3133
89
1.9328
30
12.6710
50
10.2031
70
6.0556
90
1.7303
31
12.5847
51
10.0418
71
5.7956
91
1.4532
32
12.4950
52
9.8794
72
5.5348
92
1.1573
33
12.4016
53
9.7122
73
5.2752
93
.8190
34
12.3044
54
9.5401
74
5.0195
94
.5255
35
12.2033
55
9.3631
75
4.7717
95
.2386
36
12.0980
56
9.1812
76
4.5375
96
.0000
37
11.9883
57
8.9942
17
4.3020
38
11.8740
58
8.8023
78
4.05258
39
11.7549
59
8.6055
79
3.7984
40
11.6308
60
8.4037
80
3.5350
41
11.5049
61
8.1971
81
3.2817
42
11.3774
62
7.9859
82
3.0375
43
11.2485
63
7.7653
83
2.8126
44
11.1147
64
7.5398
84
2.6417
45
10.9760
65
7.3044
85
2.4841
46
10.8319
66
7.0637
86
2.3403
47
10.6825
67
6.8180
87
2.2045
48
10.5274
68
6.5676
88
2.0902
Younger Age Thirty Yean.
Ag.
Value.
Age
Value.
Age.
Value.
Age.
90
Value.
30
12.5898
50
10.1602
70
6.0433
1.7291
31
12.5053
51
10.0008
71
5.7845
91
1.4524
32
12.4174
52
9.8402
72
5.5247
92
1.1567
33
12.3259
53
9.6747
73
5.2660
93
.8186
34
12.2306
54
9.5044
74
5.0112
94
.5253
35
12.1314
55
9.3291
75
4.7642
95
.2386
36
12.0280
SS
9.1489
76
4.5307
96
.0000
37
11.9203
57
8.9636
77
4.2958
38
11.8080
58
8.7734
78
4.0533
39
11.6909
59
8.5781
79
3.7933
40
11.5687
60
8.3780
80
3.5307
41
11.4448
61
8.1729
81
3.2780
42
11.3192
62
7.9632
82
3.0342
43
11.1923
63
7 7441
83
2.8097
44
11.0605
64
7.5200
84
2.6391
45
10.9236
65
7.2860
85
2.4817
46
10.7815
66
7.0466
86
2.3.382
47
10.6340
67
6.8022
87
2.2027
48
10.4808
68
6.5531
88
2.0886
49
10.3216
69
6.2999
89
1.9314
Digitized
by^^
uoyi*^
TABLE VIIL
261
Value of an Annuity on Two joint Lives. (Northampton 3 per Cent.)
Younger Age Thirty-One Years.
Age.
Valve.
Age.
51
Value.
Age.
71
Valae.
Age.
Value.
31
12.4227
9.9578
5.7727
91
1.4516 '
32
12.3367
52
9.7991
72
5.5140
92
1.1562
33
12.2471
53
9.6355
73
5.V563
93
.8183
34
12.1538
54
9.4670
74
5.0024
94
.5251
35
12.0565
55
9.2935
75
4.7563
95
.2385
35
11.9551
56
9.1150
76
4. 5236
96
.0000
37
11.8494
57
8.9315
77
4.2894
38
11.7391
58
8.7430
78
4.0476
39
11.6240
.'59
8.5494
79
3.7884
40
11.5039
60
8.3509
80
3.5263
41
11.3820
61
8.1475
81
3.2740
42
11.2585
62
7.9394
82
3.0307
43
11.1335
63
7.7218
83
2.8067
44
11.0037
64
7.4992
84
2.6364
45
10.8688
65
7.2667
85
2.4793
46
10.7288
66
7.0287
86
2.3360
47
10.5832
67
6.7856
87
2.2008
48
10.4320
68
6.5379
88
2.0869
49
10.2748
69
6.2859
89
1.9300
50
10.1154
70
6.0305
90
1.7280
Younger Age Thirty-Two Years.
Age.
Value.
Age.
52
Value.
Age.
72
Value.
Age.
Value.
32
12.2526
9.7559
5.5028
92
1.1556
33
12.1650
53
9.5942
73
5.2462
93
.8179
34
12.0736
54
9.4276
74
4.9932
94
.5249
35
11.9784
55
9.2561
75
4.7480
95
.2384
36
11.8790
56
9.0795
76
4.5161
96
.0000
37
11.7753
57
8.8978
77
4.2827
3S
11.6671
58
8.7111
78
4.0416
39
11.5541
59
8.5193
79
3.7831
40
11.4361
60
8.3225
80
3.5216
41
11.3164
61
8.1207
81
3.2699
42
11.1949
62
7.9143
82
3.0271
43
11.07:^0
63
7.6983
83
2.8035
44
10.9443
64
7.4773
84
2.6336
45
10.8115
65
7.2463
85
2.4768
46
10.6735
66
7.0098
86
2.3338
47
10.5300
67
6.7682
87
2.1988
48
10.3809
68
6.5218
88
2.0852
49
10.2258
69
6.2711
89
1.9286
50
10.0683
70
6.0170
90
1.7268
51
9.9127
71
5.7604
91
1.4507
Digitized by LjOOQ IC
U2
TABLE VIII.
Value of an Annuity on Two joint Livei. (Northampton 3 per Cent.)
Younger Age Thirty-Three Years.
Aft.
Vftloe.
Age.
Value.
Age.
Value.
Age.
93
Value.
33
12.0793
53
9.5509
?73
5.2354
.8175
34
11.9900
54
9.3863
74
4.9835
94
.5247
35
11.8968
55
9.2167
75
4.7392
r6
.2333
36
11.7996
56
9.0420
76
4.5082
96
.0000
37
11.6980
57
8.8623
77
4.2756
38
11.5919
58
8.6774
78
4.0353
39
11.4811
59
8.4875
79
3.7776
40
11.3653
60
8.2925
80
3.5167
41
11.2477
61
8.0925
81
3.2656
42
11.1284
62
7.8878
82
3.0233
43
11.0076
63
7.6735
83
2.8002
44
10.8821
64
7.4542
64
2.6307
45
10.7514
65
7.2248
85
2.4742
46
10.6156
66
6.9899
86
2.3315
47
10.4742
67
6.7498
87
2.1967
48
10.3272
68
6.5048
88
2.0834
49
10.1742
69
6.2555
89
1.9270
50
10.0189
70
6.0027
90
1.7256
51
9.8654
71
5.7474
91
1.4498
52
9.7106
72
5.4910
92
1.1549
Younger Age Thirty-Four Years.
Age.
Value.
Age.
Value. -
Age.
Value.
Age.
94
Value.
34
11.9028
54
9.3427.
74
4.9732
.5245
35
11.8117
55
9.17521^
75
4.7299
95
.2383
36
11.7165
56
9.0025
76
4.4998
96
.0000
87
11.6172
57
8.8248
77
4.2681
38
11.5133
58
8.6419
78
4.0286
39
11.4047
59
8.4539
79
3.7716
40
11,2911
60
8.2608
80
3.5115
41
11.1757
61
8.0627
81
3.2611
42
11.0587
62
7.8598
82
3.0193
43
10.9402
63
7.6473
83
2.7967
44
10.8168
64
7.4297
84
2.6275
45
10.6&S4
65
7.2020
85
2.4714
46
10.5548
66
6.9688
86
2.3290
47
10.4157
67
6.7302
87
2.1946
48
10^2709
68
6.4868
88
2.0815
49
10.1201
69
6.2390
89
1.9254
60
9.9670
70
5.9876
90
1.7243
51
9.8156
71
5.7335
91
1.4488
. 52
9.6629
72
5.4784
92
1.1543
53
9.5053
73
5.2-240
93
.8171
Digitized by VaUUVlC
TABLE Vni.
m
Value of an Annoity od Two joint Lives. (Xorthampion 3 per Gent)
Younger Age Thirty- Five Years.
A«e.
Value.
Age.
Vitlae.
Aje.
Value.
Age.
Viiliie.
35
11.7227
55
9.1314
76
4.7199
96
.2382
36
11.6298
56
8.9608
76
4.4909
96
.0000
37
11.5328
57
8.7852
77
4.2601
38
11.4310
58
8.6043
78
4.0214
89
11.3247
59
8.4183
79
3.7653
40
11.2134
60
8.2272
80
3.5059
41
11.1004
61
8.0311
81
3.2562
42
10.9856
62
7.8301
82
3.0151
43
10.8694
63
7.6195
83
2.7929
44
10.7483
64
7.4037
84
2.6242
45
10.6223
65
7.1778
85
2.4684
46
10.4909
66
6.9463
86
2.3254
47
10.3541
67
6.7095
87
2.1923
48
10.2116
68
6.4677
88
2.0795
49
10.0632
69
6.2214
89
1.9238
50
9.9123
70
5.9714
90
K7230
51
9.7631
71
5,7188
91
1.4478
52
9.6126
72
5.4650
92
1.1536
53
9.4372
73
5.2118
93
.8167
54
9.2968
74
4.9622
94
.6242
Younger Age Thirty-Six Ypaw.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
96
Value.
36
11.5391
56
8.9168
76
4.4812
.0000
37
11.4442
57
8.7433
77
4.2515
38
11.3449
58
8.5646
78
4.0138
39
11.2409
59
8.3807
79
3.7585
40
11.1320
60
8.1917
80
3.5000
41
11.0213
61
7.9976
81
3.2509
42
10.9089
62
7.7986
82
3.0105
43
10.7951
63
7.5900
83
2.7869
44
10.6764
64
7.3761
84
2.6206
45
10.5527
65
7.1521
85
2.4652
46
10.4238
66
6.9224
86
2.3236
47
10.2894
67
6.6874
87
2.1898
48
10.1493
68
6.4472
88
2.0774
49
10.0032
69
6.2026
89
1.9220
50
9.8547
70
5.9542
90
1.7216
51
9.7078
71
5.7031
91
1.4468
52
9.5596
72
5.4506
92
1.1529
53
9.4065
73
5.1988
93
.8163
54
9.2483
74
4.9504
94
.5240
55
9.0851
75
4.7093
95
.2381
Digitize
jby Vj^^'O'^i^
264
TABLE VIII
Value of an Aanaity on TVo joint Lives. (Northampton 3 per Cent.)
Younger Age Thirty-Seven Years.
Age,
ValM.
Age.
Value.
Age.
Valoe.
Age.
Value.
Age.
Value.
37
11.3516
49
9.9400
61
7.9619
73
5.1848
85
2.4617
38
11.2546
50
9.79.39
62
7.76*iO
74
4.9376
86
2.3i05
39
11.1531
51
9.6495
63
7.5583
75
4.6977
%1
2.1871
40
11.0466
52
9.5036
64
7.3466
76
4.4708
88
2.07.50
41
10.9383
53
9.3528
65
7.1246
n
4.2421
89
1.9201
42
10.8284
54
9.1970
66
6.8969
78
4.0054
90
1.7201
43
10.7170
55
9.0361
67
6.6637
79
3.7512
91
1.4457
44
10.6008
56
8.8701
68
6.4254
80
3.4935
92
1.1522
45
10.4796
57
8.6988
69
6.1825
81
3.2463
93
.8159
46
10.3531
58
8.5224
70
5.9357
82
3.0055
94
.5238
47
10.2212
59
8.3407
71
5.6862
83
2.7845
95
.2380
48
10.0836
60
8.1539
72
5.4352
84
2.6167
96
.0000
Younger Age Thirty-Eight Yean.
Age.
Value.
Age.
Value.
Age.
62
Value.
Age.
Value.
Age.
Value.
38
11.1601
50
9.7298
7.7293
74
4.9239
86
2.3170
39
11.0610
51
9.5878
63
7.5249
75
4.6852
87
2. J 840
40
10.9570
52
9.4444
64
7.3152
76
4.4595
88
2.0723
41
10.8512
53
9.2961
65
7.0953
77
4.2319
80
1.9179
42
10.7438
54
9.1427
66
6.6696
78
3.9963
90
1.7184
43
10.6348
55
8.9842
67
6.6383
79
3.7431
91
1.4445
44
10.5212
56
8.8206
68
6.4019
80
3.4864
92
1.1514
45
10.4026
57
8.6517
69
6.1608
81
3.2390
93
.8154
46
10.2787
58
8.4776
70
5.9158
82
3.0000
94
.5235
47
10.1494
59
8.2983
71
5.6679
83
2.7796
95
.2379
48
10.0143
60
8.1137
72
5.4185
84
2.6123
96
.0000
49
9.8733
61
7.9240
73
5.1696
85
2.4579
Younger Age Thiity-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
39
10.9644
51
9.5226
63
7.4890
75
4.6716
87
2.1805
40
10.8629
52
9.3818
64
7.2815
76
4.4471
88
2.0693
41
10.7597
53
9.2360
65
7.0638
n
4.'J207
89
1.9153
42
10.6549
54
9.0851
66
6.8402
78
3.9862
90
1.7163
43
10.5485
55
8.9292
67
6.6110
79
3.7341
91
1.4430
44
10.4375
56
8.7680
68
6.3766
80
3.4784
92
1.1504
45
10.3214
57
8.6016
69
6.1374
81
3.2320
93
.8148
46
10.2002
58
8.4300
70
5.8943
82
2.9938
94
.5233
47
10.0735
59
8.2530
71
5.6482
83
2.7742
95
.^^378
48
9.9412
60
8.0709
72
5.4005
84
2.6074
96
.0000
49
9.8028
61
7.8835
73
5.1531
85
2.4535
50
9.6620
62
7.6911
74
4.9088
86
2.3131
Digitized by VjOOQ iC
TABLE VIIL
265
Value of an Anmiiiy on Two joint liyes* (Northampton 3 per Cent.)
Younger Age Forty Years.
Age.
Value.
Age.
52
Value.
Age,
64
Value.
Age.
76
Value.
Age.
Value.
40
10.7641
9.3154
7.2453
4.4335
88
2.0656
41
10.6635
53
9.1722
65
7.0299
77
4.2083
89
1.9)21
42
10.5613
54
9.0240
66
6.8086
78
3.9751
90
1.7137
43
10.4576
55
8.8707
67
6.5816
79
3.7242
91
1.4411
44
10.3492
56
8.7121
68
6.3492
80
3.4696
92
1.1490
45
10.2359
57
8.5483
69
6.1121
81
3.2241
93
.8140
46
10.1174
58
8.3792
70
5.8709
82
2.9869
94
.5228
47
9.9935
59
8.2048
71
5.6267
83
2.7680
95
.2376
48
9.8639
60
8.0251
72
5.3808
84
2.6019
96
.0000
49
9.7283
61
7.8402
73
5.1351
85
2.4485
50
9.5902
62
7.6502
74
4.8924
86
2.3085
51
9.4535
63
7.4505
75
4.6566
87
2.1765
Younger Age Forty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
89
Value.
41
10.5656
53
9.1073
6.9957
77
4.1960
1.9090
42
10.4661
54
8.9619
6.7766
78
3.9640
90
1.7112
43
10.3650
55
8.8112
67
6.5518
79
3.7143
91
1.4391
44
10.2594
56
8.6553
68
6.3217
80
3.4608
92
1.1477
45
10.1488
57
8.4942
69
6.0866
81
3.2164
93
.8131
46
10.0331
58
8.3277
70
5.8475
82
2.9800
94
.5223
47
9.9120
59
8.1558
71
5.6051
83
2.7619
95
.2376
48
9 7852
60
7.9787
72
5.3610
84
2.5964
96
.0000
49
9.65-^4
61
• 7.7963
73
5.1170
85
2.4435
50
9.5171
62
7.6087
74
4.8759
86
2.3041
51
9.3832
63
7.4115
75
4.6417
87
2.1725
52
9.2478
64
7.2087
76
4.4199
88
2.0620
Younger Age Forty-Two Years.
Age.
Value.
Age.
Value.
Age.
66
Value.
Age.
78
Value.
Age.
Value.
42
10.3692
54
8.8988
6.7445
3.9532
90
1.7088
43
10.2709
55
8.7509
67
6.5220
79
3.7046
91
1 .4373
44
■10.1680
56
8.5977
68
6.2940
80
3.4522
92
1.1464
45
10.0602
57
8.4393
69
6.0bll
81
3.2088
93
.8123
46
9.9473
58
8.2755
70
5.8240
82
2.9733
94
.5219
47
9.8290
59
8.1063
71
5.5836
83
2.7560
95
.2373
48
9.7051
60
7.9318
72
5.3413
84
2.5911
96
.0000
49
9.5753
61
7.7519
73
5.0991
85
2.4388
50
9.4428
62
7.5669
74
4.8596
86
2.2999
51
9.3118
63
7.3722
75
4.6269
87
2.1687
52
9.1791
64
7.1718
76
4.4065
88
2.0587
53
9.0415
65
6.9612
77
4.1839
89
1.9061
Digitized by LjOOQ IC
TABLE VIII.
Value of an Annuity on Two joint Lives. (Northampton 3 per Cent.)
Younger Age Forty-Three Years.
Age.
Value.
Ag«
Valae.
Age.
Valtte.
Age.
79
Value.
Age,
Value.
43
10.1753
55
8.6898
67
6.4922
3.6954
91
1.4359
44
10.0752
56
8.5395
68
6.2665
80
3.4442
92
1.1454
45
9.9703
57
8.3838
69
6.0358
81
3.2017
93
.8117
46
9.8602
58
8.2227
70
5.8007
82
2.9671
94
.5215
47
9.7449
59
8.0563
71
5.5623
83
2.7505
95
.2372
48
9.6239
60
7.8844
72
5.3219
84
2.5862
96
.0000
49
9.4970
61
7.7072
73
5.0814
85
2.4345
50
9.3675
62
7.5248
74
4.8437
86
2.2960
51
9.2393
63
7.3327
7Si
4.6124
87
2.1653
52
9.1095
64
7.1348
76
4.39^
88
2.0558
53
8.9747
-65
6.9267
77
4.1723
89
1.9037
54
8.8349
66
6.7124
78
3.9428
90
1.7069
Younger Age Forty-Four Years.
Age,
Value.
A««.
Value.
Age.
Value.
Age.
80
Value.
Age.
Value.
44
9.9779
56
8.4779
68
6.2371
3.4355
92
1.1443
45
9.8759
57
8.3251
69
6.0087
81
3.1941
93
.8111
46
9.7688
58
8.1669
70
5.7758
82
2.9604
94
.5212
47
9.6564
59
8.0033
71
5.5395
83
2.7446
95
.2370
48
9.5385
60
7.8343
72
5.3011
84
2.5810
96
.0000
49
9.4146
61
7.6599
73
5.0625
85
2.4298
60
9.2881
62
7.4801
74
4.8265
86
2.2919
51
9.1629
63
7.2907
75;
4.5969
87
2.1618
52
9.0361
64
7.0955
76
4.3795
88
2.0526
53
8.9043
65
6.8899
77
4.1597
89
1.9011
54
8.7674
66
6.6781
7B
3.9316
90
1.7048
55
8.6253
67
6.4604
79
3.6^55
91
1.4343
YouBger Age Forty-Five Years.
Age.
Value.
Age.
57
Value.
Age.
Value.
Age.
81
• Value.
Age.
Value.
45
9.7768
8.2630
69
5.9796
3.1858
93
.8104
46
9.6728
58
8.1078
70
5.7491
82
2.9531
94
.5^08
47
9.5634
59
7.9471
71
5.5150
83
2.7388
95
.2369
48
9.4486
60
7.7810
72
5.2787
84
2.5753
96
.ooeo
49
9.3278
61
7.6095
73
5.0421
85
2.4248
50
9.2045
62
7.4326
74
4.8080
86
2.2875
51
9.0824
63
7.2460
75
4.5802
87
2.1578
52
8.9586
64
7.0536
76
4.3643
88
2.0493
53
8.8299
65
6.8507
77
4.1461
89
1.8983
54
8.6961
66
6.6416
78
3.9194
90
1.7026
55
8.5570
67
6.4263
79
3.6748
91
1.4327
56
8.4127
68
6.2U57
80
3.4260
92
1.1432
Digitized by VjUUVIC
TABLE VIU.
267
jValn« of SQ Annuity on Two joint Lives. (Nortluunpton 3 per Cent)
Yoanger Age Forty-Six Yean.
Age
Value.
Age.
Value.
Aije.
66
Value.
Ajfe.
Value.
Age.
Value.
46
9.5718
56
8.3436
6.60-25
76
4.3479
86
2.2825
47
9.4656
57
8.1970
67
6.3901
77
4.1313
87
2.1535
48
9.3539
58
8.0442
68
6.1719
78
3.9062
88
2.0455
49
9.2364
59
7.8875
69
5.9484
79
3.6631
89
1.8952
50
9.1163
60
7.7244
70
5.7203
80
3.4157
90
1.7002
51
8.9973
61
7.5559
71
5.4886
81
3.1767
91
1.4310
52
8.876S
62
7.3820
72
5.2545
82
2.9451
92
1.1420
53
8.7512
63
7.1983
73
5.0201
83
2.7312
93
.8097
54
8.6206
64
7,0088
74
4.7879
84
2.5690
94
.5205
55
8.4848
65
6.8088
75
4.5620
85
2.4192
95
96
.2367
.0000
Younger Age Forty-Seven Years.
Age.
Value.
Age.
Value.
Age
67
Value.
Age.
77
Value.
Age.
Value.
47
9.8626
57
8.1270
6.3511
4.1150
B7
2.1486
48
9.2542
58
7.9783
68
6.1357
78
3.8916
88
2.0412
49
9.1400
59
7.8240
69
5.9149
79
3.6501
89
1.8916
50
9.0232
60
7.6641
70
5.6893
80
3.4042
90
1 .6974
51
8.9075
61
7.4988
71
5.4601
81
3.1666
91
1.4290
52
8.7902
62
7.3280
72
5.2284
82
2.9362
92
1.1407
53
8.6680
63
7.1475
73
4.9962
83
2.7234
93
.8090
54
8.5407
64
6.9610
74
4.7661
84
2.5620
94
.5201
55
8.4081
65
6.7640
75
4.5421
85
2.4129
95
.2366
56
8.2703
66
6.5606
76
4.3299
86
2.2769
96
.0000
Younger Age Forty-Eight Yean.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
78
Value.
Age.
Value.
48
9.1491
58
7.9072
68
6.0966
3.8754
88
2.0362
49
9.0383
59
7.7563
69
6.8786
79
3.6357
89
1.8»74
50
8.9249
60
7.5999
70
5.6558
80
3.3915
90
1.6940
51
8.8126
61
7.4379
71
5.4^91
81
3.1553
91
1.4266
52
8.6987
62
7.2704
72
5.2000
82
2.9262
92
1.1391
53
8.5798
63
7.0930
73
4.9701
83
2.7146
93
.8080
54
8.4559
64
6.9097
74
4.7423
84
2.5540
94
.5196
55
8.3268
65
6.7159
75
4.5204
85
2.4058
95
.2364
56
8.1924
66
6.5156
76
4.3101
86
2.2705
96
.0000
57
8.0526
67
6.3091
77
4.0971
87
2.1429
Digitized by VjUUV IC
268
TABLB VIII.
Value of an Annuity on Two Joint Lwes. (Northampton 3 per Cent.)
Younger Age Forty-Nine Years.
Age.
Value.
Age.
59
Valae.
Age.
Value.
Age.
79
Valae.
Age.
89
Valae.
49
8.9309
7.6842
69
5.8394
3.6195
1.8822
50
8.8210
60
7,5313
70
5.6194
80
3.3770
90
1.6898
51
8.7122
61
7.3727
71
.^.3955
81
3.1425
91
1.4234
52
8.6017
62
7.2086
72
5.1690
82
2.9148
92
M369
53
8.4864
63
7.0347
73
4.9417
83
2.7043
93
.8067
54
8.3660
64
6.8548
74
4.7162
84
2.5449
94
.5189
55
8.2405
65
6.6642
75
4.4965
85
2.3975
95
.2362
56
8.1096
66
6.4672
76
4.2882
86
2.2630
96
.0000
57
7.9734
67
6.2638
77
4.0772
87
2.1362
56
7.8316
68
6.0544
78
3.8574
88
2.0302
Younger Age Fifty Yean.
Age.
Valae.
8.7146
Age.
60
Valoe.
Age
Value.
Ag«.
Value.
Age.
90
Value.
50
7.4609
70
5.5822
80
3.3622
1.6853
51
8.6093
61
7.3059
71
5.3611
81
3.1292
91
1.4199
52
8.5024
62
7.1454
72
5.1373
82
2.9030
92
1.1344
53
8.3906
63
6.9749
73
4.9)25
83
2.6938
93
.8051
54
8.2738
64
6.7984
74
4.6895
84
2.5353
94
.5180
55
8.1519
65
6.6113
75
4.4720
85
2.3888
95
.2358
56
8.0247
66
6.4176
76'
4.2658
86
2.2552
96
.0000
57
7.8921
67
6.2174
77
4.0.i68
87
2.1291
58
7.7539
68
6.0112
78
3.8389
88
2.0239
59
7.6102
69
5.7992
79
3.6029
89
1.8768
Younger Age Fifty-One Years.
Age.
Value.
Age.
Value.
TAge.
Value.
Age.
Value.
Age.
Value.
51
8.5075
61
7.2405
71
5.3284
81
3.1172
91
1.4170
52
8.4041
62
7.0835
72
5.1072
82
2.8924
92
1.1324
53
8.2959
63
6.9166
73
4.8850
83
2.6843
93
.8038
54
8.1828
64
6.7436
74
4.6643
84
2.5268
94
.5173
55
8.0645
65
6.5599
75
4.4491
85
2.3811
95
.2356
56
7.9410
66
6.3696
76
4.2449
86
2.2483
96
.0000
67
7.8120
67
6.1727
77
4.0378
87
2.1229
58
7.6776
68
5.9696
78
3.8219
88
2.0184
59
7.5375
69
5.7607
79
3.5877
89
1.8721
60
7.3918
70
5.5466
80
3.3486
90
1.6815
Digitized by VjOOQ IC
TABLE VIII.
269
Valofl of An Annuity on Two Joint LiTM. (Northampton 3 per Cfint.)
Younger Age Fifty-Two Yean.
A««.
Value.
Age.
63
Valae.
Age.
Valae.
Ag*
85
Value.
52
8.3043
6.8577
74
4.6395
2.3739
63
8.1997
64
6.6883
75
4.4265
86
2.2418
54
S.0903
65
6.5082
76
4.2244
87
2.1172
55
7.9757
66
6.3213
n
4.0193
88
2.0133
56
7.8559
67
6.1278
78
3.8052
89
1.8678
57
7.7307
68
5.9279
79
3.5729
90
1.6780
58
7.6001
69
5.7222
80
3.3355
91
1.4145
59
7.4638
70
5.5111
81
3.1056
92
1.1306
60
7.3218
71
5.2957
82
2.882L
93
.8028
61
7.1742
72
5.0773
83
2.6753
94
.5167
62
7.0209
73
4.8577
84
2.5186
95
.2353
.0000
Younger Age Fifty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
53
8.0989
64
6.6299
75
4.4026
86
2.2349
54
7.9932
65
6.4535
76
4.2027
87
2.1110
55
7.8825
66
6.2703
n
3.9997
88
2.0079
56
7.7665
67
6.0803
78
3.7876
89
1.8632
57
7.6452
68
5.8839
79
3.5572
90
1.6743
58
7.5185
69
5.6814
80
3.3216
91
1.4118
59
7.3861
70
5.4736
81
3.0933
92
1.1287
60
7.2481
71
5.2612
82
2.8713
93
.8016
61
7.1043
72
5.0457
83
2.6657
94
.5161
62
6.9549
73
4.8288
84
2.5100
95
.2351
63
6.7955
74
4.6131
85
2.3661
96
.0000
Younger Age Fifty^Four Years.
Age.
Value.
Age.
65
Value.
Age.
1^ Value.
Age.
87
Value.
54
7.8913
6.3957
76
4.1797
2.1045
53
7.7845
66
6.2163
71
3.9789
88
2.0021
56
7.6726
67
6.0301
78
3.768'J
89
1.8583
57
7.5553
68
5.8373
79
3.5406
90
1.6704
58
7.4326
09
5.6383
80
3.3069
91
1.4089
3t)
7.3043
70
5.4338
81
3.0803
92
1.1267
60
7.1703
71
5.2-247
82
2.8598
93
.8004
61
7.0306
72
5.0122
83
2.6555
94
.6155
62
6.8852
73
4.7982
84
2.5009
95
.2349
63
6.7298
74
4.5853
85
2.3579
96
.0000
64
6.5682
lb
4.3772
86
2.2276
Digitized by VjOOQ IC
270 TABLE VIII.
Value of AU Annuity on Two Joint Lives. (Northampton 3 per Cent.)
Younger Age Fifty-Five Years.
Age.
Value.
Age.
66
Value.
Age.
77
Value,
Age.
88
Value.
55
7.6817
6.1592
3.9568
1.9960
56
7.573!^
67
5.9769
78
3.7491
89
1.8532
57
7.4607
68
5.7879
79
3.5229
90
1.6063
58
7.3421
69
5.5927
80
3.2913
91
1.4058
59
7.2180
70
5.3917
81
3.0664
92
1.1246
60
7.0882
71
5.1860
82
2.8476
93
.7991
61
6.9528
72
4.9768
83
2.6446
94
.5148
62
6.8116
73
4.7658
84
2.4912
95
.2346
63
6.6604
74
4.5557
85
2.3492
96
.0000
64
6.5029
75
4.3504
86
2.2197
65
6.3345
76
4.1553
87
2.0976
Younger Age I
'ifty-
Six Years.
Age.
Value.
Age.
Value.
Age.
78
Value.
Age.
89
Value.
56
7.4701
67
5.9206
3.7281
1.8476
57
7.3612
68
5.7356
79
3.5042
90
1.6618
58
7.2469
69
5.5443
80
3.2747
91
1.4025
59
7.1271
70
5.3471
81
3.0.118
92
1.1223
60
7.0017
71
5.1450
82
2.8346
93
.7978
61
6.8706
72
4.9392
83
2.6332
94
.5140
62
6.7338
73
4.7315
84
2.4808
95
.2343
63
6.5870
74
4.5244
85
2.3399
96
.0000
64
6.4338
76
4.3219
86
2.2114
65
6.2698
76
4.1294
87
2.0902
66
6.0987
n
3.9334
88
1.9895
Younger Age Fifty-Seven Years.
Age.
Vnlue.
Age.
Value.
AKe.
Value.
Age.
Value.
57
7.2566
68
5.6802
79
3.4343
90
1.6571
58
7.14«7
69
5.4930
80
3.2571
91
1.3989
59
7.0314
70
5.2998
81
3.0361
92
1.1199
60
6.9105
71
5.1015
82
2.8208
93
.7963
61
6.7839
72
4.8993
83
2.6210
94
.5132
62
6.6515
73
4.6950
84
2.4699
95
.2340
63
6.5093
74
4.4912
85
2.3301
96
.0000
64
6.3607
75
4.2917
86
2.2026
65
6.2012
76
4.1019
87
2.0823
66
6.0346
77
3.9086
88
1.98-25
67
5.8608
78
3.7058
89
1.8417
Digitized by LjOOQ IC
TABLE VIII.
271
Value of an Aonuity on Two Joint Live*. (Northampton 3 per Cent.)
Younger Age Fifty-Eight Yean.
Age.
Value.
Age.
Value.
Age.
78
Value.
Age,
88
Value.
58
7.0413
68
5.6213
3.6821
1.9751
59
6.9306
69
5.4385
79
3.4632
89
1.8354
60
6.8143
70
5.2495
80
3.2384
90
1.6520
61
6.6923
71
5.0552
81
3.0197
91
1.3951
62
6.5647
72
4.8569
82
2.8062
92
1.1173
63
6.4273
73
4.6563
83
2.6080
93
.7947
64
6.2833
74
4.4559
84
2.4583
94
.5124
65
6.1286
75
4.2596
85
2.3197
95
.2337
66
5.9666
76
4.0728
86
2.1933
96
.0000
67
5.7975
71
3.8822
87
2.0740
Younger Age Fifty-Nine Yeari.
Age.
Value.
Age.
ValQe.
Age.
Value.
Age.
89
Value.
59
6.8245
69
5.3806
79
3.4409
1.8288
60
6.7129
70
5.1961
80
3.2186
;90
1.6466
€1
6.5958
71
5.0061
81
3.0022
"91
1.3911
62
6.4730
72
4.8119
82
2.7908
92
1.1145
€3
6.3405
73
4.6151
83
2.5943
93
.7930
64
6.2015
74
4.4184
84
2.4460
94
.5114
65
6.0517
75
4.2255
85
2.3087
95
.2333
66
5.8946
76
4.0418
86
2.1834
96
.0000
67
5.7303
n
3.8543
87
2.0652
68
5.5588
78
3.6570
88
1.9673
Younger Age Sixty Yeariu
Age.
Value.
Age.
70
Value.
Age.
IT
Value.
Age.
Value.
60
6.6062
5.1393
3.1977
90
1.6409
61
6.4940
71
4.9539
81
2.9837
91
1.3:^69
62
6.3763
72
4.7641
82
2.7744
92
1.1115
63
6.2488
73
4.5714
83
2.5799
93
.7912
64
6.1149
74
4.3786
84
2.4330
94
.5104
65
5.9702
75
4.1893
85
2.2970
95
.2330
66
5.8182
76
4.0090
86
2.1730
96
.0000
67
5.6590
17
3.8246
87
2.0559
68
5.4925
78'
3.6304
88
1.9592
69
5.3191
79
3.4172
89
1.8218
Digitized by VjOOQ IC
272
TABLE VIII.
Value of an Annuity on Two Joint Livet. (Northampton 3 per Cent.)
Younger Age Sixty-One Years.
Age.
Value.
Age.
Valoa.
:Age.
Value.
Age.
91
Value.
61
6.3869
71
4.8985
81
2.9642
1.3826
62
6.2742
72
4.7132
82
2.7573
92
1.1085
63
6.1520
73
4.5250
83
2.5647
93
.7893
64
6.0234
74
4.3363
84
2.4195
94
.5094
65
5.8840
75
4.1509
85
2.2849
95
• 2325
66
5.7374
76
3.9742
86
2.1622
96
.0000
67
5.5834
77
3.7932
87
2.0463
68
5.4221
78
3.6022
88
1.9507
69
5.2538
79
3.3022
89
1.8147
70
5.0790
80
3.1756
90
1.6352
Younger Age Sixty-Two Years.
Age.
Value.
Age.
;72
Value.
Age.
82
Value.
Age.
Value.
62
6.1668
4.6592
2.7393
92
1.1057
63
6.0500
73
4.4757
83
2.5489
93
.7876
64
5.9267
74
4.2914
84
2.4053
94
.5085
65
5.7930
75
4.1101
85
2.2723
95
.2322
66
5.6518
76
3.9372
86
2.1510
96
.0000
67
5.5033
77
3.7599
87
2.0365
68
5.3475
78
3.5724
88
1.9421
69
5.1846
79
3.3658
89
1.8075
70
5.0150
80
3.1523
90
1.6295
71
4.8395
81
2.9437
91
1.3784
Younger Age Sixty-Three Years.
Age.
Value.
Age.
73
Value.
Age.
Value.
Age.
Value.
63
5.9389
4.4202
83
2.5305
93
.7854
64
5.8211
74
4.2408
84
2.3889
94
.5073
65
5.6931
75
4.0641
85
2.2577
95
.2318
66
5.5577
76
3.8954
86
2.1379
96
.0000
67
5.4150
77
3.7220
87
2.0249
68
5.2650
78
3.5385
89
1 .9320
69
5.1077
79
3.3356
89
1.7989
70
4.11438
80
3.125:)
90
1.6226
71
4.7737
81
2.92U1
91
1.3733
72
4.6987
82
2.7185
92
1.1022
Digitized by VjOOQ IC
TABLE VlII.
Value of an Annuity on Two joint Lives. (Northampton 3 per Cent.)
Younger Age Sixty-Four Years.
273
Age.
Value.
Age.
ValiM*.
4.5339
Age.
Value.
Age.
Value.
64
5.7093
72
80
3.0968
88
1.9212
65
5.5872
73
4.3508
81
2.8943
89
1.7900
66
5.4579
74
4.1865
82
2.6962
90
1.61.15
67
5.3212
75
4.0146
83
2.5109
91
1.3681
68
5.1771
76
3.8504
84
2.3714
92
1.0987
69
5.0258
77
3.6814
85
2.2420
93
.7834
70
4.8677
78
3.5020
86
2.1240
94
.5063
71
4.7034
79
3.3031
87
2.0127
95
96
.2314
, .0000
Younger Age Sixty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
65
5.4713
73
4.2939
81
2.8653
89
1.7790
66
5.3481
74
4.1251
82
2.6702
90
1.6067
67
5.2177
75
3.9585
83
2.4878
91
1.3616
68
5.0799
76
3.7992
84
2.3507
92
1.0942
69
4.9349
77
3.6349
85
2.2235
93
.7807
70
4.7829
78
3.4601
86
2.1075
94
.5048
71
4.6247
79
3.2657
87
1.9980
95
.2308
72
4.4612
80
3.0636
88
1.9083 ^
96
.0000
Younger Age Sixty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
66
5.2314
74
4.0586
82
2.6416
90
1.5970
67
5.1073
75
3.8975
83
2.4625
91
1.3544
68
4.9760
76
3.7435
84
2.3279
92
1.0892
69
4.8375
77
3.5843
85
2.2031
93
.7777
70
4.6920
78
3.4144
86
2.0892
94
.5032
71
4.5401
79
3.2248
87
1.9818
95
.2302
72
4.3828
80
3.0272
88
1.8940
96
.0000
73
4.2216
81
2.8331
89
1.7669
Younger Age Sixty- Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
67
4.9899
75
3.8314
83
2.4345
91
1.3465
6S
4.8652
76
3.6829
84
2.3027
92
1.083d
69
4.7334
77
3.5291
85
2.1805
93
.7743
70
4.5945
78
3.3645
86
2.0690
94
.5014
71
4.4492
79
3.1801
87
1.9638
95
^.2295
72
4.2984
80
2.9874
88
1.8782
96
•0000
73
4.1435
81
2.7977
89
1.7536
74
3.9867
82
2.6102
90
1.5863
Digitized by VjOOQ IC
274 TABLE VIU.
Value of an Annuity on Two joint Lives. (Northampton 3 per Cent.)
Younger Age Sixty-Eight Yeare.
Age.
Valae.
Age.
Value.
Age.
Valoe.
Age.
Value.
68
4.7473
76
3.6171
84
2.2749
92
1.0776
69
4.6223
77
3.4690
85
2.1554
93
.7706
70
4.4903
78
3.3100
86
2.0165
94
.4994
71
4.3518
79
3.1312
87
1.9438
95
.2288
72
4.2077
80
2.9438
88
1.8605
96
.0000
73
4.0594
81
2.7588
89
1.7386
74
3.9089
82
2.5756
90
1.5743
75
3.7598
83
2.4037
91
1.3376
Younger Age Sixty-Nine Years.
Age.
Valne.
Ag«.
Valoe.
Age.
Valne.
Ago.
Valne.
69
70
71
72
73
74
75
4.5042
4.3793
4.2478
4.1106
3.9691
3.8252
3.6824
76
n
78
79
80
81
82
3.5458
3.4037
3.2506
3.0778
2.8960
2.7162
2.5376
83
84
85
86
87
88
89
2.369S
2.2442
2.1276
2.0214
1.9214
1.8408
1.7218
90
91
92
93
94
95
96
1.5609
1 .3276
i.0708
.7665
.4972
.2279
.0000
Younger Age Scven^ Years.
Age.
Value.
Age.
Value.
Age.
Value.
2.2103
2.0969
1.9936
1.8964
1.8186
Age.
Valne.
70
71
72
73
74
4.2614
4.1371
4.0071
3.8725
3.7355
77
78
79
80
81
3.3330
3.1862
3.0196
2.8438
2.6695
84
85
86
87
88
91
92
93
94
95
1,3164
1.0630
.7618
.4946
.2270
75
76
3.5993
3.4689
82
83
2.4960
2.3325
89
90
1.7030
1.5458
96
.0000
Younger Age Seventy-One Years.
Age.
Valae.
Age.
Val«e.
Age.
Valne.
Ag«.
Value;
71
72
73
74
lb
76
n
4.0201
3.8972
3.7698
3.6898
3.5104
3.3865
3.2570
78
79
80
81
82
83
84
3.1166
2.9566
2.7871
2.6186
2.4505
2.2916
2.1732
85
86
87
88
89
90
91
2.0631
1.9628
1.8686
1.7937
1.6817
1.5284
1.3032
92
93
94
95
96
1.0542
.7564
.4917
.2259
.0000
Digitized by LjOOQ IC
TABLE VIII. 275
Value of an Annuity oti Two joint Lives. (Northampton 3 per Cent.)
Younger Age Seventy-Two Years.
Age.
72
73
74
75
76
n
78
Valae.
3.7817
3.6616
3.5367
3.4162
3.2989
3.1760
3.0422
Age.
79
80
81
82
83
84
85
Valae.
2.8889
2.7261
2.5637
2.4011
2.2473
2.1327
2.0262
Ag..
86
87
88
89
90
91
92
Valua.
1.9292
1.8381
1.7661
1.6578
1.5089
1.2889
1.0440
Age.
93
94
95
96
Valae.
.7602
.48S4
.2246
.0000
Younger Age Seventy-Three Years
Age.
Value.
Age.
Value.
Age.
Valae.
Age.
Value.
73
74
75
76
78
3.5488
3.4331
3.3176
3.2070
3.0907
2.9637
79
80
81
82
83
84
2.8174
2.6612
2.5051
2.3484
2.1997
2.0893
85
86
87
88
89
90
1.9865
1.8929
1.8051
1.7361
1.6316
1.4871
91
92
93
94
95
96
1.2722
1.0323
.7431
.4845
.2231
.0000
Younger Age Seventy-Four Years.
Age.
74
75
76
77
78
79
Value.
3.3246
3.2161
3.1123
3.0028
2.8826
2.7432
Age.
80
81
82
83
84
8.'»
Value.
2.5939
2.4441
2.2933
2.1499
2.0437
1.9448
Age.
86
87
88
89
90
91
Value.
1.8549
1.7704
1.7045
1.6038
1.4638
1.2541
Age.
92
93
94
95
96
Valae.
1.0193
.7349
.4800
.2214
.0000
Younger Age Seventy-Five Years.
Age.
75
76
77
78
79
80
Valae.
3.1146
3.0174
2.9147
2.8014
2.6690
2.5265
Age.
81
82
83
84
85
Value.
2.3830
2.3381
2.0999
1.9979
1.9029
1.8166
Age.
87
88
89
90
91
92
Value.
1.7357
1.6731
1.5763
1.4406
1.2360
1.0059
Age.
93
94
95
Value.
.7262
.4750
.2194
.0000
t2
Digitized by
^oogle
276 TABLE VIII.
Value of an Annuity on Two joint Lives. (Northampton 3 per Cent)
Younger Age Seventy-Six Years.
Younger Age Seventy-Seven Years.
Age.
Vulue,
A»e.
Valae.
Age.
Valoe.
Age.
Value.
76
2.9269
87
1.7043
17
2.7417
87
1.6706
n
2.8308
88
1.6452
78
2.6423
88
1.6154
78
2.7243
89
1.5524
79
2.5242
89.
1.5273
79
2.5989
90
1.4211
80
2.3955
90
1.4010
80
2.4631
91
1.2212
81
2.2649
91
1.2063
81
2.3258
92
.9953
82
2.1317
92
.9851
82
2.1866
93
.7195
83
2.0039
93
.7132
83
2.0535
94.
.4712
84
1.9102
94
.4677
84
1.9555
93
.2179
85
1.8230
95
.2165
85
1.8643
96
.0000
86
1.7441
96
.0000
86
1.7816
Younger Age Seventy-Eight Years.
Younger Age Seventy -Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
78
2.5503
88
1.5803
79
2.3385
88
1.5.3.32
79
2.4401
b9
1.4975
80
2.2261
89
1.4565
80
2.3192
90
1.3774
81
2.1109
90
1.3137
81
2.1959
91
1.1891
82
1.9919
91
1.1638
82
2.0694
92
.9737
83
1.8768
92
.9561
:83
1.9475
93
.7066
84
1.79-28
93
.6959
84
1.8583
94
.4644
85
1.7147
94
.4586
85
1.7754
95
.2153
86
1.6444
95
.2132
86
1.7006
96
.0000
87
1.5796
96
.0000
87
1.6313
Younger Age
Eight}
Years.
Younger Age Eighty-One Years.
Age.
Value.
Age.
Value.
Age.
Vnlue.
Age.
Value.
so
2.1225
89
1.4071
81
1.9173
89
1.3532
81
2.0157
90
1.3023
82
1.8143
90
1.2565
82
1.9048
91
1.1320
83
1.7134
91
1.0964
83
1.7968
92
.9335
84
1.6404
92
.9081
84
1.7183
93
.6819
85
1.5721
93
.6661
85
1.6451
94;
.4508
86
1.5109
94
.4423
86
1.5795
95
.2101
87
1.4549
95
.2069
87
1.5192
96
.0000
88
1.4174
96
.0000
88
1.4774
Digitized by VjOOQ IC
TABLE VIII.
277
Value of an Annuity on Two joint Lives. (Northampton 3 pet Cent.)
Younger Age Eighty-Two Years.
Younger Age Eighty-Three Years.
Age.
Value.
Age.
Value.
Age.
Valw.
Age.
Value.
82
83
84
85
86
87
88
89
1.7191
1.6253
1.5576
1.4942
1.4373
1.3854
1.3517
1.2933
90
91
92
93
94
95
96
1.2044
1.0546
.8772
.6463
.4312
.2027
.0000
83
84
85
86
87
88
89
1.5380
1.4753
1.4164
1.3635
1.3153
1.2848
1.2314
90
91
92
93
94
95
96
1.1495
1.0094
.8423
.6223
• 4168
.1965
.0000
Younger Age Eighty-Four Years.
Younger Age Eighty-Fj
ve Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
84
85
86
87
88
89
90
1.4164
1.3610
1.3112
1.2659
1.2377
1.1879
1.1113
91
92
93
94
95
96
.97»3
.8190
.6072
.4079
.1929
.0000
85
86
87
88
89
90
1.3090
1.2622
1.2196
1.1936
1.1470
1.0748
91
92
93
94
95
96
.9482
.7959
.5919
.3989 5
.1892
.OOUO
Younger Age Eighty-Six Years.
Younger Age Eighty- Seven Years.
Age,
Value.
Age.
Value.
Age.
Value.
Age.
Value.
86
87
b8
89
90
91
1.2185
1.1786
1.1549
1.1113
1.0427
.9212
92
93
94
95
96
.7748
.5774
.3903
.1858
.0000
87
88
89
90
91
1.1416
1.1207
1.0e03
1.0153
.8981
92
93
94
95
96
.7560
.5637
.3812
.1815
.0000
Digitized by LjOOQ IC
278
TABLS VIII.
Value of an Annuity on Two joint Liven. (Northampton 3 per Cent.)
Younger Age Eighty-Eight Years.
Younger Age Eighty -Nine Years.
■Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
88
1.1030
93
.5620
89
1.0361
93
.5566
89
1.0666
94
.3804
90
.9822
94
.3776
90
1.0057
95
.1813
91
.8761
95
.1801
91
.8921
96
.0000
92
.7427
96
.0000
92
.7526
Younger Age Ninety Years.
Younger Age Ninety-One Years.
Age.
Value.
Age.
Value.
90
91
92
93
94
95
96
.9386
.8449
.7231
.5465
.3736
.1794
.0000
91
92
93
94
95
96
.7697
.6680
.5115
.3539
.1713
.0000
Younger Age Ninety-Two Years.
Younger Age Ninety -Three Years.
Age.
Value.
Age.
Value.
92
93
94
95
96
.5910
.4620
.3269
.1618
.0000
93
94
95
96
.3697
.2689
.1365
.0000
Younger Age Ninety-Four Years.
Younger Age Ninety-Five Years.
Age.
Value.
Age.
95
96
Value.
94
95
96
.2034
.1079
.0000
.0607
.0000
Digiti-zed byVjOOQlC
TABLE VIII.
279
Values of Annuities on Two joint Lives by the Northampton Table of Mortality.
A«BIL
4 per oent.
5 per cenU
6 per cent.
Age..
4 per cent.
5 per cent
Ohtor
Toangw
Older
Y'oiiDgvr
6 per cent.
1
1
8.252
7.287
6.515
18
13
18
13.303
12.841
11.864
11.483
10.685
10.365
2
2
11.107
9.793
8,741
19
4
12.876
11.447
10.284
3
12.325
10.862
9.689
9
14
13.482
13.130
12.006
11.723
10.799
10.568
4
13.185
11.621
10.365
19
12.679
11.351
10.255
5
13.591
11.984
10.691
20
5
10
12.993
13.355
11.561
11.906
10.391
10.719
6
10.741
9.479
8.467
15
12.961
11.585
10.453
14.005
12.358
11.031
20
12.535
11.232
10.156
7
12.581
11.100
'9.911
21
1
10.053
8.961
8.070
14.224
12.596
11.251
6
11
13.121
13.217
11.685
11.797
10.510
10.631
8
13.319
11.755
10.498
16
12.799
11.452
10.342
14.399
12.731
11.382
21
12.409
11.131
10.074
9
13.775
12.165
10.869
22
2
11.605
10.344
9.313
14.396
12.744
11.404
7
12
13.178
13.078
11.748
11.686
10.576
10.541
10
13.933
12.315
11.010
17
12.646
11.327
10.239
10
14.277
12.665
11.345
22
12.293
11.042
10.002
11
10.782
9.544
8.547
23
3
12.161
10.843
9.764
14.068
12.447
11.136
8
13.178
11.761
10.697
11
14.133
12.546
11.249
13
18
12.934
12.500
11.570
11.209
10.446
10.140
12
12.438
14.111
11.010
12.498
9.857
11.192
23
12.179
10.951
9.928
12
13.966
12.411
11.139
24
4
9
12.511
13.112
11.163
11.716
10.057
10.566
13
3
13.019
11.528
10.324
14
12.784
11.450
10.348
8
14.089
12.492
11.197
19
12.361
11.096
10.048
13
13.789
12.268
11.023
24
12.062
10.858
9.853
14
4
13.374
11.850
10.617
25
5
12.633
11.281
10.170
9
13.992
12.421
11.144
10
12.998
11.627
10.497
14
13.604
12.118
10.899
15
20
12.630
12.229
11.324
10.989
10.244
9.960
15
5
10
13.479
13.841
11.954
12.302
10.716
11.048
25
11.944
10.764
9.776
15
13.411
11.960
10.767
26
1
6
9.770
12.754
8.742
11.400
7.897
10.285
16
1
10.406
9.243
8.301
11
12.861
11.519
10.410
6
13.578
12.052
10.812
16
12.470
11.193
10.135
11
13.664
12.158
10.929
21
12,105
10.890
9.879
16
13.212
11.793
10.626
26
11.822
10.667
9.697
17
2
11.981
10.642
9.555
27
2
11.264
10.080
9.104
7
13.599
12.0S3
10.849
7
12.798
11.452
10.341
12
13.480
12.009
10.805
12
12.715
11.402
10.314
17
13.019
11.630
10.489
17
22
12.311
11.987
11.063
10.796
10.027
9.803
18
3
8
12.531
13.569
11.134
12.070
9.998
10.847
27
11.699
10.567
9.616
Digitized by LjOOQ IC
280 TABLE Vlll.
Values of Annuities on Tiro joint Lives by the Northampton Table of Mortality.
Av».
4 per Mat.
5 per cant
«pereeDt
Ace..
4 per cent.
Sperc-ii.
6p«r<»irt.
Older
Yoanger
Older
YooBger
28
3
11.790
10.555
9.537
35
20
11.445
10.363
9.451
8
12.786
11.455
10.354
25
11.217
10.175
9.295
13
12.564
11.280
10.215
30
10.948
9.954
9.112
18
12.158
10.939
9.924
35
.10.612
9.680
8.8b3
23
11.866
10.699
9.724
28
11.573
10.466
9.533
36
1
6
'9.047
11.812
8,173
10.656
7.442
9.687
29
4
12.116
10.855
9,813
11
11.941
10.788
9.820
9
12.710
11.401
10.315
16
11.609
10.507
9.579
14
12.408
11.153
10.110
21
11.302
10.246
9.354
19
12.013
10.820
9.826
26
11.078
10.062
9.201
24
11.743
10.600
9.643
31
10.805
9.837
9.014
29
11.445
10.362
9.448
36
10.462
9.555
8.778
30
5
12.220
10.959
9.913
37
2
10.392
9.390
8.551
10
12.586
11.304
10.-239
7
11.819
10.676
9.715
15
12.246
11.021
10.001
12
11.773
10.651
9.707
20
11.873
10.707
9.732
17
11.430
10.358
9.454
25
11.618
10.499
9.561
22
11.163
10.132
9.260
.30
11.313
10.255
9.360
27
32
10.936
10.659
9.946
9.716
9.105
8.913
31
1
6
9.438
12.322
8.483
11.062
7.691
10.015
37
10.307
9.427
8.670
u
12.441
11.188
10.144
38
3
10.838
9.800
8.928
16
12.078
10.683
9.886
8
11.772
10.648
9.701
21
11.742
10.600
9.644
13
11.600
10.509
9.538
26
11.489
10.396
9.476
18
11.257
10.214
9.333
31
11.179
10.146
9.270
23
28
11.020
10.791
10.015
9.826
9.163
9.005
32
2
10.865
9.767
8.855
33
10.508
9.591
8.608
7
12.350
11.100
10.060
38
10.149
9.294
8.558
12
12.286
11.062
10.042
17
11.911
10.746
9.771
39
4
11.097
10.043
9.157
22
11.615
10.498
9.561
9
11.665
10.565
9.637
27
11.3)9
10.289
9.389
14
11.420
10.360
9.464
32
11.042
10.034
9.178
19
24
11.089
10.874
10.074
^ 9.895
9.215
9.063
33
3
11.355
10.213
9.263
29
10.642
9.703
8.902
8
12.323
11.090
10.061
34
10.354
9.463
8.701
13
12.125
10.»32
9.934
39
9.986
9.156
8.442
18
11.750
10.613
9.660
23
11.485
10.393
9.474
40
5
11.150
10.102
9.219
28
11.225
10.181
9.299
10
11.513
10.442
9.537
33
10.902
9.919
9.082
15
20
11.234
10.924
10.205
9.937
9.333
9.100
34
4
11.651
10.488
9.518
25
10.725
9.771
8.960
9
12.234
11.024
10.012
30
10.490
9.576
8.795
14
11.969
10.796
9.822
35
10.196
9.331
8.589
19
11.595
10.486
9.554
40
9.820
9.016
8.322
24
11.352
10.285
9.386
29
11.088
10.069
9.207
41
1
•8.585
7.800
7.135
34
10.759
9.801
8.984
6
11
11.203
11.342
10.163
10.302
9.283
9.420
35
5
11.732
10.572
9.602
16
11.044
10.046
9.198
10
12.098
10.916
9.925
21
10.768
9.809
8.992
15
11.767
10.655
9.703
26
10.574
9.647
8.856
Digitized by N^UUV IC
TABLE VIII.
281
Valiiet of AnnuHiei on two joint Lives by the
Northampton Table of Mortality.
Age..
4 per cant
6 per cent.
6 per oeot
Agei.
4 per cent
5 per cent
6 per cent
Older
Yoomser
Older
47
Younger
41
31
10.336
9.448
8.688
7
10.491
9.589
8.815
36
10.037
9.198
8.476
12
10.481
9.592
8.827
41
9.654
8.876
8.202
17
22
10.208
10.001
9.353
9.173
8.617
8.458
42
2
9.839
8.942
8.182
27
9.836
9.032
8.338
7
11.190
10.165
9.296
32
9.631
8.858
8.189
12
11.165
10.156
9.298
37
9.370
8.636
7.998
17
10.856"
9.889
9.065
42
9.037
8.350
7.751
22
10.619'
9.685
8.889
47
8.637
8.008
7.455
27
10.423
9.522
8.751
32
10.182
9.320
8.580
48
3
9.566
8.759
8.063
37
9.877
9.062
8.362
8
10.404
9.524
8.767
42
9.491
8.737
8.083
13
18
10.284
10.011
9.425
9.186
8.686
8.473
43
3
10.242
9.315
8.528
23
9.833
9.031
8.338
8
11.130
10.124
9.270
28
9.667
8.890
8.217
13
10.985
10.007
9.173
33
9.461
8.714
8.066
18
10.677
9.739
8.938
38
9.195
8.487
7.870
23
10.470
9.562
8.785
43
8.862
8.200
7.621
.
28
33
10.272
10.027
9.396
9.190
8.645
8.471
48
8.453
7.849
7.316
38
9.716
8.927
8.246
49
4
9.744
8.932
8.230
43
9.326
8.599
7,965
9
14-
10.263
10.080
9.409
9.252
8.673
8.538
44
4
10.468
9.531
8.733
19"
9.818
9.021
8.332
9
11.012
10.031
9.197
24
9.661
8.886
8.214
14
10.799
9.852
9.042
29
9.495
8.744
8.092
19
10.502
9.592
8.814
34
9.286
8.565
7.938
24
10.317
9.435
8.670
39
9.015
8.333
7.737
29
10.117
9.267
8.536
44
8.683
8.046
7.488
34
9.869
9.058
8.358
49
8.266
7.686
7.173
39
9.530
8.787
8. 127
44
9.160
8.457
7.843
50
5
10
9.742
10.085
8.941
9.260
8.248
8.548
45
5
10.500
9.571
8.778
15
9.872
9.076
8.386
10
10.851
9.900
9.088
20
9.630
8.861
8.195
15
10.607
9.690
8.905
25
9.488
8.739
8.089
20
10.330
9.448
8.692
30
9.321
8.596
7.966
25
10.160
9.304
8.569
35
9.110
8.415
7.809
30
9.959
9.135
8.424
40
8.834
8.177
7.602
35
9.706
8.921
8.242
45
8.503
7.891
7.353
40
9.381
8.643
8.003
50
8.081
7.522
7.030
45
8.990
8.312
7.718
51
1
7.479
6.885
6.370
46
I
8.071
7.379
6.787
6
9.745
8.956
8.271
6
10.528
9.609
8.823
11
9.894
9. 100
8.411
11
10.697
9.774
8.962
16
9.665
8.899
8.234
16
10.408
9.522
8.702
21
9.454
8.712
8.067
2]
10.165
9.310
8.574
26
9.318
8.595
7.966
26
10.000
9.170
8.455
3)
9.151
8.451
7.841
31
9.797
8.998
8.309
36
8.937
8.267
7.681
36
9.540
8.781
8.122
41
8.658
8.025
7.470
41
9.210
8.497
7.878
46
8.326
7.737
7.219
46
8.815
8.162
7.589
51
7.900
7.366
6.893
47
2
9.221
8.435
7.760
52
2
8.520
7.848
7.264
Digitized by VjUUV IC
m TABLE VIU.
Values of Annuities on Two joint Lives by the Northampton Table of Mortality.
A«.f.
4 per cent.
5 per cent
6 per cent.
. ^^'^
4 percent
6Jper cent.
Older
Youngw
Oldrr
56
Yoanger
6 peroeot
52
7
9.690
8.919
8.248
46
7.763
7.249
6.793
12
9.698
8.934
8.270
51
7.409
6.936
6.515
17
9.461
8.724
8.083
56
6.993
6.571
6.190
22
9.284
8.568
7.944
27
9.148
8.451
7.842
57
2
7.756
7.199
6.709
32
8.980
8.306
7.716
7
8.817
8.176
7.612
37
8.763
8.119
7.553
12
8.839
8.203
7.643
42
8.483
7.875
7.340
17
8.639
8.024
7.481
47
8.147
7.582
7.084
22
8.491
7.891
7.362
52
7.724
7.213
6.758
27
32
8.383
8.250
7.797
7.680
7.279
7.175
^53
3
8.815
8.128
7.529
37
8.076
7.527
7.041
8
9.591
8.841
8.188
42
7.848
7.326
^.862
13
9.497
8.763
8.123
47
7.574
7.084
6.648
-18
9.260
8.552
7.934
52
7.225
6.774
6.371
'23
9.111
8.421
7.818
57
6.805
6.404
6.041
28
8.975
8.304
7.716
33
8.806
8.157
7.588
58
3
7.986
7.421
6.922
38
8.586
7.966
7.421
8
8.691
8.073
7.527
43
8.308
7.724
7.208
13
8.622
8.015
7.479
48
7.965
7.424
6.945
18
8.422
7.835
7.316
53
7.544
7.056
6.620
23
28
8.299
8.193
7.725
7.632
7.218
7.135
54
4
8.957
8.269
7.668
33
8.060
7.515
7.031
9
9.442
8.718
8.085
38
7.884
7.360
6.894
14
9.290
8.586
7.970
43
7.660
7.162
6.718
19
9.063
8.383
7.788
48
7.382
6.915
6.498
24
8.934
8.270
7.688
53
7.039
6.609
6.225
29
8.799
8.153
7.586
58
6.614
6.234
5.890
34
8.629
8.005
7.457
39
8.406
7.810
7.286
59
4
8.075
7.514
7.017
44
8.130
7.569
7.073
9
8.519
7.927
7.403
49
7.780
7.262
6.802
14
8.399
7.821
7,310
54
7.362
6.897
6.480
19
24
8.207
8.104
7.648
7.556
7.153
7.070
55
5
8.931
8.256
7.665
29
7.999
7.464
6.988
10
9.256
8.560
7.951
34
7.866
7.346
6.884
15
9.077
8.403
7.812
39
7.689
7.189
6.744
20
8.869
8.216
7.643
44
7.469
6.994
6.570
25
8.754
8.116
7.555
49
7.186
6.742
6.344
30
8.619
7.999
7.453
54
6.850
6.442
6.076
35
8.448
7.849
7.322
59
6.421
6.062
5.735
40
8.221
7.651
7.146
45
7.948
7.411
6.935
60
5
8.011
7.466
6.982
50
7.593
7.098
6.658
10
8.314
7.750
7.250
55
7.179
6.735
6.336
15
20
8.170
7.995
7.622
7.463
7.135
6.990
56
1
6.843
6.346
5.911
25
7.906
7.3S3
6.919
6
8.902
8.241
7.662
30
7.802
7.292
6.837
11
9.052
8.386
7.801
33
7.669
7.174
6.732
16
8.858
8.214
7.648
40
7.490
7.015
6.590
21
8.679
8.053
7.502
45
7.274
6.822
6.418
26
8.570
7.958
7.419
50
6.989
6.568
6.189
31
8.436
7.841
7.316
55
6.659
6.272
5.924
36
8.264
7.690
7.183
60
6.226
5.888
5.579
41
8.035
7.489
7.005
Digitized by LjOOQ IC
TABLE VIII.
283
VahiM of Ammities
on Two joint Lives by the Northampton Table qf UortaUty.
Afn.
4 per cent.
Speroent
6 per cent.
Agei.
4 percent.
Spereent
Older
Toungvr
Older
YooDger
t> per cent.
61
1
6.123
5.725
5.372
65
5
6.963
6.546
6.171
6
7.944
7.415
6.945
10
7.236
6.803
6.414
11
8.092
7.557
7.081
15
7.127
6.705
6.325
16
7.935
7.416
6.953
20
6.986
6.576
6.205
21
7.787
7.281
6.830
25
6.920
6.515
6.151
26
7.704
7.207
6.764
30
6.844
6.447
6.089
31
7.601
7.116
6.682
35
6.747
6.360
6.010
36
7.469
6.998
6.577
40
6.614
6.240
5.901
41
7.290
6.838
6.434
45
6.453
6.094
5.769
46
7.076
6.648
6.263
50
6.236
5.897
5.590
51
6.795
6.395
6.035
55
5.986
5.671
5.384
56
6.465
6.100
5.770
60
5.658
5.372
5.112
61
6.030
5.712
5.420
65
5.201
4.960
4.736
62
2
7
12
17
22
27
32
37
42
47
52
57
62
6.894
7.828
7.863
7.700
7.580
7.499
7.397
7.265
7.088
6.875
6.600
6.270
5.831
6.452
7.319
7.357
7.208
7.100
7.027
6.937
6.819
6.660
6.469
6.222
5.925
5.533
6.059
6.865
6.905
6.770
6,670
6.605
6.524
6.418
6.276
6.104
5.880
5.613
5.259
66
1
6
11
16
21
26
31
36
41
46
51
56
61
66
5.295
6.846
6.987
6.866
6.749
6.689
6.615
6.520
6.388
6.230
6.019
5.774
5.447
4.982
4.996
6.447
6.581
6.472
6.364
6.309
6.243
6.156
6.037
5.894
5,701
5.479
5.180
4.759
4.728
6.087
6.215
6.115
6.015
5.966
3.905
5.827
5.718
5.588
5.412
5.209
4.938
4.551
63
3
7.048
6.605
6.209
67
2
5.896
5.569
5.276
8
7.669
7.184
6.750
7
6.684
6.306
5.963
13
7.625
7.147
6.719
12
6.730
6.351
6.009
18
7.462
6.998
6.583
17
6.604
6.236
5.903
23
7.365
6.910
6.503
22
6.512
6.151
5.824
28
7.286
6.839
6.439
27
6.454
6.098
5.776
33
7.186
6.750
6.359
32
6.382
6.033
5.717
3S
7.053
6.631
6.252
37
6.288
5.948
5.639
43
6.881
6.477
6.112
42
6.159
5.831
5.532
48
6.667
6.283
5.937
47
6.004
5.690
5.403
53
6.399
6.042
5.719
52
5.801
5.504
5.233
58
6.070
5.744
5.450
57
5.559
5.283
5.031
63
5.626
6.347
5.089
62
67
5.285
4.760
4.986
4.555
4.760
4.363
64
4
9
14
19
24
29
34
39
44
49
54
59
64
7.076
7.470
7.381
7.226
7.147
7.069
6.971
6.838
6.671
6.454
6.196
5.867
5.417
6.641
7.010
6.931
6.789
6.717
6.648
6.559
6.440
6.289
6.093
5.860
5.561
5.158
6.251
6.598
6.527
6.396
6.331
6.268
6.189
6.081
5.944
5.767
5.555
5.284
4.917
68
68
3
8
13
18
23
28
33
38
43
48
53
58
63
5.965
6.490
6.468
6.343
6.271
6.215
6.146
6.052
5.929
5.774
5,580
5.341
5.017
5.641
6.134
6.116
6.001
5.934
5.883
5.820
5.735
5.622
5.481
5.303
5.084
4.786
5.352
5.811
5.796
5.689
5.628
5.581
5.524
5.446
5.343
5.213
5.050
4.849
4.576
1
68
4.537
4.348
4.171
Digitized by ^^UUV
li
284
TABLE VIII.
Values of Annul tiei on Two joint Livei by the Northampton Table of Mortality*
Apes.
4 per cent.
5 per cent
6 per cent.
Aglu.
4 per cent
5 per cent.
Older
Younger
Older
Yoanger
6 per cent.
69
4
5.924
5.611
5.332
72
52
4.845
4.630
4.430
9
6.262
5.929
5.626
57
4.679
4.477
4.289
14
6.202
5.876
5.578
62
4.458
4.272
4.099
19
6.084
5.766
5.476
67
4 124
3.960
3.811
24
6.027
5.713
5.427
72
3.639
3.510
3.387
29
5.973
5.664
5.383
34
5.906
5.603
5.326
73
3
4.811
4.591
4.389
39
5.813
5.518
5.249
8
5.204
4.963
4.752
44
5.696
5.411
5.150
13
5.212
4.972
4.751
49
5.541
5.268
5.019
18
5.123
4.889
4.673
54
5.357
5.100
4.864
23
5.072
4.841
4.628
59
5.121
4.883
4.665
28
5.036
4.808
4.597
64
4.798
4.585
4.390
33
4.991
4.766
4.559
69
4.312
4.140
3.977
38
43
4.930
4.848
4.710
4.634
4.507
4.436
70
5
5.768
5.472
5.209
48
4.746
4.539
4.348
10
6.008
5.700
5.418
53
4.614
4.417
4.234
15
5.933
5.631
5.355
58
4.455
4.269
4.096
20
5.826
5.532
5.262
63
4.236
4.066
3.908
25
5.780
5.489
5.223
68
3.901
3.752
3.616
30
5.729
5.442
5.180
73
3.421
3.304
3.193
35
5.663
5.382
5.125
40
45
50
55
60
65
70
5.571
5.460
5.306
5.132
4.900
4.573
4.087
5.298
5.195
5.054
4.893
4.680
4.378
3.930
5.047
4.953
4.822
4.674
4.478
4.199
3.781
74
4
9
14
19
24
29
34
4.726
4.969
4.950
4.866
4.827
4.792
4.749
4.516
4.747
4.731
4.651
4.615
4.583
4.543
4.323
4.556
4.528
4.453
4.419 ,
4.390
4.353
71
1
6
11
16
21
26
31
36
41
4.380
5.610
5.744
5.660
5 572
5.532
5.483
5.419
5.329
4.169
5.331
5.460
5.3«2
5.300
5.263
5.218
5.159
5.076
3.976
5.084
5.199
5.127
5.050
5.016
4.974
4.920
4.844
39
44
49
54
59
64
69
74
4.690
4.613
4.511
4.389
4.234
4.019
3.683
3.211
4.488
4.417
4.322
4.208
4. 054
3.864
3.547
3.105
1 1
4.301
4.235
4.146
4.040
3.906
3.719
3.423
3.005
46
5.222
4.978
4.753
75
5
4.557
4.362
4.181
51
5.074
4.841
4.6-i6
10
4.725
4.522
4.350
56
4.905
4.685
4.482
15
4.69.)
4.495
4.310
61
4.679
4.476
4.289
20
4.619
4.424
4.242
66
4.349
4.169
4.005
25
4.589
4.396
4.216
71
3.862
3.719
3.584
30
35
4.557
4.616
4.365
4.327
4.188
4.152
72
2
4.814
4.588
4.380
40
4.457
4.272
4.101
7
5.418
5.157
4.9-^9
45
4.386
4.2%
4.040
12
5.478
5.216
4.97G
50
4.285
^4.112
3.951
17
5.389
5.133
4.899
55
4.171
4. 006
3.852
22
5.321
5.070
4. 840
60
4.021
3.866
3.721
27
5.283
5.03')
4.807
65
3.8C6
3.665
3.533
32
5.236
4.992
4.767
70
3.471
3.347
3. '236
37
f).174
4.934
4.714
75
3.015
2.917
2.827
42
5.087
4.854
4.640
47
4.983
4.758
4.551
76
6
4.403
4.221
4.053
Digitized by VjUUVIC
TAfiLE VIII.
285
Valuei of Annuities
on Tiro joint Ldvei ]
t)y the Northampton Table of Mortality.
A«ei.
4 per cent
5 per cent
6 per cent.
Agei.
4 per cent
5 per cent
Older
Yoongnr
Older
Yonager
6 per cent.
76
11
4.487
4.301
4.148
79
49
3.490
3.369
3.256
16
4.452
4.270
4.101
54
3.416
3.299
3.189
21
4.391
4.212
4.046
59
3.322
3.210
3.105
26
4.365
4.188
4.024
64
3.192
3.083
2.990
31
4.335
4.160
3.997
69
2.979
2.887
2.799
36
4.295
4.123
3.962
74
2.659
2.580
2.511
41
4.238
4.069
3.912
79
2.271
2.217
2.161
46
4.171
4.006
3.853
51
4.074
3.916
3,768
80
10
3.517
3.395
3.281
56
3.966
3.815
3.674
15
3.492
3.372
3.259
61
3.821
3.679
3.546
20
3.443
3.325
3.214
66
3.606
3.477
3.357
25
3.425
3.308
3,198
71
3.270
3.159
3.059
30
3.406
3.290
3.181
76
2.833
2.750
2.668
35
40
3.383
3.349
3.268
3.236
3.160
3.130
77
7
4.222
4.055
3.899
45
3.308
3.197
3.093
12
4.368
4.195
3.943
50
3.247
3.140
3.039
17
4.210
4.045
3.892
55
3.180
3.076
2.978
22
4.164
4.001
3.850
60
3.092
2.992
2.899
27
4.140
3.979
3.829
63
2.965
2.873
2.786
32
4.111
3.952
3.804
70
2.757
2.675
2.598
37
4.073
3.916
3.770
76
2.448
2.381
2.323
42
4.019
3.865
3.722
80
2.068
2.018
1.969,
47
3.954
3.805
3.666
52
3.864
3.720
3.586
81
11
3.264
3.156
3.054
57
3.761
3.623
3.494
16
3.235
3.128
3.028
62
3.621
3.492
3.371
21
3.195
3.091
2.992
67
3.405
3.289
3.180
26
3.181
3.077
2.979
72
3.070
2.971
2.882
31
3.164
3.060
2.963
n
2.656
2.583
2.511
36
41
3.142
3.109
3.040
3.009
2.944
2.914
78
8
4.016
3.864
3.722
46
3.072
2.973
2.881
13
4.022
3.871
3.729
51
3.015
2.920
2.829
18
3.9G4
3.815
3.677
56
2.953
2.861
2.774
23
3.930
3.783
3.646
61
2.870
2.782
2.699
28
3.908
3.762
3.626
66
2.746
2.664
2.587
33
3.881
3.737
3.602
71
2.542
2.470
2.402
38
3.844
3.702
3.570
76
2.258
2.195
2.147
43
3.794
3.655
3.525
81
1.869
1.827
1.786
48
3.731
3.596
3.469
53
3.648
3.518
3.396
82
12
3.020
2.924
2.833
58
3.549
3.424
3.308
17
2,987
2.893
2.804
63
3.414
3.297
3.188
22
2.958
2.865
2.777
68
3.199
3.095
2.996
27
2.945
2.853
2.765
73
2.869
2.780
2.701
32
2.929
2.838
2.751
78
2.470
2.410
2.346
37
42
2.909
2.878
2.818
2.789
2.733
2.705
79
9
3.775
3.638
3.510
47
2.843
2.756
2.673
14
3.759
3.624
3.497
52
2.792
2.707
2.627
19
3.704
3.571
3.447
•
bl
2.733
2.651
2.574
24
3.679
3.548
3.424
62
2.656
2.578
2.504
29
3.659
3.528
3.406
67
2.633
2.461
2.393
34
3.633
3.505
3.384
72
2.334
2.271
2.211
39
3.598
3.471
3.352
n
2.077
2.013
1.975
44
3.552
3.428
3.312
82
1.681
1.642
1.606
Digitized by VjOOQ IC
TABLE VIII.
Values of Annuities on Two joint Lives by the Northampton Table of Mortality.
Aget.
4 per cent
6 per oent
dpereent
Ag«t.
4 percent
5 per cent
Older
Younjfer
Older
Younger
epetecot.
83
13
2.794
2.709
2.628
86
56
2.153
2.097
2.044
18
2.760
2.677
2.598
61
2.105
2.051
2.000
23
2.740
2.657
2.579
66
2.035
1.984
1.936
28
2.728
2.646
2.568
71
1.914
1.867
1.823
33
2.713
2.632
2.555
76
1.739
1.699
1.661
38
2.694
2.613
2.537
81
1.478
1.447
1.417
43
2.666
2.587
2.511
86
1.195
1.171
1.149
48
2.632
2.554
2.481
53
2.585
2.510
2.438
87
17
2.177
2.121
2.069
58
2.530
2.457
2.388
22
2.158
2.104
2.051
63
2.457
2.387
2.321
27
2.151
2.096
2.044
68
2.336
2.272
2.211
32
2.142
2.088
2.036
73
2.141
2.085
2.032
37
2.130
2.077
2.026
78
1.899
1.838
1.810
42
2.113
2.060
2.009
83
1.510
1.472
1.441
47
52
2.093
2.063
2.041
2.012
1.991
1.963
84
14
2.622
2.545
2.472
57
2.030
1.980
1.932
19
2.589
2.513
2.442
62
1.985
1.937
1.891
24
2.574
f.499
2.429
67
1.915
1.870
1.826
29
2.563
2.489
2.418
72
1.794
1.753
1.713
34
2.549
2.476
2.406
77
1.638
1.597
1.562
39
2.530
2.437
2.388
82
1.356
1.329
1.803
44
2.505
2.433
2.365
87
1.124
1.098
1.078
49
2.470
2.400
2.334
54
2.428
2.360
2.295
88
18
2.061
2.012
1.965
59
2.376
2.310
2.247
23
2.048
1.999
1.953
64
2.305
2.242
2.182
28
2.041
1.992
1.946
69
2.183
2.126
2.071
33
2.033
1.985
1.939
74
1.991
1.941
1.894
38
2.022
1.974
1.929
79
1.751
1.750
1.672
43
2.006
1.959
1.914
84
1,387
1.357
1.330
48
53
1.987
1.960
1.941
1.914
1.895
1.870
85
15
2.462
2.393
2.327
58
1.928
1.883
1.841
20
2.431
2.364
2.299
63
1.886
1.843
1.802
25
2.421
2.354
2.290
68
1.817
1.777
1.737
30
2.411
2.344
2.280
73
1.697
1.660
1.6'25
35
2.398
2.331
2.268
78
1.546
1.514
1.483
40
2.379
2.313
2.251
83
1.259
1.235
1.212
45
2.356
2.291
2.230
88
1.030
1.063
1.044
50
2.322
2.258
2.198
55
2.2S4
2.222
2.164
89
19
1.904
1.862
1.822
60
2.234
2.174
2.118
24
1.895
1.854
1.814
65
2.163
2.107
2.053
29
1.889
1.848
1.808
70
2.042
1.991
.1941
34
1.882
1.841
1.802
75
1.856
1.811
1.769
39
1.872
1.832
1.792
80
1.608
1.573
1.539
44
1.859
1.818
1.779
85
1.339
1.256
1.232
49
54
1.840
1.817
1.800
1.778
1.761
1.740
86
16
2.315
2.253
2.194
59
1.788
1.750
1.713
21
2.290
2.229
2.171
64
1.751
1.714
1.678
26
2.282
2.221
2.163
69
1.685
1.650
1.616
31
2.272
2.212
2.154
74
1.570
1.538
1.508
36
2.260
2.200
2.143
79
1.427
1.400
1.373
41
2.241
2.182
2.126
84
1.164
1.145
1.124
46
2.221
2.162
2.107
69
1.015
1.001
.984
51
2.188
2.131
2.077
Digitized by VjUUVIC
TABLS VIII.
287
ValoesW Annuities
on Two joint Lives
bythf
! Noithamiiton Table of MortaUty.
A««.
4 per cent
1.704
5 per cent.
6 per cent.
Age..
i per cent.
(percent
Older
Younger
Older
93
Younger
6 per cent
90
20
1.670
1.638
23
.809
.798
• 788
25
1.699
1.665
1.633
28
.808
.797
.786
30
1.694
1.660
1.628
33
.806
.795
.785
35
1.688
1.654
1.622
38
.804
.793
.783
40
1.679
1.646
1.614
43
.800
.790
•779
45
1.668
1.635
1.604
48
.797
.786
•776
50
1.651
1.619
1.590
53
.790
.780
• 770
53
1.633
1.601
1.570
58
.784
• 773
•763
60
1.608
1.577
1.547
63
.774
.764
.754
65
1.575
1.544
1.515
68
.760
.750
• 740
70
1.515
1.486
1.459
73
.733
.723
.714
75
1.413
1.387
1.361
78
.697
.688
.679
80
1.278
1.255
1.234
83
.614
.606
.599
85
1.054
1.038
1.021
88
.554
.547
.541
90
.922
.909
.895
93
.365
.361
.357
91
21
1.432
1.407
1.382
94
24
.520
.514
•508
26
1.429
1.404
1.379
29
.519
•513
.507
31
1.425
1.400
1.376
34
.518
.512
• 506
36
1.420
1.395
1.371
39
.517
.511
.505
41
1.413
1.388
1.364
44
.515
.509
•503
46
1.405
1.380
1.356
49
.512
.507
.501
51
1.391
1.367
1.343
54
.5C9
.503
•498
56
1.377
1.353
1.330
59
.505
.499
.494
61
1.358
1.334
1.311
64
•500
.494
•489
66
1.330
1.307
1.285
69
.491
.485
.480
71
1.280
1.259
1.238
74
.474
.469
.464
76
1.200
1.180
1.160
79
.453
• .448
• 443
81
1.078
1.061
1.044
84
.403
.398
.394
86
.902
.892
.879
89
.373
.369
.365
91
.756
.748
.737
94
.201
.199
.197
92
22
1.142
1.124
1.107
95
25
.236
.234
.232
27
1.140
1.122
1.105
30
.236
.234
.231
32
1.137
1.119
1.102
35
.235
.233
.231
37
1.134
1.116
1.099
40
.235
.233
.231
42
1.128
1.111
1.094
45
.234
.232
.230
47
1.122
1.105
1.089
50
.233
.231
.229
52
1.113
1.095
1.079
55
.232
.230
.228
57
1.102
1.085
1.069
60
.230
.228
.226
62
1.088
1.071
1.055
65
.228
.226
• 224
67
1.067
1.050
1.035
70
• 224
.222
.220
72
1.028
1.012
.997
7^
.2J7
.215
.213
n
.970
.955
.942
80
.208
.206
.204
82
.864
.852
.840
85
.187
.185
• 183
87
.738
.734
.725
90
.177
.175
.174
92
.583
.576
•569
95
.060
.059
• 058
Digitized by VjOOQTC
288
TABLE IX.
Value of Revenion of £1 on a Single Life. (Northampton Rate of Mortality.)
3 per cent.
4 per cent.
5 per cent.
6 per eeut.
Age.
Sinxle Prem.
AnnaalPien.
Sinffle Prem.
Sinsle Prem.
SinsU Prem.
8
.362554
.016566
.282185
.22733
.18847
•9
.364690
.016719
.2S3615
.22810
.18853
10
.369029
.017035
.287508
.23148
.19142
11
•374368
.017429
.292523
.23605
.19555
12
.380086
.017858
.297985
.24110
.20019
13
.385980
.018309
.303654
.24638
.20506
14
.392056
.018783
.309550
.25191
.21021
15
.39S320
.019282
.315681
•25771
.21564
16
.404782
.019808
.322058
.26381
.22142
17
.411116
.020334
.328315
.26981
.2-2708
18
.417095
.020841
.334183
.27538
.23234
19
.422696
.021326
.339650
.28057
.23716
20
.428006
.021794
.344792
.2a538
.24162
21
.432890
.022233
.349458
.28967
.24553
22
.437540
.022657
.353858
.29367
.24915
23
.442275
.023097
•358358
.29781
.25283
24
.447097
.023553
•362962
.30200
.25668
25
.452010
.024025
.367673
.30633
.26059
26
.4:)7016
.024515
.37-2492
.31081
.26461
27
•462115
.025023
.377423
.31538
.26885
28
.46/312
.025552
.382473
.32010
.27315
29
.472609
.026101
.387646
.32491
.27757
30
.478009
.026672
.39-2942
.32991
.28215
31
.483516
.027267
.398373
.33500
.28691
32
.489132
.027887
.403935
.34029
.29177
33
.494860
.028533
.409638
.34571
.29681
34
.500704
.029208
.415565
.35129
.30202
35
.506667
^029914
.421481
.35705
.30740
36
.512754
.030651
.427635
.36300
.31300
37
.518969
.031423
.433954
.36910
.31877
38
.525314
.032233
.440438
.37543
.32477
39
.531796
.033082
.447100
.38195
.33100
40
.538419
.033975
.453946
.3887)
.33745
41
.545060
.034896
.460831
.39548
.34402
42
.551713
.035846
.467750
.40-233
.35059
43
.558371
.036826
.474692
.40919
.35721
44
.565158
.037855
.481958
.41629
.36406
45
.572077
.038938
.489096
.42357
.37113
46
.579133
.040079
.496569
.43110
.37849
47
.586328
.841283
.504235
.43886
.38608
48
.593668
.042555
.512054
.44686
.39394
49
.601156
.043900
.520162
.46510
.40209
50
.608661
.045301
.528273
•46338
.41036
61
.616035
.046730
.636208
.47167
•41851
52
.623391
.048212
• 54424-2
.47976
.4-2666
Digitized by VjOOQ IC
TABLB IX.
2S»
Value of Revenion of £1 on a Single Life. (Northampton Rate of Mortality.)
3p<»
cent.
4 per cent.
5 per cent.
6pereettt.
Alt.
Single Pram.
AmuulPrem.
Single Prem.
Single Prem.
Single Piem.'
&3
•630857
•049776
.552388
.48819
.43509
54
.638432
.051429
.560692
.49681
.44375
55
.646115
.053178
.569188
.50562
.45264
56
.653906
.055031
.577781
.51462
.46175
57
.661801
•056996
.586562
.52386
.47115
58
.669801
.059082
.595504
.53329
.48077
59
.677901
.061300
.604600
.54291
.49062
60
.686096
.063661
.613846
.55276
.50075
61
.694382
.066176
.623242
.56281
.51111
62
.702752
.068860
.632777
.57305
.52175
63
.711359
.071782
.642642
.58371
.53285
64
•720052
.074916
.652654
.59457
.54423
65
.728990
.078347
.663015
.60591
.56617
66
.738017
.082050
.673531
.61743
.56840
67
.747123
.086053
.684196
.62919
.58085
68
.756292
.090387
.694996
.64114
.59364
69
.765504
.095081
.705873
.65329
.60666
70
.774733
.100170
.716850
.66557
.61985
71
.783946
.105684
.727854
.67791
.63326
72
.793096
•111645
.738831
.69029
.64674
73
.802121
.118066
.749708
.70262
.66015
74
.810938
.124930
.760369
.71476
.67345
73
.819426
.182172
.770669
.72648
.68631
76
•827415
.139638
.780377
.73757
.69853
77
.835381
.147805
.790100
.74871
.71082
78
.843519
.157007
•800081
.76024
.72355
79
.852121
. 167834
•810704
.77257
.73730
80
•860733
.180013
.821388
.78600
.75128
H
.868951
.193128
.831627
.79700
.76475
8i
.876815
.207317
.841465
.80857
.77777
83
•884013
.221987
.850485
.81919
.78983
84
.889503
.234467
.857369
.82729
.79900
85
.894559
.247107
'.863708
.83471
.80743
86
.899170
.259739
.869485
.84152
.81513
87
.903523
.272773
.874938
.84795
.82238
88
.907227
.284824
.879554
.85333
.82843
89
.912239
.302754
.885858
.86076
.83687
90
.918599
.328687
.893915
.87033
.84779
91
.927154
.370708
.904850
.88348
.86291
92
.936206
.427439
.916481
.89748
.87909
93
•946438
.514659
.929708
.91353
.89777
94
.955253
.621817
.941150
.92743
.91408
95
.963804
.775562
.952292
.94105
.93004
96
•970874
,970874
Digitized b?G00gle
290
TABLE X.
Logarithm and its Arithmetical Complement of the number which completea eack
Year of Age according to the Cariiale Table of Mortality.
Age.
LogA«-
-Log A.
Age.
Log 4.
-Log^
0
4.0000000
?. 0000000
52
3.6310377
4.3689623
1
3.9274217
.0725783
53
.6243852
.3756148
2
.8909238
.1090762
54
.6173149
.3826851
3
.8617733
.1382267
55
.6099144
.3900856
4
.8449739
.1550261
56
.6020600
.3979400
5
.8323173
.1676827
57
.5937290
.4062710
6
.8245163
.1754837
58
.5845574
.4154426
7
.8191489
.1808511
59
.5739154
.4260846
8
.8153120
.1846880
60
.5614592
•4385408
9
.8124454
.1875546
61
.5466660
.4533340
10
.8102325
.1897675
62
.5308398
.4691602
11
.8082785
.1917215
63
.5142820
.4857180
12
.8061800
.1938200
64
.4973444
.5026556
13
.8040030
.1959970
65
.4797192
.5202808
14
.8017466
.1982534
66
.4614985
.5385015
15
.7993405
.2006595
67
.4426365
.5573635
16
.7966437
.2033563
68
.4229180
.5770820
17
.7937206
.2062794
69
.4022614
.6977386
18
.7907073
.2092927
70
.3803922
.6196078
19
.7876730
.2123270
71
.3573630
.6426370
20
.7846173
.2153827
72
.3310222
.6689778
21
.7815400
.2184600
73
.3003781
.6996219
22
.7785130
.2214870
74
.2650538
•7349462
23
.7754648
.2245352
75
.2240148
.7759852
24
.7723951
.2276049
76
.1804126
.8195874
25
.7693035
.2306965
n
.1332195
.8667805
26
.7661153
.2338847
78
.0838608
.9161392
27
.7629035
.2370965
79
.0338257
-.9661743
28
.7595168
.2404832
80
2.9790929
3.0209071
29
.7557224
.2442776
81
.9227255
.0772745
30
•7514331
.2485669
82
.8603380
•1396620
31
.7470232
.2529768
83
.7944880
.2055120
32
.7425680
.2574320
84
.7234557
.2765443
33
.7381461
.2618539
85
.6483600
.3516400
34
.7337588
.2662412
86
.5646661
.4353339
35
.7293268
.2706732
87
.4712917
^ .5287083
36
.7248491
.2751509
88
.3654880
* .6345120
37
.7202420
.2797580
89
.2576786
.7423214
38
.7155019
.2844981
90
.1522883
.8477117
39
.7106250
.2893750
91
.0211893
^.9788107
40
.7054360
.2945640
92
1.8750613
2.1249387
41
.6997510
.3002490
93
.7323938
.2676062
42
.6937269
.3062731
94
.6020600
.3979400
43
.6874398
.3125602
95
.4771213
.5228787
44
.6810602
.3189398
96
.3617278
.6382722
45
.6745856
.3254144
97
.2552725
.7447275
46
.6681062
.3318738
98
.1461280
.8538720
47
.6616234
.3383766
99
.0413927
^.9586073
48
.6552345
.3447655
100
0.9542425
1.0457575
49
.6491401
.3508599
101
.8450980
.1549020
50
.6431565
.3568435
102
.6989700
.3010300
51
.6372895
.3627105
103
.4771213
.5228787
Digitized by VjOOQ iC
TABLB XI.
391
Preparatory Table for finding the Values of Annuities^ AMuraneea, &c.
(Carlisle 3 per Cent.)
A«e.
D.
N.
S.
M.
R.
0
10000.000
173197.234
3702001.698
4664.129
70035.663
1
8214.563
164982.671
3528804.464
3169.954
65371.534
2
7332.464
157650.218
3363821.793
2.527.104
62201.580
3
6656.740
160993.477
3206171.575
2064.957
59674.476
4
6217.632
144775.845
3055178.098
1819.735
57609.519
5
5863.152
138912.6Sf3
2910402.253
1646..351
55789.784
6
6591.045
133321.648
2771489.560
1545.015
54143.434
1
5361.525
127960.123
2638167.912
1478.341
52598.419
8
5159.579
122800.544
2610207.790
1432.556
51120.078
9
4976.344
117824.200
2387407.246
1.399.600
49687.522
10
4806.847
113017.353
2269583.046
1375.045
48287.922
11
4645.891
108371.462
2156565.693
1354.095
46912.877
12
4488.831
103882.631
2048194.230
1332.352
45558.783
13
4336.298
99546.383
1944311.599
1310.561
44226.431
14
4188.181
95358.152
1844765.266
1288.744
42915.870
15
4043.730
91314.421
1749407.115
1266.279
41627.126
16
3901.648
87412.773
1658092.694
1241.976
40360.847
17
3762.597
83650.176
1570679.920
1216.565
39118.871
18
3627.749
80022.427
1487029.745
1191.307
37902.306
19
3497.564
76524.862
1407007.318
1166.785
36710.999
20
3371.885
73152.977
1330482.456
1142.977
35544.214
21
3250.560
69902.417
1257329.478
1119.862
34401.2.38
22
3133.964
66768.452
1187427.062
1097.943
33281.376
23
3021.403
63747.049
1120658.609
1076.662
32183.434
24
2912.740
6U834.310
1056911.560
1056.000
31106.773
25
2807.843
58026.467
996077.251
1035.741
30050.773
26
2706.122
55320.344
938050.784
1016.002
'29014.832
27
2607.945
52712.399
882730.440
996.6439
27998.830
28
2512.317
50200.082
830018.041
976.9755
27002.186
29
2417.926
47782.156
779817.959
955.7581
26025.211
30
2324.429
45457.727
732035.803
932.6869
25069.453
31
2233.928
43223.799
686578.076
909.8876
24136.766
32
2146.727
41077.072
643354.278
887.7524
23226.879
33
2063.088
39013.984
602277.206
866.6389
22339.127
34
1982.865
37031.119
563263.222
846.5065
21472.488
35
1905.566
35125.553
526232.103
826.9604
20625.982
36
1831.087
33294.466
491106.550
807.9836
19799.022
37
1758.995
31533.470
457812.085
789.2245
18991.039
38
1689.225
29846.246
426276.614
770.6867
18201.815
39
1621.710
28224.536
396430.368
752.3729
17431.129
40
1555.^76
26668.760
368205.833
733.6730
16678.756
41
1490.819
25177.941
341537.073
714.0295
15945.083
42
1427.459
23750.482
316359.132
694 0913
15231.0.54
43
1365.964
22384.519
292608.650
674.1728
14536.963
44
1306.840
21077.679
270224,131
654.8344
13862.790
45
1250.001
19827.678
249146.452
636.0593
13207.966
46
1195.^22
18632.056
229318.774
618.0877
12671. {^^97
47
1143.599
17488.457
210686.718
600.8888
11953.810
48
1093.077
16395.380
193198.262
584.6749
11352.921
49
1047.408
15347.972
176802.882
569.8371
10768.246
SO
1002.987
14344.985
161454.911
555.9585
10198.373
51
960.7073
13384.277
147109.926
542.8922
9642.415
Digit^dSiy Google
292 TABLE XI.
Preparatory Table for finding the Values of Annuities, AuuranceS| &c.
(Carlisle 3 per Cent)
Ag«.
D.
N.
S.
M.
R.
52
919.3947
12464.883.
1.33725.648
529.5614
9099.522
53
879.0475
11585.835
121260.766
515.9926
8569.9610
. 54
839.6626
10746.173
109674.930
502.2111
8053.9683
55
801.4327
9944.7400
98928.7577
488.4374
7551.7573
56
764.1444
9180.5956
88984.0177
474.4917
7063.3199
57
727.7919
8452.8038
79803.4221
460.3959
6588.8282
58
691.8233
7760.9755
71350.6183
445.6301
6128.4323
59
655.4193
7105.5562
63589.6429
429.3714
5682.8022
60
618.3376
6487.2186
56484.0867
411.3797
5253.4308
61
580.2235
5906.9951
49996.8681
391.2754
4842.0511
62
543.1651
5363.8300
44089.8730
371.1167
4450.7757
63
507.6178
4856.2121
38726.0431
351 .3898
4079.6590
64
473.9822
4382.2300
33869.8310
332.5391
3728.2692
65
441.8752
3940.3548
29487.6010
314.2374
3395.7301
66
411.3786
3528.9762
25547.2462
296.6110
3081.4927
67
382.4216
3145.5546
22018.2700
279.6359
2784.8817
68
354.8025
2791.7521
18871.7155
263.1553
2505.2458
69
328.4679
2463.2842
16079.9634
247.1547
2242.0905
70
303.2400
2160.0442
13616.6792
231.4938
1994.9358
71
279.2030
1880.8412
11456.6350
216.2891
1763.4420
72
255.1185
1625.7227
9575.7937
200.3367
1547.1529
73
230.8132
1394.9095
7950.0710
183.4621
1346.8161
74
206.5852
1188.3243
6555.1615
165.9567
1163.3541
75
182.4832
1005.8411
5366.8372
147.8718
997.3973
76
160.2447
845.5965
4360.9960
130.9483
849.5255
77
139.5575
706.0390
3515.3996
114.9285
718.5772
78
120.9365
585.1025
2809.3606
100.3722
603.6487
79
104*6369
480.4656
2224.2581
87.5951
503.2765
80
89.56018
390.9054
1743.7925
75.5660
415.6814
81
76.36780
314.5376
1352.8871
64.9822
340.1153
82
64.22226
250.3153
1038.3495
55.0610
275.1331
83
53.57947
196.7359
788.03419
46.2887
220.0722
84
44.17014
152.5657
591.29831
38.4400
173.7834
85
36.07413
116.4916
438.73257
31.6305
135.3435
86
28.88449
87.60711
322.24097
25.4915
103.7130
87
22.61795
64.98917
234.63386
20.0663
78.22142
88
17.21124
47.77792
169.64470
15.3184
58.15517
89
13.03664
34.74128
121.86677
11.6450
42.83661
90
9.929746
24.81154
87.12549
8.91786
31, 19177
91
7.128560
17.68298
62.31395
6.40589
22.27390
92
4.943523
12.73946
44.63097
4.42849
15.86801
93
3.455667
9.28379
31.89152
3.08461
11.43952
94
2.485197
6.79859
22.60773
2.21480
8.35491
95
1.809610
4.98898
15.80914
1.61159
6.14011
96
1.346959
3.64202
10.82016
1.20165
4.52852
97
1.023438
2.6185S
7.17813
.917360
3.32687
98
.772823
1 .84576
4.55955
.696554
2.40951
99
.589532
1.25623
2.71379
.535772
1.71295
100
.468296
.787934
1.45756
.431706
1.17718
101
.353621
.434312
.669626
.330672
•745480
102
•245230
.189083
.235313
.232580
.414809
103
104
•142852
.046231
.046231
.137345
•044884
.182229
.044884
Digitized by VjUUVIC
TABLE XII.
293
Preparatory Table for finding the Values of Annuities, Assurances, &c.
(Carlisle 3^ per Cent.)
Age.
D.
N.
S.
M.
R.
0
10000.0000
156719.2811
3126762.5941
4362.1499
55413.1307
I
8174.8792
148544.4019
2970043.3130
2875.1934
51050.9808
2
7261.7797
141282.6222
2821498. 9111
2238.5391
48175.7874
3
6560.7312
134721.8910
2680276.2889
1783.0580
45937.2484
4
6098.3527
128623.5383
2545494.3979
1542.5400
44154.1903
5
5722.8916
122900.6466
2416870.8596
1373.3034
42611.6504
6
5430.9303
117469.7164
2293970.2130
1274.8698
41238.3470
7
5182.8244
112286.8920
2176500.4966
1210.4185
39963.4772
8
4963.5140
107323.3780
2064213.6046
1166.3726
38753.0387
9
4764.1152
102559.2629
1956890.2266
1134.8222
37586.6861
10
4579.6155
97979.6473
1854330.9637
1111.4279
36451.8639
11
4404.8859
93574,7615
1754351.3164
1091.5645
35340.4360
12
4235.4131
89339.3484
1660776.5549
1071.0492
34248.8715
13
4071.7256
85267.6227
1571437.2065
1050.5883
33177.8223
14
3913.6476
81353.9751
1486169.5838
1030.2015
32127.2341
15*
3760.4109
77593.5642
1404815.6087
1009.3103
31097.0326
16
3610.7557
73982.8085
1327222.0445
986.8188
30087.7223
17
3465.2503
70517.5582
1253239.2360
963.4162
29100.9036
18
3324.9184
67192.6398
1182721.6778
940.2667
28137.4874
19
3190.1149
64002.5249
1115529.0380
917.9000
27197.2207
20
3060.6262
60941.8987
1051526.5131
896.2896
26279.3208
21
2936.2472
58005.6515
990584.6144
875.4101
25383.0311
22
2817.2495
55188.4020
932378.9629
855.7058
24507.6210
23
2702.9422
52485.4597
877390.5609
836.6678
23651.9153
24
2593.1442
49892.3156
824905.1012
818.2735
22815.2475
25
2487.6811
47404.6344
775012.7856
800.5014
21996.9740
26
2385.9766
45018.6578
727608.1512
782.9214
21196.4726
27
2288.3059
42730.3519
682589.4934
765.9358
20413.5512
28
2193.7491
40536.6028
639859.1415
748,7614
19647.6154
29
2101.1270
38435.4758
599322.5387
730.33'JO
18898.8540
30
2010.1228
36425.3530
560887.0629
710.3724
18168.5309
31
1922.5265
34502.8265
524461,7099
690.7513
17458.1576
32
1838.5559
32664.2706
489958.8834
671.7937
16767.4063
33
1758.3873
3U905.8833
457294.6128
653.7985
16093.6127
34
1681.8488
29224.0345
426388.7295
636.7223
15441.8142
33
1608.4759
27615.5586
.^97164.6950
620.22.36
14805.0919
36
1538.1422
26077.4164
369549.1364
604,2828
14134.8684
37
1470.4460
24606.9704
343471.7200
588.6010
13580.5856
38
1405.2987
23201,6717
318864.7496
573.1790
12991.9846
39
1342.6146
21859.0571
295663.0779
558.0170
12418.8057
40
1281.8053
20577.2518
273804.0208
542.6101
11860.7887
41
1222.3531
19354.8937
253226.7690
526.5040
11318.1786
42
1164.7488
18190.1499
233871.8703
510.2353
10791.6745
43
1109.1869
17080.9630
215681.7204
494.0611
10281.4393
44
1056,0509
16024.9121
198600.7575
478.4338
9787.3782
45
1005.2402
15019.6719
182575.8453
463.3350
930S.9444
46
956.8639
14062.8080
167556.1731
448.9522
8845.6094
47
910.8083
13151.9998
153493.3654
435.2544
8396.6572
48
867.1570
12284.8428
140341.3656
422,4033
7961.4028
49
826.1576
11458.6852
128056.5228
410.7282
• 75.38.9995
50
787.2977
10671.3875
116597.8376
399.8059
7128.2713
51
750.4672
9920.9203
105926.4501
389.5990
6728.4654
Digitized 1:
V^^uuqIc
994 TABLE XU.
Preparaiozy Table for finding the Values of Annoitiet^ AwmaDcet, Itc.
(Carlule 3^ per Cent)
A«e.
D.
N.
S.
M.
R .
52
714.7259 ,
9206.1945
96005.5298
379.2358
6338.8664
53
680.0592
8526.1353
86799.3353
368.7386
5959.6305
54
646.4516
7879.6836
78273.2000
358.1282
5590.8920
55
614.0379
7265.6457
70393.5164
347.5752
5232.7637
56
582.6402
6683.0056
63127.8707
336.9420
4885.1886
57
552.2415
6130.7640
56444.8651
326.2462
4548.2466
58
522.4167
5608.3473
50314.1012
315.0962
4222.0004
59
492.5324
5115.8149
44705.7538
302.8781
3906.9042
60
462.4217
4633.3932
39589.9389
289.4231
3604.0261
61
431.8219
4221.5713
34936.5457
274.4608
3314.6030
62
402.2889
3819.2824
30714.9744
259.5305
3040.1422
63
374.1450
3445.1373
26S95.6920
244.9906
2780.6117
64
347.6658
3097.4715
23450.5547
231.1636
2535.6212
65
322.5496
2774.9219
20353.0832
217.8042
2304.4576
66
298.8377
2476.0842
17578.1613
204.9998
2086.6534
67
276.4605
2199.6237
15102.0771
192.7282
1881.6536
68
255.2550
1944.3687
12902.4534
180.8715
1688.9254
69
235.1675
1709.2013
10958.0847
169.4159
1508.0539
70
216.0567
1493.1446
9248.8834
158.2576
1338.6380
71
197.9695
1295.1751
7755.7388
147.4766
1180.3804
72
180.0184
1115.1567
6460.5637
136.2202
1032.9038
73
162.0812
9J3.0756
5345.4070
124.3705
896.6835
74
144.3670
808.7086
4392.3314
112.1374
772.3130
75
126.9079
681.8007
3383.6228
99.56024
660.1756
76
110.9037
570.8970
2901.8221 ■
87-84764
560.6154
V
96.1197
474.7773
2330.9251
76.81403
472.7677
78
82.8922
391.8851
1856.14780
66.83690"'
395.9537
79
71.3737
320.51141
1464.26271
58.12152'
329.1168
80
60.79459
2:)9. 71682
1143.75130
49.95604
270.9953
81
51.589005
208.127819
884.034478
42.80631
221.0392
82
43.174700
164.953119
675.906659
36.13656
178.2329
83
3:). 845863
129.107256
510.953540
30.26774
142.0964
84
29.408051
99.699205
381.846284
25.04211
111.8286
85
23.9017b2
75.797423
282.147079
20.53031
86.78652
86
19.045660
56.751763
206.349656
16.48246
'66.25621
87
14.841618
41.910145
149.597893
'l2.92248
49.77375
88
11.239247
30.670898
107.687748
9.821995
36.85128
89
8.472029
22.198869
77.016850
7.434849
* 27,02928
90
6.421801
15.777068
54.817981
5.671114
19.59443
91
4.587937
11.1891305
39.0409134
4.054413
13.92332
92
3.166278
8.0228525
27.8517829
2.787902
9.868906
93
2.2026281
5.8202244
19.8289304
1.931324
7.081005
; 94
1.5764024
4.2438220
14.0087060
1.379583
5.149681
* 95
1.1423205
3.1015015
9.7648840
.9988096
3.770098
96
.8461633
2.2553382
6.6633825
.7412817
2.771288
97
.6398212
1.6155170
4.4080443
.5635536
2.030006
98
.4808101
1.1347069
2.7925273
.4261792
1 .466453
99
.3650043
.7697026
1.6578204
.3266326
1.040274
100
.2885410
.4811616
.8881178
.2625124
.713641
101
.2168317
.2643300
.4069562
.2005605
.451129
102
.1496423
^ .1146877
' .1426262
.1407036
' .250568
103
.0867491
.0279385
.0279385
.0828708
.109865
104
.0269938
.026994
Digitized by VjUUVLC
TABLE XIII.
295
PkvpvBioTj T«blt fn finding the Values of Annoiiies, Af surances, &c.
(Garli8le4perCeDi)
Age.
D.
N.
S.
M.
R.
10000.0000
142816.4335
2661123.5878
4122.4446
44587.9275
8135.5769
134680.8566
2518307.1543
2642.6369
40465.4829
7192.1228
127488.7339
2383626.2977
2012.0895
37822.8460
6466.5595
121022.1744
2256137.5638
1563.1464
35810.7565
5981.9197
115040.2547
2135115.3894
1327.2204
34247.6101
5586.6386
109453.6161
2020075.1347
1162.0131
32920.3897
5276.1398
104177.4763
1910621.5186
1066.3850
31758.3766
5010.8980
99166.5788
1806444.0423
1004.0718
30691.9916
4775.7912
94390.7871
1707277.4641
961.6917
29687.9198
4561.8957
89828.8914
1612886.6770
931.4805
28726.2281
4364.1445
85464.7469
1523057.7856
909.1869
27794.7476
4177.4550
81287.2919
1437593.0387
890.3490
26885.5607
3997.4211
77289.8708
1356305.7468
870.9865
25995.2117
3824.4558
73465.4150
1279015.8760
851.7682
25124.2252
3658.3046
69807.1103
1205550.4610
832.7115
24272.4570
3498.1664
66308.9440
1135743.3507
813.2772
23439.7455
3342.7991
62966.1449
1069434.4067
792.4548
22626.4683
3192.6682
59773.4766
1006468.2618
770.8931
21834.0135
3048.6473
56724.8294
946694.7852
749.6671
21063.1204
2910.9820
53813.8474
889969.9558
729.2575
20313.4533
20
2779.3965
51034.4509
836156.1084
709.6329
19584.1958
21
2653.6268
48380.8241
785121.6575
690.7630
18874.5629
22
2533.8421
45846.9820
736746.8334
673.0409
18183.7999
23
2419.3461
43427.6359
690893.8514
656.0004
17510.7590
24
2309.9092
41117.7267
647466.2155
639.6153
16854.7586
25
2205.3117
38912.4150
606348.4888
623.8604
16215.1433
26
2104.9823
36807.4327
567436.0738
608.3507
15591.2829
27
2009.1084
34798.3243
530628.6411
593.4376
14982.9322
28
1916.8285
32881.4958
495830.3168
578.4311
14389.4946
20
1827.0717
31054.4240
462948.3210
562.3986
13811.0635
30
1739.5339
29314.8901
431894.3970
545.1327
13248.6649
31
1655.7306
27659.1596
402579.5069
528.2345
12703.5322
38
1575.8003
26083.3593
374920.3473
511.9862
12175.2977
33
1499.8433
24583.5160
348836.9880
496.6369
11663.3115
34
1427.6617
23155.8543
324253.4720
482.1415
11166.6746
35
1358.8137
21797.0406
301097.6177
468.2037
10684.5331
36
1293.1499
20503.8907
279300.5771
454.8019
10216.3294
37
1230.2928
19273.5979
258796.6864
441.6813
9761.5275
38
1170.1325
18103.4654
239523.0885
428.8100
9319.8462
39
1112.5635
16990.9019
221419.6231
416.2760
8891.0062
40
1057.0669
15933.8350
204428.7212
403.5704
8474.7302
41
1003.1921
14930.6430
188494.8862
390.3520
8071.1598
42
951.3202
13979.3228
173564.2432
377.0644
7680.8078
43
901.5840
13077.7388
159584.9204
363.9174
7303.7434
44
854.2664
12223.4724
146507.1816
351. '2761
6939.8260
45
809.2549
11414.2176
134283.7092
'339.1211
6588.5499
46
766.6067
10647.6108
122869.4916
327.5981
6249.4288
47
726.2004
9921.4104
112221.8808
316.6766
5921.8307
48
688.0725
9233.3379
102300.4704
306.4795
5605.1541
49
652.3887
8580.9492
93067.1325
297.2600
5298.6746
50
618.7134
7962.2358
84486.1833
' 288.6766
5001.4146
51
586.9340
7375.3019
76523.9475
280.6938
4712.7380
296
TABLE Xlir.
Preparatory Table for finding the Values of Annuities, Assurances, &c.
(Carlisle 4 per Cent.)
Age.
D.
N.
S.
M.
R.
52
556.2936
6819.0083
69148.6456
272.6278
4432.0442
53
526.7666
6292.2417
62329.6373
264.4968
4159.4164
54
498.3272
5793.9145
56037.3956
256.3176
3894.9196
55
471.0649
5322.8496
50243.4811
248.2218
3638.6020
56
444.8289
4878.0207
44920.6315
240.1036
3390.3802
57
419.5934
4458.4273
40042.6108
231.9770
3150.2766
58
395.0242
4063.4031
35584.1835
223.5459
2918.2996
59
370.6367
3692.7664
31520.7804
214.3517
2694.7537
60
346.3050
3346.4614
27828.0140
204.2753
2480.4020
61
321.8343
3024.6271
24481.5526
193.1240
2276.1267
!
62
298.3821
2726.2451
21456.9255
182.0500
2083.0027
63
276.1733
2450.0718
18730.6804
171.3174
1900.9527
64
255.3940
2194.6778
16280.6086
161.1602
1729.6353
65
235.8046
1958.8732
14085.9308
151.3936
1568.4751
66
217.4193
1741.4540
12127.0576
142.0778
1417.0815
67
200.1717
1541.2822
10385.6036
133.1925
1275.0037
68
183.9293
135T.3530
8844.3214
124.6489
1141.8112
69
168.6402
1188.7128
7486.9684
116.4340
1017.1623
70
154.1908
1034.5220
6298.2556
108.4708
900.7283
71
140.6034
893.9186
5263.7336
100.8139
792.2576
72
127.2395
766.6792
4369.8150
92.8577
691.4436
73
114.0103
652.6688
3603.1358
84.5224
598.5659
74
101.0617
551.6071
2950.4670
75.9588
514.0635
75
88.4126
463.1945
2398.8599
67.1967
438.1047
76
76.8916
386.3028
1935.6654
59.0762
370.9080
77
66.3212
319.9817
1549.3626
51.4631
311.8318
78
56.9194
263.0623
1229.3809
44.6121
260.3H87
79
48.7744
214.2878
966.3186
38.6563
215.7566
80
41.34527
172.9426
752.0308
33.1031
177.1003
81
34.91604
138.02654
579.08815
28.26413
143.99717
82
f 29.08066
108.94588
441.06161
' '23.77167
115.73304
83
24.02818
84.91770
332.11573
19.83768
91.96137
84
19.61802
65.29968
247.19803
16.36168
72.12369
85
15.86814
49.43154
181.89835
13.35635
55.77201
86
12.58342
36.84812
132.46681
10.68194
42.41566
%7
9.75868
27.08943
95.61869
8.34118
31.73372
88
7.35452
19.73492
68.529J6
6.31235
23.39254
89
5.51711
14.21781
48.79434
4.75780
17.08019
90
4.16186
10.05595
34.57653
3.61475
12.32239
91
2.95907
7.09688
24.52058
2.57203
8.70764
92
2.032329
5.064547
17.423696
1.75910
6.13561
93
1.406997
3.657550
12.359149
1.21194
4.37651
94
1.002135
2.655416
8.701599
.861190
3.164572
95
.722693
1.932722
6.046183
.620292
2.303382
96
.532755
1.399967
4.113461
.458149
1.683090
97
.400902
.999065
2.713494
.346787
1.224941
98
.299820
.699245
1.714429
.261124
.878154
99
.226512
.472733
1.015184
.199618
.617030
too
.178200
.294532
.542451
•160018
.417412
101
.133270
.161263
.247919
.121941
.257394
102
.091531
1 .069731
.086656
.085329
.135453
103
.052806
, .016925
.016925
.050124
■ .050124
Digitized by VjUUVIC
TABLE XIV.
297
IVspaimtory Table for finding the Values of Annnities, AsBurances^ &c»
(Carlisle 4) per Cent.)
Ay.
D.
N.
S.
M.
R.
0
10000.0000
130984.0987
2275559.365
3928.914391
36491.796787
1
8096.6507
112887.4480
2144575.266
2456.187131
32562.882396
2
7123.4633
115763.9847
2031687.818
1831.659305
30166.695265
3
6374.1815
109389.8032
1915923.833
1389.129522
28275.035960
4
5868.2523
103521.5510
1806534.030
1157.686592
26885.906438
5
5454.2598
98067.2912
1703012.479
996.393931
25728.219846
6
5126.4720
92940.8192
1604945.188
903.478546
24731.825915
7
4845.4589
88095.3604
1512004.369
843.222612
23828.347369
8
4596.0180
83499.3424
1423909.008
802.437874
22985.124757
9
4369.1685
79130.1739
1340409.666
773.502983
22182.686883
10
4159.7728
74970.4011
1261279.492
752.253370
21409.183900
11
3962.7741
71007.6270
1186309.091
734.383606
20656.930530
12
3773.8487
67233.7783
1115301.464
716.104026
19922.546924
13
3593.2818
63640.4065
1048067.686
698.047333
19206.442898
14
3420.7281
60219.7684
984427.189
680.228229
18508.395565
15
3255.3388
56964.4297
924207.421
662.143014
17828.167336
16
3095.8724
53868.5573
867242.991
642.858710
17166.024322
17
2942.6840
50925.8733
813374.434
622.985302
16523.165612
18
2796.4951
48129.3782
762448.561
603.514886
15900.180310
19
2657.4399
45471.9384
714319.182
584.882909
15296.665424
20
2525.1750
42946.7633
668847.244
567.053266
14711.782516
21
2399.3736
40547.3898
625900.481
649.991406
14H4. 729249
22
2280.1038
38267.2869
585353.091
534.043969
13694.737843
23
2166.6568
36100.6291
547085.805
518.783263
13060.693874
24
2058.7522
34041.8768
510985.176
504.179717
12541. 9106U
25
1956.1232
32085.7537
476943.299
490.205032
12037.730894
26
1858.1969
30227.5568
444857.545
476.513725
11547.525862
27
1765.0771
28462.4797
414629.989
463.411996
11071.012137
28
1675.9483
26786.5314
386167.509
450.291315
10607.600141
29
1589.8276
25196.7038
359380.978
436.340564
10157.308826
30
1506.4141
23690.2897
334184.274
421.388563
9720.968262
31
1426.9810
22263.3088
310493.984
406.824926
9299.579699
32
1351.5955
20911.7133
288230.675
392.888431
8892.754773
33
1280.2905
19631.4228
267318.962
379.786043
8499.866342
34
1212.8440
18418.5788
247687.539
367.471769
8120.080299
35
1148.8323
17269.7465
229268.960
355.687775
7752.608530
36
1088.0845
16181 .6620
211999.214
344.411226
7396.920755
37
1030.2421
15151.4199
195817.552
333.424070
7052.509529
38
975.1758
14176.2442
180666.132
322.722295
6719.085459
39
922.7620
13253.4822
166489.888
312.301697
6396.363164
40
872.5382
12380.9441
153236.406
301.814046
6084.061467
41
824.1061
11556.8380
140855.461
290.955391
5782.247421
42
777.7549
10779.0831
129298.623
280.092013
6491.292030
43
733.5662
10045.5169
118519.540
269.395115
5211.200017
44
691.7409
9353.7761
108474.023
259.158849
4941.804902
45
652.1576
8701.6185
99120.247
249.363379
4682.646063
46
614.8326
8086.7859
90418.629
240.121747
4433.282674
47
579.6392
7507.1467
82331.843
231.404418
4193.160927
48
546.5786
6960.5681
74824.696
223.304271
3961.756509
49
515.7531
6444.8151
67864.128
216.015701
3738.45223S
50
486.7903
5958.0247
61419.313
209.262412
3522.436537
51
459.5775
5498.4473
55461.288
203.011819
3313.174125
Digitized by^^UUVlC
m
TABLE XIV.
Prtparatoiy TsbU for finding the Valnet of AnnniiiM, Awmnnciw, fte.
(Carlisle 4^ per Cant.)
Age.
D.
N.
S.
BL
R.
52
433.5015
5064.9458
49962.841
196.726250
.3110.162306
53
408.5280
4656.4178
44897.895
190.420308
2913.436056
54
384.6230
4271.7948
40241.478
184.107404
2723.015748
55
361.8415
3909.9533
35969.683
177.888669
2538.908344
56
340.0539
3569.8994
32059.730
171.682686
2361.019675
57
319.2276
3250.6718
28489.830
165.499888
2189.336989
58
299.0973
2951.5745
25239.159
159.116239
2023.837101
59
279.2893
2672.2852
22287.584
152.188017
1864.720862
60
259,7059
2412.5793
19615.299
144.631382
1712.532845
61
240.1996
2172.3797
17202.720
136.308646
1567.901463
62
221.6306
1950.7491
15030.340
123.083180
1431.592817
63
204.1530
1746.5961
13079.591
120.149450
1303.509637
64
187.8892
1558.7069
11332.995
112.676924
1183.360187
65
172.6475
1386.0593
9774.2880
105.526181
1070.683263
66
158.4249
1227.6345
8388.2286
98.738107
965.157082
67
145.1594
1082.4751
7160.5942
92.294729
866.418975
68
132.7426
949.7325
6078.1191
86.128817
774.124246
69
121.1260
828.6065
5128.3866
80.228422
687.995429
70
110.2178
718.3887
4299.7800
74.536206
607.767007
71
100.0245
618.3642
3581.3913
69.089109
533.230801
72
90.08433
528.2799
2963.0271
63.456211
464.141692
73
80.33205
447.9478
2434.7472
57.583161
400.685481
74
70.86768
377.0801
1986.7994
51.578076
343.102320
75
61.70111
315.3790
1609.7193
45.463220
291.524244
76
53.40410
261.9749
1294.3402
39.823183
246.061024
77
45.84216
216.1328
1032.3653
34.560948
206.237841
78
39.15527
176.9775
816.2325
29.848113
171.676893
79
33.39172
143.5858
639.2550
25.770678
141.828780
80
28.17018
115.4156
495.6693
21.987067
116.058102
81
23.67587
91.73973
380.2537
18.705824
94.071035
82
19.62466
72.11507
288.5139
15.674152
75.365211
83
16.13749
55.97758
216.3989
13.032059
59.691059
84
13.11256
42.86502
160.4213
10.702040
46.659U00
85
10.55541
32.30962
117.5562
8.709557
35.956960
86
8.330386
23.97923
85.24663
6.939066
27.247403
87
6.429461
17.54977
61.26741
5.396864
20.308337
88
4.822303
12.72747
f 43.71764
4.066573
14.911473
89
3.600217
9.127248
30.99017
3.052147
10.844900
90
2.720852
6.424396
21.86292
2.309814
7.792753
91
1.912524
4.511872
15.43853
1.635877
5.482939
92
1.307262
3.204610
10.92666
1.112972
3.847062
93
.9006973
2.303912
7.722046
.762701
3.734090
94
.6384528
1.665460
5.41S134
.539242
1.971389
95
.4582197
1.207240
3.752674
.386502
1.432147
96
.3361740
.8710663
2.545433
.284188
1.045645
97
.2517633
.6193030
1.674367
.214254
.761457
98
.1873836
.4319194
1.055064
.160716
.547803
99
.1408899
.2910295
.6231447
.122291
.386487
100
.1103097
.1807199
.3321151
.097778
.264196
101
.0821018
•0986181
.1513953
.074320
.166418
102
.0561188
.0424993
.0527772
.051872
.092098
103
.0322213
.0102779
.0102779
.030391
.040226
104
.0102779
.0000000
.009835
.009835
Digitized by^^UUVlC
rABLKXV.
9M
Pnpvatoiy Table hs finding the Values of Anpuitiei, Astttranoei, &ۥ
(Carlisle 5 per Gent)
A«e.
D.
N.
S.
M.
R.
0
10000.0000
120830.3190
1978788.651
3769.98954
30372.181932
J
8058.1952
112772.1238
1857958.332
2304.275259
26602.192392
2
7055.7823
105716.3415
1745186.208
1685.681154
24297.917133
3
6283.5547
99432.7868
1639469.867
1249.443166
22612.235979
4
5757.2719
03675.5149
1540037.080
1022.377285
21362.792813
5
5325.6273
88349.8376
1446361.565
864.888527
20340.415528
6
4981.7340
83368.1536
1358011.677
774.596464
19475.527001
7
4686.2327
78681.9209
1274643.524
716.320595
18700.930537
8
4423.8221
74258.0989
1195961.603
677.063912
17984.609942
9
4185.4457
70072.6532
1121703.504
649.345728
17307.546030
10
3965.8796
66196.7736
1051630.851
629.086591
16658.200302
11
3760.0725
62346.7011
985524.077
612.130892
16029.113711
12
3563.7595
58782.9416
923177.376
594.868932
15416.982819
13
3377.0864
55405.8552
864394.434
577.898649
14822.113887
14
3199.6055
52206.2497
808988.579
561.231407
14244.215238
15
3030.4077
49175.8420
756782.329
544.395808
13682.983331
16
2868.2362
46307.6058
707606.487
526.529459
13138.588023
17
2713.3291
43594.2767
661298.882
508.204998
12612.058564
18
2566.2555
41028.0212
617704.605
490.337610
12103.853566
19
2427.0364
38600.9848
576676.584
473.321050
11613.515956
20
2295.2569
36305.7278
538075.599
457.114802
11140.194906
21
2170.5244
34135.2034
501769.871
441.680280
10683.080104
22
2052.8085
32082.3949
467634.668
427.322585
10241.399824
23
1941.3817
30141.0132
435552.273
413.648590
9814.077239
24
1835.9121
28305.1011
405411.260
400.625738
9400.428649
25
1736.0850
26569.0161
377106.159
388.223022
8999.802911
26
1641.3209
24927.6952
350537.142
376.129671
8611.579889
27
1551.6453
23376.0499
325609.4-17
364.612193
8235.450218
28
1466.2782
21909.7717
302233.397
353.132979
7870.838025
29
1384.3081
20525.4636
280323.626
340.985663
7517.706046
30
1305.4316
19220.0320
259798.162
328.028526
7176.719383
31
1230.7076
17989.3244
240578.130
315.468036
6848.690857
32
1160.1402
16829.1842
222588.806
303.505664
6533.222821
33
1093.7025
15735.4816
205759.021
292.312802
6229.717^57
34
1031.1520
14704.3297
190024.140
281.843288
5937.404355
35
972.0785
13732.2612
175319.810
271.872322
5655.561067
36
f 16.2929
12815.9583
161587.559
262.376164
5383.688745
37
863.4515
11952.5068
148771.601
253.167770
5121.312581
38
813.4082
11139.0985
136819.094
244.241264
4868.144811
39
766.0240
10373.0746
125679.995
235.590682
46-23.903547
40
720.8818
9652.1928
115306.921
226.925895
4388.312865
41
677.6255
8974. 567i
105664.728
217.997309
4161.386970
42
636.4677
8338.0995
%680.161
209.107375
3943.389661
43
597.4477
7740.6518
88342.061
200.395363
3734.282286
44
560.7007
7179.9511
80601.410
192.098209
3533.8^6923
45
526.0986
6653.8525
73421.458
184.196157
3341.788714'
46
493.6265
6160.2260
66767.606
176.776389
3167.592557
47
463.1550
6697.0710
60607.380
169.810893
2980.816168
48
434.6585
5262.4125
54910.309
163.369372
2811.005275
49
408.1919
4854.2206
49647.896
157.600846
2647.635903
50
383.4348
4470.7858
44793.676
152.281418
2490.035057
51
360.2760
4110.5099
40322.890
147.381399
2337.753639
52
338.2160
3772.2939
36212.380
142.477425
2190.372240
--
.
Digit
zedbyVjUUVlC
300 TABLK XV.
Preparatory Table for finding the Values of Annuities, Aisurances, ftc.
(Carlisle 5 per Cent.)
Art.
D.
N.
S.
M.
R.
53
317.2140
3455.0798
32440.086
137.580984
2047.894815
54
297.*J301
3157.8498
28985.006
132.702479
1910.313831
55
278.2934
2879.5563
25827.157
127.919631
1777.611352
56
260.2910
2619.2653
22947.600
123.169319
1649.691721
57
243.1862
2376.0791
20328.335
118.459290
1526.522402
58
226.7660
2149.3131
17952.256
113.619411
1408.063112
59
210.7399
1938.5731
15802.943
108.391667
1294.443701
60
195.0299
1743.5432
13864.370
102.716902
1186.052034
61
179.5225
1564.0208
12120.827
96.496585
1083.335132
62
164.8554
1399.1654
10556.806
90.378240
986.838547
63
151.1319
1248.0334
9157.6404
84.604998
896.460307
64
138.4297
1109.6037
7909.6069
78.999522
811.955309
65
126.5945
983.0093
6800.0032
73.756212
732.955787
66
115.6125
867.3968
5816.9939
68.802532
659.199575
67
105.4274
761.9694
4949.5971
64.122788
590.397043
68
95.95014
666.0192
4187.6278
59.665889
526.274255
69
87.13644
578.8828
3521.6085
55.421223
466.608366
70
78.91168
499.9711
2942.7257
51.345819
411.187143
71
71.27263
428.6985
2442.7546
47.464482
359.8413-24
72
63.88407
364.8144
2014.0562
43.469865
312.376842
73
56.69689
308.1175
1649.2417
39.324775
268.906977
74
49.77894
258.3386
1341.1242
35.106679
229.582202
75
43.13377
215.2048
1082.7856
30.831930
194.475523
76
37.15574
178.0491
867.58083
26.907892
163.643593
n
31.74266
146.3064
689.53176
23.264142
136.735701
'78
26.98333
119.32308
543.22535
20.016354
113.471559
79
22.90187
96.42121
423.90227
17.219825
93.455205
80
19.22866
77.19255
327.48106
14.637172
76.235380
81
16.08393
61.10861
250.28852
12.408096
61.598208
82
13.26831
47.84031
189.17991
10.358372
49.190112
83
10.85866
36.98165
141.33960
8.580550
38.831740
84
8.781214
28.20043
104.35796
7.020183
30.251190
85
7.035090
21.16534
76.15752
5.692211
23.231007
86
5.525687
15.63966
54.99218
4.517814
17.538796
87
4.244462
11.39519
39.35253
3.499717
13.020982
88
3.168324
8.226869
27.95733
2.625696
9.521265
89
2.354133
5.872736
19.73047
1.962377
6.895569
90
1.758941
4.113795
13.8.5773
1.479288
4.933192
91
1.238691
2.875104
9.743934
1.042796
3.453904
92
.8426475
2.032457
6.868830
.705737
2.411108
93
.5778151
1.454642
4.836373
.481032
1.705371
94
.4076296
1.047012
3.381732
.338361
1.224339
95
.2911641
.7558478
2.334720
.241306
.885978
96
.2125961
.5432517
1.578872
.176603
.644672
97
.1584567
.3847950
1.035620
.132588
.468069
98
.1173753
.2674197
.6508254
.099052
.335481
99
.0878318
.1795879
.3834057
.075098
.2.16429
100
.0684404
.1111474
.2038179
.059889
.161331
101
.0506966
.0604509
.0926704
.045404
.101442
102
.0344875
.0259634
•0322196
.031609
.056038
103
.0197071
.0062562
•0062562
.018471
.024429
104
.0062562
•005958
.005958
TABLB XVI.
301
Preparatory Table for findinff the Values of Anmiitiefl, Assurances, &e,
(Carlisle 6 per Cent)
Age.
D.
N.
S.
M.
R.
0
10000.0000
104397.1220
1516505.181
3524.691199
22081.897273
1
7982.0755
96415.0465
1412108.059
2072.804399
18557.206074
2
6923.2823
89491.7642
1315693.012
1465.826827
16484.401675
3
6107.3906
83384.3735
1226201.248
1041.819091
15018.574848
4
5543.0714
77841.3021
1142816.874
823.201241
13976.755757
5
5079.1138
72762.1884
1064975.572
673.002349
13153.554516
6
4706.3166
68055.8718
992213.384
587.702123
12480.552167
7
4385.3866
63670.4852
924157.512
533.167440
11892.850044
8
4100.7673
59569.7180
860487.027
496.777522
11359.682604
9
3843.1967
55726.5213
800917.309
471.325888
10862.905082
10
3607.2303
52119.2910
745190.788
452.898860
10391.579194
U
3387.7706
48731.5204
693071.497
437.622022
9938.680334
12
3180.6039
45550.9165
644339.976
422.215972
9501.058312
13
2985.5669
42565.3496
598789.060
407.213123
9078.842340
14
2801.9766
39763.3730
556223.710
392.617191
8671.629217
15
2628.7699
37134.6031
'516460.337
378.012914
8279.012026
16
2464.6194
34669.9838
479325.734
362.660709
7900.999112
17
2309.5153
32360.4685
444655.750
347.063403
7538.338403.
18
2163.7232
30196.7452
412295.2S2
331.998620
7191.275000
19
2027.0363
28169.7089
382098.537
317.786561
6859.276380
20
1898.8908
262^0.8181
353928.828
304.378958
6541.489819
21
1778.7577
24492.0604
327658.010
291.730276
6237.110861
22
1666.4181
22S23.6423
303165.949
280.075062
5945.380585
23
1561.0971
21264.5452
280340.307
269.079577
5665.305523
24
1462.3600
19802.1852
259075.762
258.706478
5396.225946
25
1369.7989
18432.3863
239273.576
248.920535
5137.519468
26
1282.8113
17149.5750
220841.190
239.468704
4888.598933 .
27
1201.2825
15948.2925
203691.615
230.551882
4649.130229
28
1124.4820
14823.8104
187743.323
221.748526
4418.578347
29
1051.6043
13772.2061
172919.512
212.520689
4196.829821
30
982.3294
12789.8768
159147.306
202.770522
3984.309132
31
917.3633
11872.5135
146357.429
193.407996
3781.538610
32
856.6045
11015.9090
134484.916
184.576424
3588.130614
33
799.9310
10215.9780
123469.007
176.388996
3403.555190
34
747,066&
9468.9112
113253.029
168.803862
3227.166194
'35
697.6242
8771.2871
103784.118
161.648075
3058.362332
36
651.3853
8119.9018
95012. 83J
154.897333
2896.714257
37
608.0301
7511.8717
86892.929
148.412915
2741.816924
33
567.3866
6944.485]
79381.057
142.186300
2593.404009
39
529.2932
6415.1920
72436.572
136.209080
2451.217709
40
493.4026
5921.7894
66021.380
130.278526
2315.008629
41
459.4207
5462.3686
60099.591
124.225069
2184.730103
42
427.4454
5034.9-2;i3
54637.222
118.254678
2060.505034
43
397.4546
4637.4687
49602.299
112.458975
1942.250356
44
369.4896
4267.9791
44964.830
106.991330
1829.791381
45
343.4169
3924.5622
40696.851
101.833175
1722.800051
46
319.1806
3605.3816
36772.289
97.035528
16120.966876
47
296.6523
3308.7293
33166.907
92.574105
1523.931348
48
275.7738
3032.9556
29858.178
88.487212
1431.357243
49
256.5385
2776.4170
26825.222
84.861835
1342.870031
50
238.7059
2537.7111
24048.805
81.550245
1258.008196
51
222.1726
2315.5385
21511.094
78.528534
1176.457951
52
206.6011
2108.9374
19195.556
75.532914
1097.929417
Digitized by VjOOQ IC
302 TABLB XVI.
Preparatory Tabla for finding the Values of Annnitiei) Afltarancea, ftc
(Carliile 6 per Cent)
Age.
D.
N.
S.
M.
R.
53
191.9440
1916.9934
17086.618
72.570113
1022.396503
54
178.1551
1738.8383
15169.625
69.646013
949.826390
65
165.2311
1573.6072
13430.786
66.806294
880.180377
56
153.0846
1420.5226
11857.179
64.012500
813.374083
b7
141.6755
1278.8472
10436.657
61.268531
749.361583
58
130.8631
1147.9841
9157.809
58.475513
688.093052
59
120.4674
1027.5167
8009.825
55.487125
629.617539
60
110.4351
917.0816
6982.309
52.273805
574.130414
61
100.6951
816.3865
6065.227
48.784796
521.S56609
62
915.9590
724.7906
5248.841
45.385360
473.071813
63
83.17877
641.6118
4524.050
42.152892
427.686453
64
75.46905
566.1428
3882.438
39.151418
385.533561
65
68.36567
497.7771
3316.295
36.319838
346.382143
66
61.84597
435.9312
2818.518
33.669907
310.062305
67
55.86549
380.0657
2382.587
31.190133
276.392398
68
50.36386
329.7018
2002.521
28.850723
245.202265
69
45.30611
284.3957
1672.820
26.643733
216.351542
70
40.64262
243.7531
1388.424
24.544740
189.707809
71
36.36188
207.3912
1144.671
22.564558
165.163069
72
32.28494
175.1063
937.2796
20.545806
142.598511
73
28.38244
146.7238
762.1734
18.470777
122.052703
74
24.68424
122.0396
615.4496
16.379120
103.581926
75
21.18727
100.8523
498.4100
14.279367
87.202806
76
18.07870
82.77360
392,5577
12.370066
72.923439
77
15.29916
67.47444
a09.7841
10.613869
60.553373
78
12.88259
54.59185
242.3096
9.063285
49.939504
79
10.83084
43.76101
187.7178
7.740740
40.876219
80
9.007899
34.75311
143.9568
6.530865
33.135479
81
7.463638
27.28948
109.2037
5.496478
26.604614
82
6.098976
21.19050
81.91419
4.554291
21.108136
83
4.944259
16.24624
60.72369
3.744798
16.553845
84
3.960617
12.28562
44.47745
3.041021
12.809047
85
3.143124
9.142500
32.19182
2.447712
9.768026
86
2.445468
6.697032
23.04932
1.927967
7.320314
87
1.860721
4.836311
16.35229
1.481645
5.392347
88
1.375853
3.460458
11.51598
1.102099
3.910702
89
1.012645
2.447813
8.055520
.816768
2.808603
90
.749480
1.698333
5.607707
.610925
1.991835
91
.522824
1.175509
3.909374
.426692
1.380910
92
.352307
.823202
2.733865
.285769
.954218
93
.239303
.583898
1.910663
.192707
.668449
94
.167228
.416670
1.326765
.134177
.475742
95
.118322
.298349
.910095
.094736
.341565
96
.085579
.212770
.611746
.068690
.246829
97
.063183
.149587
.398976
.051139
.178139
98
.046361
.103226
.*249389
.037893
.127000
99
.034365
.068861
.146163
.028521
.089107
100
.026525
.042336
.077302
.022627
.060586
101
.019463
.022873
.034966
.017066
.037959
102
.013115
.009758
.012093
.011820
.020893
103
.007424
.002334
.002334
.006871
•009073
104
.002334
.002202
.002202
Digitized by VjUUVIC
TABLB XVlh
SOS
Being the pnpuaioiy Table for detenmning the Valoet of Awmitiei, ftc, on
Sin{^ Lives, accordiog to the Cariisle Rate of Mortality. (7 per Cent)
Ages.
D.
N.
8.
0
10000.00000
91758.33141
1193476.03436
1
7907.47664
83850.85477
1101717.70295
2
6794.47987
77056.37490
1017866.84818
3
5987.75078
71118.62412
940810.47328
4
5338.74068
65779.88344
869691.84916
5
4846.16706
60933.71638
803911.96572
6
4448.50065
56485.21573
742978.24934
7
4106.41178
52378.80395
686493.03361
8
3804.01147
48574.79248
634114.22966
9
3531.76177
45043.03071
685539.43718
10
3283.93643
41759.09429
540496.40647
11
3055.32179
38703.77250
498737.31218
12
2841.67654
35862.09596
460033.53968
13
2642.49361
33219.60235
424171.44372
14
2456.82222
30762.78013
390951.84137
15
2283.40993
28479.37020
360189.06124
16
2120.81732
26358.55288
331709.69104
17
1968.77613
24389.77675
305351. 13819
18
1827.25556
22562.52119
280961.36144
19
1695.82558
20866.69561
258398.84025
20
1573.77171
19292.92390
2.37532.14464
21
1460.42965
17832.49425
218239.22074
22
1355.40759
16477.08666
200406.72649
23
1257.87624
15219.21042
183929.63983
24
1167.30514
14051.90528
168710.42941
25
1083.20092
12968.70436
154658.52413
26
1004.93287
11963.77149
141689.81977
27
932.26963
11031.50186
129726.04828
28
864.51191
10166.98995
118694.54642
29
800.92694
9366.06301
108527.55647
30
741.17328
8624.88973
99161.49346
31
685.68727
7939.20246
90536.60373
32
634.28897
7304.91349
82597.40127
33
586.78828
6718.12521
75292.48778
34
542.88817
6175.23704
68574.36257
35
502.22068
5673.01636
62399.12553
36
464.55069
5208.46567
56726.10917
37
429.57822
4778.88746
51517.64350
38
397.11692
4381.77053
46738.75605
39
366.99293
4014.77760
42356.98552
40
338.91042
3675.86718
38342.20792
41
312.61955
3363.24763
34668 34074
42
288.14313
3075.10450
31303.09311
43
265.42223
2809.68227
28227.98861
44
244.44097
2565.24130
25418.30634
45
225.06896
2340.17234
22853.06504
46
207.22994
2132.94240
20512.89270
47
190.80331
1942.13909
18379.95030
48
175.71677
1766.42232
16437.81121
49
161.93283
1604.48949
14671.38889
50
149.26830
1455.22119
13066.89940
51
137.63119
1317.59000
11611.67821
Digitized byLjOOQlC
304
TABLE XVII.
BsiDg the propavatory Table for determininf^ the Values of Aimnitiefl« &&, on
Single Livesi according to the Carlisle Kate of Mortality. {7 per Cent.)
AgM.
D.
N.
S.
52
126.78892
1190.80108
10294.08821
53
116.69304
1074.10804
9103.28713
54
107.29781
966.81023
8029.17909
55
98.58402
868.22621
7062.36886
56
90.48332
777.74289
6194.14265
57
82.95712
694.78577
5416.39976
58
75.90989
618.87588
4721.61399
59
69.22653
549.64935
4102.73811
60
62.86841
486.78094
3553.08876
61
56.78789
429.99305
3066.30782
62
51.17355
378.81950
2636.31477
63
46.08668
332.78282
2257.49527
64
41.37926
291.40356
1924.71245
65
37.13416
254.26940
1633.30889
66
33.27891
220.99049
1379.03949
67
29.77991
191.21058
1158.04900
68
26.59630
164.61428
966.83842
69
23.70177
140.91251
802.22414
70
21.06337
119.84914
661.31163
71
18.66874
101.18040
541.46249
72
16.42066
84.75974
440.28209
73
14.30085
70.45889
355.52235
74
12.32123
58.13766
285.06346
75
10.47687
47.66079
226.92580
76
8.85617
38.80462
179.26501
77
7.42453
31.38009
140.46039
78
6.19336
25.18673
109.080301
79
5.15830
20.028431
83.893571
80
4.250018
15.778413
63.865140
81
3.488507
12.289906
48.086727
82
2.824020
9.465886
35.796821
83
2.267957
7.197929
26.330935
84
1.799774
5.398155
19.133006
85
1.414944
3.983211
13.734851
86
1.090588
2.892623
9.751640
87
.822060
2.070563
6.859017
88
.602165
1.468398
4.788454
89
.439059
1.029339
3.320056
90
.321920
.707419
2.290717
91
.222467
.4849516
1.5832973
92
.1483090
.3364426
1.0983457
93
.0999314
.2365112
.7619031
94
.069)808
.1673304
.52.53919
95
.0484911
.1188393
.3580615
96
.0347445
.0840948
.2392222
97
.0254124
.0586824
.1551274
98
.0814722
.0402102
.0964450
99
.0135643
.02664589
.05623479
100
.01037205
.01627384
.02958890
101
.00753942
.00873442
.01331506
102
.00503300
.00370144
.00458064
103
.00282222
.00087920
.00087920
Digitized by LjOOQ iC
TABLS XVIII.
309
A PrepantoTy Table for finding the Values of Annuitiei, 9lc.,\>j the Carlisle Table
of Mortality. (8 per €ent.)
Ag..
D.
N.
S.
0
10000.00000
81791.63708
961227.96771
1
7834.25929
73957.37779
879436.33063
2
6669.23867
67288.13912
805478.95284
3
5774.33571
61513.80341
738190.81372
4
5143.73888
56370.06453
676677.01031
6
4625.92401
51744.14052
620306.94578
6
4207.01243
47537.12809
563562.80526
7
3847.53570
43689.59239
521025.67717
8
3531.19739
40158.39500
477336.08478
9
3248.11655
36910.27845
437177.68978
10
2992.22994
33918.04851
400267.41133
11
2753.14566
31159.90285
366349.36282
12
2541.52806
28618.37479
335189.45997
13
2341.50036
26276.87443
306571.08518
14
2156.82069
24120.05374
280294.21075
15
1986.02277
22134.03097
256174.15701
16
1827.52622
20306.50475
234040.12604
17
1680.80259
18625.70216
213733.62129
18
1545.53800
17080.16416
195107.91913
19
1421.09007
15659.07409
178027.76497
20
1306.59860
14352.47549
162368.66088
21
1201.27132
13151. i04l7
148016.20539
22
1104.56276
12046.64141
134865.00122
23
1015.59001
11031.05140
122818.35981
24
933.73780
10097.31360
111787.30841
26
858.43922
9238.87438
101689.99481
26
789.03747
8449.83691
9LM51. 12043
27
725.20724
7724.62967
84001.28352
28
666.27205
7058.35762
76276.65335
29
611.55221
6446.80541
69218.29623
30
560.68689
5886.118.')2
62771.49082
31
513.90964
5372.20888
56885.37230
32
470.98588
4901.22300
51513.16342
33
431.68022
4469.54278
46611.94042
34
395.68644
4073.85634
42142.39764
35
362.65640
3711.19994
38068.54130
36
332.34664
3378.85130
34357.34136
37
304.48302
3074.36828
30978.49006
38
278.86835
2795.49993
27904.12178
39
255.32807
2540.17186
25108.62185
40
233.60696
2306.56490
22568.44999
41
213.48974
2093.07516
20261.88509
42
194.95270
1898.12246
18168.80993
43
177.91734
1720.20512
16270.68747
44
162.33606
1557.86906
14550.48235
45
148.08689
1409.78217
12992.61329
46
135.08700
1274.69517
11582.83112
47
123.32730
1151.36787
10308.13595
48
112.43311.
1038.9S476
9156.76809
49
102.65405
936.28071
8117.83332
50
93.74945
842.53126
7181.55261
51
85.64026
756.89100
6339.02135
Digitizediy^UUV
te
306
TABLE XVIII.
A Preparatory Table for finding the Values of Anniutie8>&c»y by the Carlisle Table
of Mortality. (8 per Gent.)
)
Age.
D.
N.
S.
52
78.16322
678.72778
5582.13035
53
71.23720
607.45458
' 4903.40257
54
64.92802
542.52656
4295.94799
55
59.10277
483.42379
3753.42143
56
53.74396
429.67983
3269.99764
67
48.81742
380.86241
2840.31781
58
44.25677
336.60564
2459.45540
59
39.98653
296.61911
2122.84976
60
35.97772
260.64139
1826.23065
61
32.19712
228.44427
1565.58926
62
28.74532
199.69895
1337.14499
63
25.62035
174.07860
1137.44604
64
22.81520
151.26340
963.36744
65
20.28500
130.97840
812.10404
66
18.01069
112.96771
681.12564
67
15.96780
96.99991
568.15793
68
14.12871
82.87120
471.15802
69
12.47449
70.39671
388.28682
70
10.98320
59.41351
317.89011
71
9.64442
49.76909
258.47660
72
8.40449
41.36460
208.70751
73
7.25177
34.11283
167.34291
74
6.19006
27.92277
133.23008
75
5.21474
22.70803
105.30731
76
4.36725
18.34078
82.59928
77
3.62736
14.71342
64.25850
78
2.99782
11.71560
49.54508
79
2.47370
9.241896
37.829482
80
2.019264
7.222632
28.587586
81
1.642110
6.580522
21.364954
82
1.317013
4.263509
15.784432
83
1.047892
3.215617
11.520923
84
.823875
2.391742
8.305306
85
.641712
1.750030
5.913564
86
.490029
1.260001
4.163534
87
.365954
.8940469
2.903534
88
.265582"
.6284649
2.009487
89
.191851'
.4366139
1.381022
90
.139365
.2972489
.9444077
91
.095418
.2018309
.6471588
92
.0631065
.1387244
.4453279
93
.0420714
.0966530
.3066035
94
.0288552
.0677978
.2099505
95
.0200385
.0477593
.1421527
96
.0142248
.0335345
.0943934
97
.0103079
.0232266
.0608589
98
.0074234
.0158032
.0376323
99
.0054006
.0104026
.0218291
100
.0040913
.0063113
.0114265
101
•0029464
.0033649
.0051152
102
.0019487
.0014162
.0017503
103
.0010821
.0003341
.0003341
Digitized by VjUU*ilC
TABLE XVIII.
807
A Preparatory fable for finding the Values of Annuities, ftc.| bj the Carlisle Table
of Mortality. (9 per Cent.)
Age.
D.
N.
S.
0
10000.0000
73759.0568
789839.1337
1
7762.3853
65996.6715
716080.0769
2
6547.4286
59449.2429
650083.4054
3
5616.8626
53832.3802
590634.1625
4
4957.5596
48874.8206
536801.7823
5
4417.4837
44457.3370
487926.9617
6
3980.6807
40476.6563
443469.6247
7
3607.1438
36869.5125
402992.9685
8
3280.1980
33589.3145
366123.4560
9
2989.5576
30599.7569
332534.1415
10
2728.7738
27870.9831
301934.3846
11
2492.2238
25378.7593
274063.4015
12
2275.4223
23103.3371
248684.6422
13
2077.1056
21026.2314
225581.3051
14
1895.7264
19130.5050
204556.0737
15
1729.5897
17400.9154
185424.5687
16
1576.9566
15823.9588
168023.6533
17
1437.0441
14386.9147
152199.6945
18
1309.2733
13077.6414
137812.7798
19
1192.8052
11884.8362
124735.1384
20
1086.6441
10798.1921
112850.3022
21
989.8822
9808.3099
102052.1101
28
901.8412
8906.4688
92243.8002
23
821.5904
8084.8784
83337.3314
24
748.4437
7336.4347
75252.4530
25
• 681.7749
6654.6598
67916.0183
26
620.9067
6033.7531
61261.3586
27
565.4420
5468.3111
55227.6055
28
514.7245
4953.5866
49759.2944
29
468.1166
4485.4700
44805.7079
30
425.2440
4060.2260
40320.2379
31
386.1906
3674.0354
36260.0118
32
350.6874
3323.3480
32585.9764
33
318.4723
3004.8758
29262.6284
34
289.2397
2715.6361
26257.7526
35
262.6633
2452.9728
23542. 1166
36
238.5038
2214.4690
21089.1438
37
216.5018
1997.9672
18874.6748
38
196.4694
1801.4978
16876.7076
39
178.2344
1623.2634
15075.2098
40
161.5757
1461.6876
13451.9465
41
146.3068
1315.3808
11990.2588
42
132.3775
1183.0034
10674.8780
43
119.7017
1063.3016
9491.8747
44
108.2167
955.0849
8428.5730
45
97.8122
857.2727
7473.4882
46
88.4071
768.8655
6616.2155
47
79.9058
688.9598
5847.3499
48
72.2375
616.7223
5158.3902
49
65.3494
551.3729
4541.6679
50
59.1332
492.2396
3990.2950
51
53.5227
438.7169
3498.0554
Digitize? b?G00gle
308
TABLE XVIII.
A Preparatory Table for finding the Valueaof Annuities, &c., by the Carliile TUik
of Mortality. {9 per Cent.)
Age.
D.
N.
S.
52
48.4016
.390.3153
3059.3384
53
43.7301
346.6862
2669.0231
54
39.4715
307.1137
2322.4379
56
35.6006
271.5131
2015.3242
56
32.0767
239.4374
1743.8111
67
28.8681
210.5693
1504.3737
58
25.9311
184.6382
1293.8046
59
23.2141
161.4241
1109.1663
60
20.6952
140.7289
947.7422
61
18.3506
122.3783
807.0133
62
16.2329
106.1464
684.6350
63
14.33J6
91.8099
678.4896
64
12.6488
79.1611
486.6797
65
11.1429
68.0182
407.5186
66
9.8028
68.2164
339.6004
67
8.6112
49.6043
281.2860
68
7.5495
42.0648
231.6807
69
6.6044
36.4504
189.6259
70
5.7615
29.6889
154.1765
71
5.0128
24.6761
124.4867
72
4.3283
20.3478
99.8106
73
3.7003
16.6475
79.4628
74
3.1296
13.6178
62.8163
75
2.6123
10.9065
49.2975
76
2.1677
8.7378
38.3920
77
1.7839
6.9539
29.6641
78
1.4608
5.4931
22.7002
79
1.1943
4.2987
17.20714
80
.96599
3.33276
12.90839
81
.77836
2.56440
9.57564
82
.61863
1.93686
7.02124
83
.48763
1.44823
5.08638
84
.37986
1.06837
3.63716
85
.29316
.77521
2.56877
86
.22182
.56339
1.79367
87
.16413
.38927
1.24017
88
.11802
.27125
.86091
89
.08447
.18677
.67966
90
.06080
.12597
.39289
91
.04125
.08473
.26692
92
.02703
.05770
•18219
93
.01785
.03984
.12449
94
.01213
.02771
.08466
95
.00836
.01936
.05694
96
.0U5S7
.01349
.03768
97
.00422
.00927
.02409
98
.00301
.00627
.01482
99
•00217
.00410
.00855
100
.00163
.00247
.00445
101
.00116
.00131
.00198
102
.00076
.00055
.00067
103
.00042
.00013
.00013
Digitized by VjOOQIC
TABLE XVIII.
309
A Preptratory Table for finding the VbIims of Annuities. &c^ by (he Carlisle Table
of Mortality. ( 10 per Gent.)
Age.
D.
N.
a
0
10000.0000
67162.7485
660369.1292
1
7691.8182
59470.9304
593206.3807
3
6428.9256 '
53042.0048
533735.4503
3
5465.0639
47576.9409
480693.4456
4
4779.7282
42797.2127
433116.5047
5
4220.4021
38576.8105
390319.2920
6
3768.4280
34808.3825
351742.4815
7
3383.7646
31424.6179
316934.0990
8
3049.0922
28375.5257
285509.4811
9
2753.6658
25621.8598
257133.9554
10
2490.6097
23131.2502
231512.0956
11
2254.0263
20877.2239
208380.8454
12
2039.2373
18837.9867
187503.6215
13
1844.5828
16993.4039
168665.6348
14
1668.2035
15325.2004
151672.ii309
15
1508.1699
13817.0305*
136347.0305
16
1362.5761
12454.4545
122530.0000
17
1230.3960
11224.0585
110U75.5456
18
1110.8079
10113.2506
98851.4871
19
1002.7945
9110.4561
88738.2365
20
905.2397
8205.2164
79627.7805
21
817.1346
7388.0818
71422.5641
22
737.6901
6650.3918
64034.4823
23
665.9369
5984.4549
57384.0906
24
601.1331
5383.3218
51399.6357
25
542.6082
4840.7136
46016.3138
26
489.6722 '
4351.0414
41175.6002
27
441.8766
3909.1649
36824.5588
28
398.5856
3510.5793
32915.3939
29
359.1986
3151.3807
29404.8146
30
323.3348
2828.0459
26253.4339
31
290.9711
2537.0748
23425.3880
32
261.8196
2275.2552
20888. 313i
33
235.6066
2039.6486
18613.0581
34
212.0350
1827.6136
16573.4095
35
190.8020
1636.8117
14745.7958
36
171.6771
1465.1346
13108.9841
37
154.4233
1310.7114
11643.849.)
38
138.8609
1171.8505
10333.1382
39
124.8.75
1047.0230
9161.2877
40
112.1318
934.8912
8114.2647
41
100.6123
834.2790
7179.3735
42
90.2057
744.0732
6345.0945
43
80.8266
063.2466
5601.0213
44
72.4072
590.8394
4937.7747
4.)
64.8507
525.9387
4346.9353
46
58.0822
467.9065
3820.9466
47
52.0196
415.8870
3353.0401
48
4G.6000
369.2870
2937.1532
49
41.7733
3.'r.5136
2567.8663
50
37.4561
290.0376
2240.3526
51
33.5941
256.4635
1950.29.')0
DlyliLbdUy V_iC
Google
910
AlVtpantory Table for fii
TABLE XVIII.
Bding the Values of Aniraitief , &e., by the Cariule Table
of Mortality, (10 per Cent.)
Age.
D.
N.
S.
52
30.1036
226.3599
1693.8315
b3
26.9509
199.4090
1467.4716
54
24.1052
175.3039
1268.0626
55
21.5435
153.7604
1092.7587
56
19.2340
134.5264
938.9984
57
17.1532
117.3731
804.4720
58
15.2680
102.1051
687.0989
59
13.5440
88.5611
584.9938
60
11.9646
76.5965
496.4326
61
10.5127
66.0839
419.8361
62
9.2149
56.8690
353.7522
63
8.0639
48.8051
296.8832
64
7.0504
41.7547
248.0781
65
6.1545
35.6002
206.3234
66
5.3651
30.2351
170.7232
67
4.6701
25.5650
140.4881
68
4.0571
21.5079
114.9231
69
3.5170
17.9909
93.4152
70
3.0402
14.9507
75.4243
71
2.6211
12.3296
60.4736
72
2.2426
10.0870
48.1440
73
1.8998
8.1872
38.0569
74
1.5922
6.5950
29.8697
75
1.3169
5.2781
23.2747
76
1.0829
4.1952
17.9966
77
.8830
3.3122
13.8014
78
.7165
2.59567
10.48920
79
.5805
2.01517
7.89353
80
.46525
1.54992
5.87836
81 .
.37147
1.17845
4.32844
82
.29251
.88595
3.14999
83
.22850
.65744
2.26404
84
.17639
.48105
1.60660
85
.13489
.34616
1.12555
86
.10113
.24502
.77939
87
.07415
.17087
.53437
88
.05284
.11804
.36350
89
.03747
.08056
.24546
90
.02673
.05383
.16490
91
.01797
.03587
.11107
92
.01167
.02420
.07520'
93
.00764
.01657
.05100
94
.00514
.01142
.03444
95
.00351
.00792
.02301
96
.00244
.00547
.01510
97
.00174
.00374
.00962
98
.00123
.00251
.00589
99
.00088
.00163
.00338
100
.00065
.00098
.00175
101
.00046
.00051
.00078
102
.00030
.00021
.00026
103
.00016
.00005
.00005
Digitized by ^
TABLE XIX. SU
VtloM of Annmtiefl on Single Lmt according to the Carlisle' Table of Mertality.
Age.
3 per Mnt.
di per orat.
4 per cent
4i per cent
5 per eent .
0
17.320
15.67193
14.28164
13.09841
12.083
1
20.085
18.17084
16.55455
15.17757
13.995
2
21.501
19.45565
17.72616
16.25108
14.983
3
22.683
20.53459
18.71508
17.16139
15.824
4
23.285
21.09152
19.23133
17.64095
16.271
5
23.693
21.47527
19.59203
17.97995
16.590
6
23.846
21.62976
19.74502
18.12959
16.735
7
23.867
21.66519
19.79019
18.18101
16.790
8
23.801
21.62246
19.76443
18.16776
16.786
9
23.677
21.52745
19.69114
18.11104
16.74^
10
23.512
21.39473
19.58339
18.02272
16.669
11
23.327
21.24340
19.45857
17.91867
16.581
12
23.143
21.09342
19.33493
17.81571
16.494
13
22.957
20.94140
19.20937
17.71097
16.406
14
22.769
20.78725
19.08182
17.60437
16.316
15
22.582
20.63433
18.95534
17.49877
16.227
16
22.404
20.48956
18.83636
17.40012
16.144
17
22.232
20.34992
18.72111
17.30593
16.066
18
22.058
20.20881
18.60656
17.21061
15.987
19
21.879
20.06277
18.48649
17.11118
15.904
'^20
21.694
19.91158
18.36170
17.00744
15.817
21
21.504
19.75503
18.23196
16.89916
15.726
22
21.304
19.58946
18.09386
16.78313
15.628
23
21.098
19.41790
17.95016
16.66190
15.525
24
20.885
19.24009
17.80058
16.53519
15.417
25
20.665
19.05575
17.64486
16.40273
15.303
26
20.442
18.86802
17.48586
16.26715
15.187
27
20.212
18.67335
17.32023
16.12535
15.065
28
19.981
18.47823
17.15412
15.98291
14.942
29
19.761
18.29279
16.99683
15.84870
14.827
30
19.556
18.12096
16.85215
15.72628
14.723
31
19.348
17.94660
16.70511
15.60169
14.617
32
19.134
17.76626
16.55246
15.47187
14.506
33
18.910
17.57627
16.39072
15.33357
14.387
34
18.675
17.37613
16.21943
15.18627
14.260
35
' '18.433
17.16877
16.04123
15.03243
14.127
36
18.183
16.95384
15.85677
14.87169
13.987
37
17.928
16.73436
15.66586
14.70666
13.843
38
17.669
16.51013
15.47129
14.53712
13.695
39
17.405
16.28096
15.27184
14.36284
13.542
40
17.143
16.05334
15.07363
14.18957
13.390
41
16.890
15,83413
14.88314
14.02348
13.245
42
16.640
15.61723
14.69466
13.85923
13.101
43
16.389
15.39954
14.50529
13.69409
12.957
44
16.130
15.17437
14.30874
13.52208
12.806
45
15.863
14.94138
14.10460
13.34281
12.648
46
15.585
14.69677
13.88928
13.1528;i
12.480
47
15.294
14.43992
13.66208
12.9M41
12.301
48
14.986
14.16680
13.41914
12.73480
12.107
49
14.654
13.86985
13.15312
12.49593
11.892
50
14.303
13.55445
12.86902
12.23941
11.660
51
13.932
13.21966
12.56581
11.96414
11.410
-L
Digitized by VjicJiJV
312 TABLV XIX.
ValiiM of Annuities oa Single lives according to the Caiiisle Table of Mortility.
Aip^
3 per cent.
Bi per cent.
4 per cent.
4i per cent.
Sporoem
52
13.558
12.88072
12.25793
11.68380
11.154
53
13.180
12.53734
11.94503
11.39804
10.892
51
12.798
12.18913
11.62673
11.10645
10.624
55
12.408
11.83257
11.29961
10.80571
10.347
56
12.014
11.47021
10.96607
10.49804
10.063
57
11.614
11.10160
10.62559
10.18293
9.771
58
11.218
10.73539
10.28647
9.86828
9.478
59
10.841
10.38676
9.96331
9.56817
9.199
60
10.491
10.06309
9.66333
9.28966
8.940
61
10.180
9.77619
9.39809
9.04406
8.712
62
9.875
9.49388
9.13676
8.80180
8.487
63
9.567
9.20803
8.87150
8.55533
8.258
64
9.246
8.90934
8.59330
8.29589
8.016
65
8.917
8.60309
8.30719
8.02826
7.765
66
8.578
8.28572
8.00966
7.74900
7.503
67
8.228
7.95638
7.69980
7.45715
7.227
68
7.869
7.61735
7.37976
7.15469
6.941
69
7.499
7.26802
7.04881
6.84087
6.643
70
7.123
6.91089
6.70936
6.51790
6.336
71
6.737
6.54230
6.35773
6.18213
6.015
72
6.373
6.19468
6.02548
5.86428
5.711
73
6.044
5.88024
5.72465
5.57620
5.435
74
5.752
5.60175
5.45812
5.32090
5.190
75
5.512
5.37241
5.23901
5.11140
4.989
76
5.277
5.14769
5.02399
4.90552
4.792
77
5.059
4.93944
4.82473
4.71472
4.609
78
4.838
4.72765
4.62166
4.51989
4.422
79
4.592
4.49061
4.39345
4.30004
4.210
80
4.365
4.27204
4.18289
4.09708
4.015
81
4.119
4.03434
3.95309
3.87482
3.799
82
3.898
3.82060
3.74634
3.67472
3.606
83
3.672
3.60173
3.53409
3.46879
3. 405
84
3.454
3.39020
3.32856
3.26900
3.211
85
3.229
3.17120
3.11515
3.06096
3.009
86
3.033
2.97977
2.928dl
2.87853
2.830
87
2.873
2.82383
2.77593
2.72959
2.685
88
2.776
2.7J891
2.68337
2.63929
2.597
89
2.665
2.62025
2.57704
2.63519
2.495
90
2.499
2.45680
2.41621
2.37689
2.339
91
2.481
2.43882
2.39835
2.35912
2.321
92
2.577
2.53384
2.49199
2.45139
2.412
93
2.687
2.64240
2.59955
2.55792
2.518
94
2.736
2.69209
2.64976
2.60859
2.569
95
2.757
2.71500
2.67433
2.63463
2.596
96
2.704
2.66537
2.62779
2.59112
2.555
97
2.559
2.52495
2.49204
2.45986
2.428
98
2.388
2.35999
2.33222
2.30500
2.278
v99
2.131
2.10875
2.08700
2.06565
2.045
100
1.683
1.66757
1.65282
1.63829
1.624
101
1.228
1.21906
1.21005
1.20117
1.192
102
0.771
0.76641
0.76183
0.75731
0.753
103
0.324
0.32206
0.32051
0.31898
0.317
Digitized by VjUUVJIC
TABLE XIX. 313
VaIum of A]maiii«s ou Single Lives according to the Carlisle Table of Morialiiy.
Age.
6perc«Bt.
7 per cent.
8 per cent.
9peroifiit
10 per cent.
0
10.439
9.177
8.178
6.716
1
12.078
10.605
9.439
8.502
7.732
2
12.925
11.342
10.088
9.080
8.251
3
13.652
11.978
10.651
9.584
8.705
4
14.042
12.322
10.957
9.858
8.954
5
14.325
12.574
11.184
10.064
9.141 *
6
14.460
12.698
11.298
10.168
9.237
7
14.518
12.756
11.354
10.221
9.287
8
14.526
12.770
11.371
10.240
9.306
9
14.500
12.754
11.362
10.236
9.304
10
14.448
12.717
'11.334
10.214
9.286
11
14.384
12.669
11.296
10.183
9.261
12
14.321
12.621
11.259
10.153
9.238
13
14.257
12.572
11.2-21
10.123
9.213
14
14.191
12.522
11.182
10.091
9.187
15
14.126
12.473
11.144
10.061
9.161
16
14.067
12.429
11.111
10.034
9.140
17
14.012
12.389
11.081
10.011
9.122
18
13.956
12.348
11.051
9.988
9.104
19
13.897
12.305
11.019
9.963
9.085
20
13.835
12.259
10.985
9.937
9.064
21
13.769
12.210
10.948
9.909
9.041
22
13.697
12.156
10.906
9.876
9.015
23
13.621
12.098
10.861
9.841
8.987
24
13.541
12.037
10.813
9.802
8.955
25
13.456
11.972
10.762
9.761
8.921
26
13.368
11.904
10.709
9.718
8.886
27
13.275
11.832
10.652
9.671
8.847
28
13.182
11.759
10.594
9.624
8.808
29
13.096
11.693
10.542
9.582
8.773
30
13.020
11.636
10.498
9.548
8,747
31
12.942
J1.578
10.454
9.514
8.719
32
12.860
11.516
10.407
9.476
8.690
33
12.771
11.448
10.305
9.435
8.657
34
12.675
11.374
10.297
9.389
8.619
35
12.573
11.295
10.235
9.339
8.578
36
12.465
11.211
10.108
9.285
8.534
37
12.354
11.124
10.098
9.228
8.488
38
12.239
11.033
10.026
9.169
8.439
39
12.120
10.939
9.950
9.107
8.388
40
12.002
10.845
9.875
9.046
8.337
41
11.890
10.757
9.805
8.991
8.292
42
11.779
10.671
9.737
8.937
8.249
43
11.668
10.585
9.669
8.883
8.206
44
11.551
10.494
9.597
8.826
8.160
45
11.428
10.397
9.520
8.764
8.111 '
46
11.296
10.292
9.436
8.697
8.056
47
11.154
10.178
9.314
8.622
7.995
48
10.998
10.052
9.241
8.537
7.925
49
10.823
9.908
9.121
8.437
7.840
50
10.631
9.749
8.987
8.324
7.744
51
10.422
9.573
8.838
8.197
7.634
Digitize
dbyGoO^I
.314 TABLE XIX.
Valoes of Aimuitiet on Single Lives according to the Carlisle TaUe of Mortality.
A«t.
6 per eent.
7 per cent.
8 per cent
9perenit
lOptreeat.
52
10.208
9.392
8.684
8.064
7.519
53
9.988
9.205
8.523
7.926
7.399
54
9.761
9.011
8.356
7.781
7.272
55
9.524
8.807
8.179
7.627
7.137
56
9.280
8.595
7.995
7.465
6,994
57
9.027
8.375
7.802
7.294
6.843
58
8.772
8.153
7.606
7.120
6.687
59
8.529
7.940
7.418
6.954
6.539
60
8.304
7.743
7.245
6.800
6.402
61
8.108
7.572
7.095
6.669
6.285
62
7.913
7.403
6.947
6.539
6.171
63
7.714
7.229
6.795
6.404
6.052
64
7.502
7.042
6.630
6.258
5.922
65
7.281
6.847
6.457
6.104
5.784
66
7.049
6.641
6.272
5.938
5.633
67
6.803
6.421
6.075
5.760
5.474
68
6.546
6.189
5.866
5.570
5.301
69
6.277
5.945
5.643
5.368
5.115
70
5.998
5.690
5.410
5,153
4.918
71
5.704
5.420
5.160
4.923
4.704
72
5.424
5.162
4.922
4.701
4.498
73
5.170
4.927
4.704
4.499
4.309
74
4.944
4.719
4.511
4.319
4.142
75
4.760
4.549
4.355
4.175
4.008
76
4.579
4.382
4.200
4.031
3.874
17
4.410
4.227
4.056
3.898
3.751
78
4.238
4.067
3.908
3.760
3.623
79
4.040
3.883
3.736
3.599
3.471
80
3.858
3.713
3.577
3.450
3.331
81
3.656
3.523
3.398
3.282
3.172
82
3.474
3.352
3.237
3.130
3.029
83
3.286
3.174
3.069
2.970
2.877
84
3.102
2.999
2.903
2.813
2.728
85
2.909
2.815
2.727
2.644
2.567
86
2.739
2.652
2.571
2.495
2.423
87
2.599
2.519
2.443
2.372
2.304
88
2.515
2.439
2.366
2.299
2.234
89
2.417
2.344
2.276
2.211
2.150
90
2.266
2.198
2.133
2.072
2.015
91
2.248
2.180
2.115
2.054
1.997
92
2.337
2.266
2.198
2.135
2.075
93
2.440
2.367
2.297
2.232
2.170
94
2.492
2.419
2.350
2.284
2.221
95
2.522
2.451
2.383
2.319
2.263
96
2.486
2.420
2.358
2.298
2.239
97
98
99
2.368
2.309
2.253
2.199
2.150
2.227
2.177
2.129
2.083
2.039
2.004
1.964
1.926
1.889
1.856
lOU
1.596
1.569
1.543
1.517
1.493
101
1.175
1.159
1.142
1.127
1.112
102
103
0.744
0.735
0.727
.719
.713
0.314
0.312
0.309
.305
.304
*
Digitized by
^oogle
TABLE XXI.
315
Value of £1 per Annmii during the joint Continuance of Two lives.
(Carlisle 3 per Cent.)
Older Age 0 Years.
Older Age One Year.
Ag«.
Value.
Ag«.
Valoe.
0
10.480
1
0
14.079
12.144
Older Age Two Years.
Older Age Three Years.
Age.
Value.
Age.
Value.
2
1
0
16.155
15.079
13.002
3
2
1
0
18.030
17.066
15.927
13.730
Older Age Four Years.
Older Age Five Years.
Age.
Valoe.
Age,
Value.
4
3
2
1
0
19.066
18.540
17.547
16.374
14.113
5
4
3
2,
1
0
19.815
19.436
18.900
17.886
16.689
14.384
Older Age
Six Years.
Older Age Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Aire.
Value.
6
5
4
3
20.156
19.985
19.601
19.058
2
1
0
18.036
16.828
14.503
7
6
5
4
20.281
20.218
20.044
19.658
3
2
1
0
19.113
18.087
16.874
14.042
Digitized by LjOOQ IC
316
TABLE XXI.
Value of £1 per Annum daring the joint Continunnce of Two Livei.
(Carlisle 3 per Cent.)
Older Age Eight Years.
Older Age Nine Years.
Age.
Vnlae.
Age.
Value.
Age.
Value.
Ar.
Value.
8
7
6
5
4
20.261
20.270
20.206
20.032
19.645
1
1
0
19.100
18.072
16.860
14.530
9
8
7
6
5
20.146
20.203
20.211
20.146
19.970
4
3
2
1
0
19.584
19.038
18.014
16<80€
14.483
Older Age Ten Years.
Older Age Eleven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
10
9
8
7
6
5
19.963
20.054
20.109
20.115
20.049
19.874
4
3
2
1
0
19.487
18.944
17.924
16.722
14.418
11
10
9
8
7
6
19.748
19.855
19.944
19.997
20.002
19.935
5
4
3
2
1
0
19.758
19.373
18.832
17.818
16.623
14«325
Older Age Twelve Years.
Older Age Thirteen Years.
Age.
Value.
Age.
Value.
Age,
Value.
Age.
Value.
12
11
10
9
8
7
6
19.538
19.642
19.747
19.834
19.885
19.889
19.820
5
4
3
2
I
0
19.644
19.260
18.721
17.713
16.524
14.240
13
12
11
10
9
6
7
19.327
19.432
19.534
19.636
19.721
19.771
19.772
6
5
4
3
8
1
Q
19.703
19.527
19.144
18.609
17.605
16.423
1«.153
Digitized by LjOOQ IC
TABLE XXI*
317
Value of £1 per AnDum durini; the joint Contmuance of Two Lives.
(Garlitle 3 per Cent.)
Older Agd Fourteen Years.
Older Age Fifteen Years.
A««.
Valae.
A««.
Value.
Age.
Value.
Age.
Value.
14
13
12
11
10
9
8
7
19.115
19.220
19.322
19.422
19.523
19.606
19.653
19.654
6
5
4
3
2
1
0
19.5S4
19.407
19.027
18.493
17.494
16.319
14.065
15
14
13
12
11
10
9
8
18.908
19.010
19.113
19.213
19.311
19.410
19.490
19.537
7
6
5
4
3
2
1
0
19.536
19.465
19.289
18.909
18.377
17.384
16.217
13.975
Older Age Sixteen Yean.
Older Age Seventeen Years.
Age.
Valae.
Age.
Value.
Age.
Value.
Age.
Value.
16
18.719
7
19.425
17
18.542
8
19.321
15
18.812
6
19.354
16
18.629
7
19.319
14
18.912
5
19.177
15
18.720
6
19.246
13
19.013
4
18.797
14
18.819
5
19.068
12
19.111
3
18.268
13
18.917
4
18.690
11
19.208
2
17.281
12
19.014
3
18.164
10
19.303
1
16.119
11
19.107
2
17.180
9
19.368
0
13.894
10
19.201
1
16.027
8
19.427
9
19.278
0
13.813
Older Age Eighteen
Years.
Older Age Nineteen Years.
Age.
Value.
Age.
ValM.
Age.
Value.
Age.
Value.
18
18.365
8
19.215
19
18.182
9
19.062
17
18.452
7
19.210
18
18.272
8
19.102
16
16.637
6
19.136
17
18.357
7
19.095
15
18.626
5
18.958
16
18.440
6
19.020
14
18.723
4
18.582
15
18.527
6
18.843
13
18.620
3
18.056
14
18.622
4
18.467
12
16.913
2
17.080
13
18.716
3
17.946
11
19 005
1
15,932
12
18.808
2
16.974
10
19.097
0
13.731
11
18.897
I
15.833
9
19.172
10
18.987
0
13.647
Digitized by LjOOQ IC
318
TABLE XXI.
Value of £1 per Annum daring the joint Continuance of Two Liveg
(Carliile 3 per Cent.)
Older Age Twenty
Yeare-
Ago.
Value.
Age,
Valae.
Age.
Value.
Age.
Value.
20
19
18
17
16
15
17.993
18.086
18.174
18.257
18.338
18.423
14
13
12
11
10
9
18.514
18.607
18.696
18.784
18.873
18.945
8
7
6
5
4
3
18.982
18.975
18.900
18.722
18.349
17.829
2
1
0
16.863
13.730
13.559
Older Age Twenly-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
21
20
19
18
17
16
17.797
17.893
17.9i4
19.069
18.150
18.230
15
14
13
12
11
10
18.312
18.402
18.492
18.579
18.666
18.752
9
8
7
6
5
4
18.821
18.858
18.849
18.773
18.596
18.224
3
2
1
0
17.707
16.748
15.623
13.465
Older Age Twenty-Two Yean.
Age.
Value.
Age.
Value.
Ag«.
Value.
Age.
Value.
22
21
20
19
18
17
17.589
17.691
17.785
17.874
17.957
18.036
16
15
14
13
12
11
18.112
18.192
18.280
18.367
18.454
18.538
10
9
8
7
6
5
18.621
18.689
18.724
18.714
18.638
18.461
4
3
2
1
0
18.090
17.577
16.625
15.507
13.366
Older Age Twenty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
23
22
21
20
19
18
17
17.372
17.478
17.579
17.670
17.756
17.838
17.913
16
15
14
13
12
11
10
17.988
18.066
18.151
18.238
18.320
18.402
18.484
9
8
7
6
5
4
3
18.550
18.583
18.S73
18.496
18.319
17.9.51
17.441
2
1
0
16.494
15.386
13.263
Digitized by VjOOQ IC
TABLE XXI.
319
Value of £1 per Annan doringp the joint Continuance of Two Lives.
(Carlisle 3 per Cent)
Older Age Twenty-Four Yean.
Af.
Value.
Age.
Value.
A»e.
Value.
Age.
Value.
24
23
22
21
20
19
18
17.148
17.258
17.362
17.460
17.549
17.633
17.711
17
16
15
14
13
12
11
17.785
17.857
17.933
18.017
18.099
18.181
18.260
10
9
8
7
6
5
4
18.340
18.404
18.436
18.424
18.347
18.171
17.805
3
2
1
0
17.298
16.359
15.260
13.155
Older Age Twenty-Five Years.
Age.
Valae.
Age.
Value.
Age.
Value.
Age.
Value.
25.
24
23
22
21
20
19
16.916
17.030
17.138
17.239
17.334
17.421
17.501
18
17
16
15
14
13
12
17.577
17.649
17.719
. 17.794
17.873
17.955
18.034
11
10
9
8
7
6
5
18.111
18.189
18.252
18.282
18.269
18.191
18.016
4
3
2
1
0
17.652
17.149
16.218
15.129
13.042
Older Age Twenty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
26
25
24
23
22
21
20
16.691
16.796
16.908
17.013
17.111
17.204
17.287
19
18
17
16
1-3
14
13
17.3C6
17.440
17.509
17.578
17.648
17.727
17.806
12
11
10
9
8
7
6
17.883
17.958
18.035
18.095
18.124
18.110
18.032
5
4
3
2
1
0
17.857
17.495
16.996
16.074
14.994
12.927
OWer Age Twenty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
27
26
25
24
23
22
21
16.437
16.557
16.671)
16.779
16.881
16.977
17.066
20
19
•18
17
16
15
14
17. M7
17.223
17.294
17.363
17.427
17.496
17.572
13
12
11
10
9
8
7
17.650
17.724
17.798
17.872
17.931
17.958
17.944
6
5
4
3
2
1
0
17.865
17.690
17.331
16.837
15 923
14.853
12.806
Digitized by VjOOQ IC
820
TABLK XXI.
Yalua of £1 per ▲nnnm during tb« joint Continuance of Two livei,
(CerUftle 3 per Cent*)
Older Age Twenty-Eight Years.
Age.
Valw.
A««.
Y«lM.
A«t.
Vslne.
▲l«.
ValMb
28
16.196
20
17.009
12
17.565
4
17.167
27
16.315
19
17.079
11
17.636
3
16.676
26
16.432
16
17.149
10
17.708
2
15.771
25
16.642
17
17.212
9
17.765
1
14.712
24
16.647
16
17.275
8
17.791
0
12.685
23
16.747
15
17.3J3
7
17.775
22
16.639
14
17.417
6
17.697
21
16.926
13
17.491
5
17.523
Older Age Twenty-Nine Years.
Ate.
Voloe.
A«e.
Value.
Age.
Veloe.
Age,
Value.
29
15.976
21
16.794
13
17.342
5
17.364
28
16.084
20
16.871
12
17.418
4
17.011
27
16.200
19
16.942
11
17.483
S
16.524
26
16.314
18
17.008
10
17.553
9
15.626
25
16.421
17
17.071
9
17.609
1
14.578
24
16.524
16
17.132
8
17.633
0
19.570
83
16.620
15
17.197
7
17.616
22
16.710
14
17.269
6,
17.537
Older Age Thirty Years.
Aje.
Value.
Age.
Yaloe.
Age.
Valne.
Age.
Valne.
30
15.784
22
16.592
14
>7.134
6
17.390
29
15.878
21
16.674
13
17.205
5
17.218
28
15.984
20
16.748
12
17.274
4
16.863
27
16.096
19
16.817
11
17.342
3
16.381
26
16.207
18
16.881
10
17.441
2
15.494
25
16.311
17
16.941
9
17.464
L
14.454
24
16.411
16
17.000
8
17.487
0
12.464
23
16.505
15
17.053
7
17.470
Older Age Thirty-One Years.
Ag«.
Value.
Age.
Valu*.
Age.
Value.
Age.
Value.
31
15.591
23
16.386
15
16.927
7
17.320
30
15.685
22
16.471
14
16.995
6
17.241
29
15.777
21
16.550
13
17.064
5
17.069
28
15.879
20
16.621
12
17.131
4
16.720
27
15.9S9
19
16.688
n
17.197
3
16.240
26
16.097
18
16.750
10
17.264
2
15.358
95
16.198
17
16.809
9
17.316
1
14.328
94
16.293
16
16.865
8
17.338
0
12.356
Digitized by LjOOQ IC
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carliile 3 per Cent)
Older Age Thirty-Two Years.
Ar«.
Value.
A<e.
Value.
Aje.
Valu«.
Age.
Value.
32
15.392
23
16.261
14
16.850
5
16.913
31
15.489
22
16.344
13
16.917
4
16.567
30
16.581
21
16.420
12
16.983
3
16.091
29
15.669
20
16.489
11
17.047
2
15.217
28
15.769
19
16.553
10
17.112
1
14.197
27
16.875
18
16.613
9
17.162
0
12.244
26
15.980
17
16.669
8
17.183
25
16.078
16
16.724
7
17.164
24
16.172
15
16.784
6
17.084
Older Age Thirty-Three Years.
Aife.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
33
15.180
24
16.040
15
16.630
6
16.91S
32
15.283
23
16.126
14
16.694
5
16.748
31
15.378
22
16.205
13
16.760
4
16.404
30
15.466
21
16.279
12
16.824
3
15.933
29
15.552
20
16.346
11
16.886
2
15.068
28
15.648
19
16.408
10
16.949
1
14.038
•J7
15.751
18
16.4i&6
9
16.998
0
12.1J5
2C
15.853
17
16.320
8
17.018
25
15.948
16
16.573
7
16.998
Older Age Thirty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
34
14.954
25
15.808
16
16.411
7
16.821
33
15.064
24
15.897
25
16.466
6
16.741
32
15.165
23
15.979
14
16.529
5
16.573
31
15.236
22
16.056
13
16.592
4
16.231
30
15.342
21
16.128
12
16.654
3
15.766
29
16.424
20
16.192
11
16.715
2
14.909
28
15.517
19
16.232
10
16.776
1
13.910
27
15.617
18
16.308
9
16.824
0
11.999
26
15.716
17
16.360
8
16.842
1
Digitized by VjOOQ iC
TABLE XXL
Value of £1 per Annum during the joint Continuance of Two Lifet.
(Garliile 3 per Cent)
Older Age Thirty-Five Years.
Age.
Value.
Age.
ValM.
Age.
Value.
Age.
Value.
35
14.720
26
15.570
17
16.192
8
16.659
34
14.835
25
15.660
16
16.241
7
16.637
33
14.942
24
15.745
15
16.295
6
16.557
32
15,039
23
15.825
14
16.355
5
16.389
31
15.127
22
15.900
13
16.417
4
16.052
30
15.209
21
15.969
12
16.477
3
15.591
29
15>.288
20
16.031
11
16.536
2
14.744
28
15.378
19
16.088
10
16.596
1
13.757
27
15.475
18
16.142
9
16.642
0
11.867
Older Age Thirty-Six YeaiB.
Age.
Value.
Age.
Valoo.
Age.
Value.
Age.
Valae.
36
14.477
26
15.417
16
16.063
6
16.365
35
14.596
25
15.503
15
16.115
5
16.199
34
14.707
24
15.586
14
16.173
4
15.865
33
14.811
23
15.663
13
16.233
3
15.408
32
14.905
22
15.735
12
16.292
2
14.571
31
14.989
21
15.801
11
16.349
1
13.597
30
15.068
20
15.861
10
16.407
0
11.730
29
15.144
19
15.916
9
16.451
28
15.230
18
15.968
8
16.468
27
15.324
17
16.016
7
16.445
Older Age Thirty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
37
14.231
27
15.168
17
15.834
7
16.248
3r,
14.352
26
16.257
16
15.880
6
16.169
35
14.467
25
15.340
15
15.930
5
16.003
34
14.574
24
15.420
14
15.987
4
15.673
33
14.674
23
15.495
13
16.044
3
15.222
32
14.764
22
15.564
12
16.101
2
14.395
31
14.845
21
15.628
11
16.156
1
13.432
30
14.921
20
15.685
10
16.213
0
11.590
29
14.993
19
15.739
9
16.256
28
15.077
18
15.788
8
16.271
Digitized by LjOOQ iC
TABLE XXI.
323
Value ot£l per Annum during the joint ContiDUAiice of Two LirM.
(Carlule 3 per Cent.)
Older Age Thirty-Eight Years.
Af..
TalM.
A^.
Valae.
Aje.
Value.
Age.
ValiM.
38
13.981
28
14.918
18
15.603
8
16.069
37
14.104
27
15 005
17
15.647
7
16.046
36
14.221
26
15.092
16
15.691
6
15.966
35
14.332
25
15.172
15
15.739
5
15.802
34
14.435
24
15.249
14
15.794
4
15.475
33
14.531
23
15.322
13
15.851
3
15.030
32
14.618
22
15.388
12
15.905
2
14.213
31
14.696
21
15.450
11
15.959
1
13.264
30
14.768
20
15.505
10
16.014
0
11.446
29
14.837
19
15.556
9
16.055
Older Age Thirty-Nine Yeara.
Age.
Value.
Age.
Value.
Age.
Valoe.
Age.
Valoe.
39
13.727
29
14.675
19
15.367
9
15.849
38
13.853
28
14.752
18
15.412
8
15.862
37
13.971
27
14.837
17
15.455
7
15.838
36
14.083
26
14.920
16
15.497
6
15.759
35
14.191
25
14.998
15
15.543
5
15.596
34
14.290
24
15.073
14
15.597
4
15.273
33
14.382
23
15.141
13
15.651
3
14.833
32
14.465
22
15.205
12
15.704
2
14.028
31
14.540
21
15.265
11
15.756
1
13.091
30
14.608
20
15.318
10
15.809
0
11.298
Older Age Forty Years.
Ajje.
Valtte.
Age.
Value.
Age.
Value.
Age.
Value.
40
13.481
29
14.512
18
15.222
7
15.631
39
13.603
28
14.587
17
15.263
6
15.552
38
13.723
27
14.668
16
15.303
5
15.391
37
13.837
26
14.748
15
15.348
4
15.071
36
13.945
25
14.824
14
15.399
3
14.637
35
14.048
24
14.895
13
15.452
2
13.842
34
14.144
23
14.961
12
15.503
1
12.919
33
14.233
22
15.023
11
15.554
0
11.151
32
14.312
21
15.080
10
15.605
31
14.333
20
15.131
9
15.644
30
14.449
19
15.178
8
15.656
Dhgitized by LjOOQ IC
384
TABLE XXI.
Value of £1 per Annum duriug the joint Continuaaee of Two Lirei.
(Carliale 3 per Cent.)
Older Age Forty-One Years.
Age.
Value.
Ag«.
Value.
Age.
Value.
Ar.
Value:
41
13.254
30
14.295
19
1.4.997
8
15.457
40
13.366
29
14.356
18
15.038
7
15.431
39
13.483
28
14.427
17
15.077
6
15.353
38
13.598
27
14.505
16
15.116
5
15.193
37
13.708
26
14.584
15
16.159
4
14.877
36
13.812
2>
14.655
14
15.209
3
14.448
35
13.912
24
14.724
13
15.260
2
13.664
34
14.003
23
14.788
12
15.310
1
12.753
33
14.088
22
14.848
n
15.358
0
11.009
32
14.164
21
14.903
10
15.409
31
14.232
20
14.951
9
15.446
Older Age Forty-Two Years.
Age.
Value.
Age.
Value.
A«e.
Value.
Age.
Value.
42
13.036
31
14.082
20
14.773
9
15.250
41
13.143
30
14.142
19
14.816
8
15.259
40
13.250
29
14.199
18
14.856
7
15.234
39
13.36i
23
14.268
17
14.894
6
15.155
3a
13.474
27
14.344
16
14.931
5
14.997
37
13.579
26
14.4]8
J5
14.972
4
14.685
36
13.680
25
14.487
)4
15.020
3
14.261
35
13.775
24
14.554
13
15.070
2
13.487
34
13.863
23
14.616
12
15.117
1
12.589
33
13.945
22
14.673
11
15.165
0
10.869
32
14.017
21
14,726
10
15.214
Older Age Forty-Three Years.
Age.
Value.
Age.
32
Value.
Age.
Value.
Age.
Value.
43
12.822
13.868
21
14.548
10
15.013
42
12.927
31
13.929
20
14.592
9
15.052
41
13.029
30
13.986
19
14.634
8
15.C61
40
13.132
29
14.041
18
14.673
7
15.034
39
13.239
28
14.107
17
14.708
6
14.956
38
13.346
^7
14.179
16
14.744
5
14.800
37
13.448
26
14.251
15
14.784
4
14.491
36
13.544
25
14.318
14
14.830
3
14.073
35
13.636
24
14.382
13
14.877
2
13.310
34
13.720
23
14.442
12
14.925
1
12.424
33
13.798
22
14.497
U
14.970
0
10.72S
Digitized by VjOOQ IC
TABLK XXI.
324
Value of £1 per Annum during the joint Coniinuance of Tuo Lives.
(Carlisle 3 per Gent.)
Older Age Forty-Four Years.
Age.
Valuer
Age.
Vnlne.
Age,
Valae.
Age.
Valne.
44
12.600
32
13.709
20
14.404
8
14.854
43
12.709
31
13.768
19
14.444
7
14.827
42
12.809
30
13.822
18
14.481
6
14.750
41
12.907
29
13.tf75
17
14.515
5
14.595
40
13.005
28
13.037
16
14.549
4
14.290
39
13.107
27
14.007
15
14.587
3
13.877
38
13.211
26
14.076
14
14.631
2
13.125
37
13.308
25
14.140
13
14.678
1
12.253
36
13.400
24
14.202
12
14.724
0
10.682
35
13.488
23
14.259
11
14.768
34
13.569
22
14.312
10
14.813
33
13.643
21
14.361
9
14.847
Older Age Forty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
45
12.371
33
13.479
21
14.166
9
14.632
44
12.483
32
13.542
20
14.207
8
14.639 .
43
12.587
31
13.598
19
14.245
7
14.612
42
12.682
30
13.650
18
14.280
6
14.535
41
12.775
29
13.698
17
14.313
5
14.382
40
12.868
28
13.758
16
14.346
4
14.081
39
12.967
27
13.825
15
14.381
3
13.674
38
13.066
26
13.892
14
14.426
2
12.933
37
13.151
25
13.954
13
14.470
1
12.075
3G
13.248
24
14.013
12
14.514
0
10.430
35
13.331
23
14.068
11
14.557
34
13.409
22
14.119
10
14.601
Older Age Forty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
46
12.128
34
13.236
22
13.914
10
14.376
45
12.247
33
13.303
21
13.959
9
14.406
44
12.354
32
13.363
20
13.998
8
14.412
43
12.452
31
13.416
19
14.035
7
14.385
42
12.543
30
13.463
18
14.068
6
14.309
41
12.630
29
13.510
17
14.099
5
14.156
40
12.720
28
13.567
16
14.129
4
13.860
39
12.814
27
13.632
15
14.166
3
13.460
38
12.909
26
13.696
14
14.207
2
12.731
37
12.998
25
13.755
13
14.260
I
11.888
36
13.082
24
13.812
12
14.292
0
10.270
35
13.162
23
13.865
11
14.334
Digitized by LjOOQ iC
326 TABLE XXI.
Value of £1 per Annam during the joint Continuance of Two LiTea.
(Cailiftle 3 per Gent.)
Older Age Forty-Sevea Yean.
A«e.
Value.
•
Age.
Valne.
Age.
Value.
Age.
Value
47
11.870
35
12.980
23
13.649
11
14.098
46
11.996
34
13.060
22
13.696
10
14.139
45
12.110
33
13.114
21
13.739
9
14.168
44
12.211
32
13.171
20
13.777
8
14.173
43
12.304
31
13.219
19
13.811
7
14.146
42
12.389
30
13.265
18
13.843
6
14.069
41
12.474
29
13.309
17
13.873
5
13.919
40
12.568
28
13.363
16
13.902
4
13.627
39
12.648
27
13.425
15
13.935
3
13.234
38
12.738
26
13.487
14
13.976
2
12.518
37
12.823
25
13.544
13
14.018
1
11.690
36
12.903
24
13.699
12
14.059
0
10.101
Older Age Forty-Eight Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
48
11.591
35
12.780
22
13.461
9
13.912
47
11.728
34
12.846
21
13.503
8
13.917
46
11.848
33
12.908
20
13.538
7
13.888
45
11.956
32
12.960
19
13.571
6
13.813
44
12.052
31
13.007
18
13.602
5
13.666
43
12.139
30
13.049
17
13.630
4
13.379
42
12.221
29
13.091
16
13.658
3
12.993
41
12.300
28
13.143
15
13.690
2
12.290
40
12.380
27
13.202
14
13.729
1
11.479
39
12.465
26
13.261
13
13.769
0
9.922
38
12.550
25
13.316
12
13.807
37
12.631
24
13.368
11
13.845
36
12.708
23
13.417
10
13.885
Older Age Forty- Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
49
11.279
36
12.488
23
13.160
10
13.606
48
11.432
35
12.556
22
13.203
9
13.633
47
11.562
34
12.620
21
13.242
8
13.636
46
11.676
33
12.676
20
13.276
7
13.608
45
11.778
32
12.726
19
13.307
6
13.533
44
11.868
31
12.770
18
13.336
5
13.388
43
11.951
SO
12.810
17
13.363
4
13.107
42
12.027
29
12.849
16
13.389
3
12.729
41
12.102
28
12.898
15
13.420
2
12.042
40
12.177
27
12.965
14
13.437
1
11.249
39
12.257
26
13.012
13
13.495 ,^
0
9.725
38
12.339
25
13.064
12
13.532
37
12.416
24
13.114
11
13.569
Digitized by LjOOQ IC
TABLE XXI.
Value of £1 per Anniun daring the joint Continuance of Two Lives.
(Carlisle 3 per Cent.;
Older Age Fifty Years.
327
Ag8.
Valae.
Age.
Viaae.
Age.
Value.
•
A«6.
Value.
50
10.942
37
12.180
24
12.841
u
13.273
49
11.107
36
12.248
23
12.885
10
13.310
48
11.253
35
12.314
22
12.925
9
13.334
47
11.377
34
12.372
21
12.963
8
13.337
46.
11.484
33
12.426
20
12.995
7
13.308
45
11.580
32
12.473
19
13.024
6
13.235
44
11.665
31
12.514
18
13.052
5
13.092
43
11.743
30
12.551
17
13.077
4
12.817
42
11.814
29
12.588
16
13.102
3
13.448
41
11.884
28
12.635
15
13.131
2
11.777
40
11.954
27
12.689
14
13.166
1
11.003
39
12.031
26
12.743
13
13.203
0
9.517
38
12.108
25
12.793
12
13.238
Older Age Fi%-One Years.
Age.
Value.
Age.
Value.
A«e.
Value.
Age.
Value.
51
10.579
38
11.856
25
12.502
12
12.924
50
10.757
37
11.924
24
12.547
11
12.958
49
10.914
36
11.989
23
12.589
10
12.992
48
11.053
35
12.049
22
12.628
9
13.016
47
11.170
34
12.105
21
12.663
8
13.107
46
11.271
33
12.155
20
12.694
7
12.989
45
11.362
32
12.199
19
12.722
6
12.916
44
11.441
31
12.237
18
12.747
5
12.777
43
11.514
30
12.272
17
12.771
4
12.509
42
11.580
29
12.306
16
12.794
3
12.149
41
11.645
28
12.351
15
12.822
2
11.495
40
11.711
27
12.402
14
12.855
1
10.743
39
11.783
26
12.454
13
12.890
0
9.293
Older Age Fifty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
52
10.215
39
11.528
26
12.160
13
12.573
51
10.393
38
11.596
25
12.205
12
12.606
50
10.563
37
11.661
24
12.248
11
12.637
49
10.713
36
11.721
23
12.288
30
12.670
48
10.845
35
11.778
22
12.325
9
12.692
47
10.955
34
11.830
21
12.358
8
12.693
4G
11.051
33
11.878
20
12.387
7
12.664
45
11.135
32
11.919
19
12.413
6
12.593
44
11.209
31
11.955
18
12.437
5
12.457
43
11.277
30
11.987
17
12.459
4
12.196
42
11.338
29
12.019
16
12.481
3
11.845
41
11.399
28
12.061
15
12.508
2
11.210
40
11.461
27
12.110
14
12.540
1
0
10.476
9.066
Digitized by LjOOQ iC
328
TABLK XXI.
Valud of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 3 per Cent)
•
Older Age Fifty-Three Years.
Age.
Valae.
Age.
Value.
Age.
31
VAlne.
Age.
Value.
Age.
Valu^.
53
9.849
42
11.089
11.665
20
12.075
9
12.363
52
10.028
41
11.145
30
11.696
19
12.099
8
12.363
51
10.198
40
11.202
29
11.725
18
12.122
7
12.335
50
10.360
39
11.265
28
11.765
17
12.142
6
12.265
49
10.503
38
11.330
27
11.812
16
12.163
5
12.132
48
10.628
37
11.390
26
11.859
15
12.188
4
11.877
47
10.732
36
11.446
25
11.902
14
12.219
3
11.538
46
10.821
35
11.500
24
11.943
13
12.251
2
10.918
45
10.900
34
11.549
23
11.981
12
12.281
1
10.207
44
10.969
33
11.594
22
12.016
11
12.311
0
8.836
43
11.031
32
11.632
21
12.048
10
12.343
Older Age Fifty-Four Ycetb.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
21
Value.
Age.
Value.
54
9.480
43
10.778
32
11.338
11.731
10
12.009
53
9.660
42
10.830
31
11.369
20
11.756
9
12.029
52
9.831
41
10.882
30
11.397
19
11.785
8
12.028
51
9.994
40
10.936
29
11.425
18
11.801
7
12.000
50
10.148
39
10.995
28
11.463
17
11.820
6
11.932
49
10.284
38
11.055
27
11.507
16
11.839
5
11.802
48
10.402
37
11.111
26
11.552
15
11.863
4
11.556
47
10.499
36
11.164
25
11.593
14
11.892
3
11.223
46
10.683
35
11.215
24
11.632
13
11.922
2
10.623
45
10.656
34
11.261
23
11.668
12
11.951
1
9.933
44
10.720
33
11.302
22
11.701
11
11.980
0
8.603
Older Age Fifty-Five Years
.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
55
9.103
43
10.513
31
11.063
19
11.450
r
11.656
54
9.2*^7
42
10.561
30
11.089
18
11.470
6
11.589
53
9.459
41
10.608
29
11.115
17
11.488
5
11.465
52
9.622
40
10.658
28
11.151
16
11.506
4
11.223
51
9.777
39
10.713
27
11.193
15
11.528
3
10.902
50
9.924
38
10.769
26
11.235
14
11.556
2
10.320
49
10.052
37
10.822
25
11.274
13
11.584
1
9.B52
48
10.163
36
10.872
24
11.312
12
11.612
0
8.363
47
10.254
35
10.919
23
11.346
11
11.639
46
10.332
34
10.962
22
11.376
10
11.667
45
10.400
33
11.001
21
n.405
9
11.686
44
10.459
32
11.034
20
11.429
8
11.684
Digitized by VjOOQ IC
TABLE XXI.
Value of £1 per Annum durini^ the joint Continuance of Two Lives.
(CarUtile 3 per Cent.)
Older Age Fifty-Six Years.
329
Af.
Value.
A«e.
Value.
Age.
32
Valae.
A«e,
•
Valne.
Age.
8
Value.
56
8.721
44
10.189
10.722
20
11.094
11.334
55
8.908
43
10.237
31
10.749
19
11.114
7
11.306
54
9.084
42
10.2yi
30
10.773
18
11.132
6
11.242
53
9.248
41
10.325
29
10.797
17
11.149
5
11.118
52
9.403
40
10.371
28
10.831
16
11.166
4
10.885
5i
9.549
39
10.422
27
10.871
15
11.187
3
10.575
50
9.689
38
10.474
26
10.911
14
11.213
2
10.011
49
9.810
37
10.524
23
10.948
13
11.240
1
9.367
48
9.9M
36
10.570
24
10.984
12
11.266
0
8.119
47
9.999
35
10.615
23
11.016
11
11.292
46
10.071
34
10.655
22
11.045
10
11.318
45
10.134
33
10.691
21
11.072
9
11.336
Older Age Fifty-Seven Years.
Aft.
Value.
A«e.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
.57
8.334
45
9.858
33
10.373
21
10.731
9
10.979
56
8.523
44
9.908
32
10.402
20
10.751
8
10.976
55
8.701
43
9.952
31
10.427
19
10.770
7
10.950
54
8.869
42
9.992
30
10.449
18
10.787
6
10.885
53
9.025
41
10.032
29
10.472
17
10.803
5
10.766
52
9.172
40
10.074
28
10.504
16
10.819
4
10.641
51
9.311
39
10.122
27
10.541
15
10.838
3
10.241
50
9.442
38
10.171
26
10.580
14
10.863
2
9.697
49
9.556
37
10.216
25
10.615
13
10.888
1
9.075
i%
9.654
36
10.260
24
10.648
12
10.913
0
7.869
47
9.733
35
10.302
23
10.678
U
10.937
46
9.801
34
10.339
22
10.706
10
10.963
Older Age Fifty-Eight
Years.
A«^
Valae.
Age.
46
Value.
Age.
Value.
Age.
Value.
Age.
Value.
58
7.954
9.527
34
10.023
22
10.367
10
10.608
57
8.140
45
9.579
33
10.055
21
10.391
9
10.623
56
8.321
44
9.625
32
10.082
20
10.410
8
10.621
55
8.490
43
9.665
31
10.105
19
10.428
7
10.593
54
8.650
42
9.701
30
10.126
18
10.444
6
10.531
53
8.797
41
9.737
29
10.146
17
10.458
5
10.416
52
8.937
40
9.776
28
10.176
16
10.473
4
10.198
51
9.068
39
9.820
27
10.212
15
10.491
3
9.909
50
9.193
38
9.865
26
10.249
14
10.514
2
9.383
49
9.300
37
9.909
2.3
10.281
13
10.538
1
8.784
48
9.392
9.46^
36
9.949
24
10.313
12
10.ri62
0
7.621
47
35
9.988
23
10.342
11
10.684
Digitized by LjOOQ iC
330
TABLE XXI.
Value of i^I per Annum dttring the joint Continuance of Two livee*
(Carliile 3 per Cent)
Older Age Fifty-Nine Yeari.
Ag«.
Valae.
■«
Value.
Age.
Valae.
A«e.
VeliM.
A«e.
ValiM.
59
7.605
47
9.207
35
9.688
23
10.020
11
10.248
58
7.776
46
9.264
34
9.721
22
10.045
10
10.271
57
7.953
45
9.312
33
9.751
21
10.067
9
10.285
56
8.125
44
9.353
32
9.776
80
10.085
8
10.281
55
8.287
43
9.389
31
9.797
19
10.101
7
10.255
54
8.439
42
9.422
30
9.816
18
10.116
6
10.194
53
8.579
41
9.455
29
9.836
17
10.129
5
10.083
52
8.711
40
9.490
28
9.864
16
10.143
4
9.872
51
8.835
39
9.531
27
9.898
15
10.160
3
9.592
50
8.953
38
9.574
26
9.933
14
10.181
2
9.085
49
9.053
37
9.614
25
9.964
13
10.204
1
8.507
48
9.139
36
9.652
24
9.994
12
10.227
0
7.383
Older
Age Sixty Yean.
Age.
Velae.
Age.
Velne.
Age.
Value.
Age.
Value.
Age.
8
Value.
60
7.295
47
8.967
34
9.440
21
9.765
9.966
59
7.446
46
9.019
33
9.468
20
9.782
7
9.940
58
7.610
45
9.063
32
9.492
19
9.798
6
9.881
57
7.780
44
9.100
31
9.511
18
9.811
5
9.773
56
7.944
43
9.132
30
9.529
17
9.823
4
9.568
55
8.098
42
9.162
29
9.547
16
9.836
3
9.298
54
8.243
41
9.192
28
9.674
15
9.8r)2
2
8.808
53
8.376
40
9.224
27
9.606
14
9.873
1
8.250
52
8.501
39
9.263
26
9.639
13
9.894
0
7.163
51
8.619
38
9.303
25
9.669
12
9.915
50
8.729
37
9.340
24
9.697
11
9.936
49
8.824
36
9.376
23
9.722
10
9.9:>7
48
8.904
35
9.410
22
9.745
9
9.970
Older .
\ge Sixty-One Years,
Age.
Value.
Age.
Value.
Age.
35
Value.
Age.
Value.
Age.
Value.
61
7.044
48
8.697
9.164
22
9.480
9
9.691
60
7.166
47
8.756
34
9.193
21
9.499
8
9.687
59
7.311
46
8.803
33
9.219
20
9.515
7
9.661
58
7.468
45
8.843
32
9.241
19
9.529
6
9.604
57
7.630
44
8.876
31
9.259
18
9.542
5
9.499
56
7.788
43
8.906
30
9.276
17
9.553
4
9.300
55
7.935
42
8.933
29
9.292
16
9.565
3
9.038
54
8.073
41
8.960
28
9.318
15
9.580
2
8.562
53
8.199
40
8.990
27
9.348
14
9.599
1
8.022
52
8.318
8.429
39
9.026
26
9.380
13
9.620
0
6.969
51
38
9.063
25
9.407
12
9.639
50
8.634
37
9.098
24
9.434
11
9.659
49
8.623
36
9.132
23
9.458
10
9.679
Digitized by VjOOQ IC
TABLB XXL
331
Vftloe of £1 per Ammm during the joint Gontiniumoe of Tiro Livev.
(C«rUale3perCent)
Older Age Sixty-Two Yean.
Agt:
YaliM.
Age.
Taloe.
Age.
Yalne.
Age.
Velae.
62
6.804
42
8.705
22
9.218
2
8.321
61
6.921
41
8.730
21
9.236
1
7.798
60
7.037
40
8.757
20
9.251
0
6.778
59
7.175
39
8.791
19
9.264
58
7.325
38
8.826
18
9.276
57
7.480
37
8.859
17
9.287
56
7.631
36
8.890
16
9.297
65
7.772
35
8.921
15
9.311
54
7.902
34
8.948
14
9.330
53
8.023
33
8.972
13
9.349
52
8.135
32
8.993
12
9.368
51
8.240
31
9.009
n
9.386
50
8.339
30
9.025
10
9.405
49
8.422
29
9.041
9
9.416
48
8.492
28
9.064
8
9.412
47
8.545
27
9.094
7
9.387
46
8.588
26
9.123
6
9.331
45
8.624
25
9.150
5
9.228
44
8.654
24
9.175
4
9.035
43
8.681
23
9.198
3
8.782
Older Age Sixty-Three Years.
Age.
Valoe.
Age.
Value.
Age.
Value.
Age.
Value.
63
6.563
43
8.450
23
8.933
3
8.522
62
6.680
42
8.471
22
8.952
2
8.076
61
6.791
41
8.494
21
8.969
1
7.572
60
6.901
40
8.519
20
8.983
0
6.584
59
7.032
39
8.550
19
8.995
58
7.175
38
8.584
18
9.006
57
7.324
37
8.615
17
9.015
56
7.468
36
8.644
16
9.025
55
7.601
35
8.672
15
9.038
54
7.725
34
8.698
14
9.056
53
7.839
33
8.721
13
9.074
52
7.945
32
8.740
12
9.092
51
8.044
31
8.755
11
9.109
50
8.1.37
30
8.770
10
9.127
49
8.215
29
8.784
9
9.138
48
8.279
28
8.807
8
9.133
47
8.328
27
8.835
7
9.108
46
8.367
26
8.863
6
9.053
45
8.400
25
8.888
5
8.954
44
8.426
24
8.912
4
8.767
Digitized by VjOOQ IC
TABLE XXL
Value of £\ per Annum ikam^ the Joint Contiouance of Two Lifes«
(GarlUle 3 per Cent)
Older Age Sixty-Foar Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
64
6.308
44
8.183
24
8.635
4
8.486
63
6.432
43
8.205
23
8.655
3
8.250
62
6.542
42
8.224
22
8.673
2
7.820
61
6.646
41
8.244
21
8.689
1
7.334
60
6.750
40
8.267
20
8.701
0
6.382
59
6.875
3D
8.296
19
8.712
58
7.011
38
8.327
18
8.722
57
7.152
37
8.356
17
8.731
56
7.289
36
8.384
16
8.740
55
7.416
35
8.411
15
8.752
54
7.533
34
8.434
14
8.769
53
7.640
33
8.456
13
8.786
52
7.740
32
8.473
12
8.803
51
7.833
31
8.488
11
8.819
50
7.920
30
8.501
10
8.836
49
7.992
29
8.515
9
8.846
. 48
8.0.)1
28
8.536
8
8.841
47
8.096
27
8.562
7
8.816
46
8.131
26
8.589
6
8.762
45
8.160
25
8.612
5
8.667
Older Age Sixty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
65
6.047
45
7.910
25
8.329
5
8.372
64
6.174
44
7.931
24
8.350
4
8.198
63
6.291
43
7.950
23
8.369
3
7.970
62
6.394
42
7.967
22
8.385
2
7.557
61
6.492
41
7.985
21
8.400
1
7.091
60
6.589
40
8.006
20
8.411
0
6.174
59
6.707
39
8.033
19
8.422
58
6.836
38
8.062
18
8.430
57
6.970
37
8.089
17
8.438
56
7.100
36
8.115
16
8.447
65
7.219
35
8.140
15
8.458
54
7.330
34
8.162
14
8.474
53
7.431
33
8.182
13
8.490
52
7.524
32
8.198
12
8.506
51
7.611
31
8.212
11
8.521
50
7.691
30
8.224
10
8.537
49
7.758
29
8.236
9
8.546
48
7.813
28
8.256
8
8.541
47
7.853
27
8.281
7
8.517
46
7.884
26
8.306
6
8.465
Digitized by VjOOQ IC
TABLE XXL
Value of jCl per Annum duriug the joint Continuance of Two Lives.
(Carlisle 3 per Cent.)
Older Age Sixty-Six Yeaw.
Age.
Value.
Age.
Vala«.
Age.
Value.
Age.
Value.
66
5.774
46
7.624
26
8.012
6
8.156
65
5.906
45
7.647
25
8.033
5
8.066
64
6.0*26
44
7.666
24
8.053
4
7.899
63
6.135
43
7.682
23
8.070
3
7.681
62
6.*232
42
7.697
22
8.086
2
7.284
61
6.323
41
7.713
21
8.099
1
6.838
60
6.414
40
7.732
20
8.110
0
5.958
59
6.525
39
7.757
19
8.119
58
6.647
38
7.784
18
8.127
57
6.774
37
7.810
17
8.134
56
6.896
36
7.834
16
8.142
55
7.009
35
• 7.857
15
8.152
64
7.112
34
7.878
14
8.16/
53
7.206
33
7.896
13
8.182
52
7.293
32
7.911
12
8.197
51
7.374
31
7.924
11
8.211
50
7.449
30
7.936
10
8.227
49
7.510
29
• 7.946
9
8.235
48
7.560
28
7.965
8
8.229
47
7.596
27
7.988
7
8.206
Older Age Sixty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
67
5.486
47
7.325
27
7.683
7
7.882
66
5.626
46
7.350
26
7.705
6
7.834
65
5.750
45
7.379
25
7.724
6
7.748
64
5.862
44
7.386
24
7.743
4
7.588
63
5.964
43
7.401)
23
7,759
3
7.380
62
6.054
42
7.41S
22
7.773
2
7.001
61
6.138
41
7.427
21
7.786
1
6.575
60
6.223
40
7.445
20
7.795
0
5.734
59
6.327
39
7.468
19
7.804
58
6.442
38
7.493
18
7.811
67
6.662
37
7.517
17
7.817
56
6.677
36
7.540
16
7.824
55
6.782
35
7.561
15
7.834
54
6.879
34
7.581
14
7.848
53
6.967
33
7.598
13
7.862
52
7.047
32
7.612
12
7.876
51
7.122
31
7.622
11
7.889
50
7.191
30
7.632
10
7.904
49
7.247
29
7.643
9
7.911
48
7.293
28
7.660
8
7.905
Digitized by LjOOQ iC
334
TABLE XXL
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 3 per Cent.)
Older Age Sixty-Eight Yeart.
A«c.
Value.
Ag».
ValiM.
Age.
Value.
Age.
Value.
68
5.188
48
7.012
28
7.346
8
7.571
67
5.333
47
7.041
27
7.366
7
7.549
G6
5.463
46
7.063
26
7.387
6
7.603
66
5.580
45
7.080
25
7.405
5
7.421
64
5.684
44
7.094
24
7.423
4
7.268
5.779
43
7.106
23
7.438
3
7.070
5.862
42
7.117
22
7.461
2
6.709
Gl
5.940
41
7.130
21
7.462
1
6.305
60
6.018
40
7.146
20
7.470
0
5.593
59
6.116
39
7.168
19
7.478
58
6.224
38
7.191
18
7.484
57
6.336
37
7.213
17
7.490
56
6.444
36
7.234
16
7.496
55
6.542
35
7.254
15
7.606
54
6.632
34
7.272
14
7.518
53
6.713
33
7.288
13
7.632
52
G.787
32
7.301
12
7.545
51
6.856
31
7.311
11
7.557
50
G.920
30
7.320
10
7.570
49
6.971
29
7.328
9
7.577
Older Age Sixty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Volne.
69
4.877
49
6.682
29
7.004
9
7.233
68
5.028
48
6.719
28
7.019
8
7.227
67
5.163
47
6.744
27
7.039
7
7.206
66
5.286
46
6.763
26
7.058
6
7.161
G5
5.394
45
6.778
26
7.075
5
7.083
64
5.490
44
6.790
24
7.091
4
6.938
63
6.578
43
6.800
23
7.105
3
6.750
62
5.654
42
6.810
22
7.116
2
6.407
61
6.726
41
6.821
21
7.127
1
6.025
60
6.738
40
6.836
20
7.135
0
5.263
59
5.890
39
6.866
19
7.141
58
5.990
3^
6.877
18
7.147
57
6.095
37
6.898
17
7.152
56
6.196
36
6.917
16
7.158
55
6.287
35
6.936
15
7.166
54
6 370
34
6.952
14
7.178
53
6.445
33
6.967
13
7.191
52
6.513
32
6.978
12
7.203
51
6.576
31
6.987
11
7.214
50
6.G35
30
6.995
10
7.226
Digitized by LjOOQ iC
TABLE XXI.
Valae of iSl per Annum during the joint Continuance of Two Lifei*
(Carlisle 3 per Cent)
Older Age Seventy Years.
335
A|«.
Valiw.
Age.
Va]iw.
Age.
Valiw.
Age.
Value.
70
4.556
50
6.338
30
6.662
10
6.874
69
4.711
49
6.380
29
6.670
9
6.880
68
4,853
48
6.413
28
6.684
8
6.874
67
4.979
47
6.436
27
6.702
7
6.853
66
5.093
46
6.452
26
6.720
6
6.811
65
5,193
45
6.465
25
6.736
5
6.737
64
5.282
44
6.475
24
6.750
4
6.599
63
5.363
43
6.484
23
6.763
3
6.422
62
5.433
42
6.492
22
6.774
2
6.098
61
5,498
41
6.502
21
6.783
1
5.738
60
5.565
40
6.515
20
6.790
0
5.018
59
5.649
39
6.534
19
6.796
58
5.743
38
6.554
18
6.801
57
5.841
37
6.573
17
6.806
56
5.934
36
6.591
16
6.811
55
6.019
35
6.608
15
6.818
54
6.096
34
6.623
14
6.829
53
6.164
33
6.636
13
6.841
52
6.227
32
6.646
12
6.852
51
6.285
31
6.655
11
6.863
Older Age Seventy-One Yean.
Age.
Value.
Age*
Valae.
Age.
Volne.
Age.
Value.
71
4.217
51
5,977
31
6.309
11
6.500
70
4.381
50
6.026
30
6.316
10
6.510
69
4.527
49
6.064
29
6.323
9
6.515
68
4.659
48
6.094
28
6.336
8
6.509
67
4.777
47
6.113
27
6.353
7
6.489
66
4.882
46
6.127
26
6.369
6
6.450
65
4.974
45
6.138
25
6.384
5
6.380
64
5.056
44
6.146
24
6.397
4
6.250
63
5.130
43
6.153
23
6.409
3
6.083
62
5.194
42
6.160
22
6.418
2
5.779
61
5.254
41
6.169
21
6.427
1
5.441
60
5.314
40
6.181
20
6.433
0
4.763
59
5.392
39
6.198
19
6.438
58
5.479
38
6.217
18
6.443
57
5.570
37
6.234
17
6.447
56
5.656
36
6.251
16
6.452
55
5.734
35
6.267
15
6.459
54
5.805
34
6.280
14
6.469
53
5.867
33
6.293
13
6.480
52
5.925
32
6.302
12
6.490
Digitized by VjOOQ IC
336
TABLE XXI.
Value of £1 per Annum during the joint Continuanee of Two Livei.
(^ Carlisle 3 per Cent.)
Older Age Seventy-Two Yean.
A«e.
Value.
A«..
Value.
Age.
Valw.
Age.
Valoe.
n
3.904
52
5.636
32
5.976
12
6.148
71
4.056
51
5.684
31
5.983
11
6.157
70
4.211
50
5.729
30
5.989
10
6.166
69
4.348
49
5.763
29
5.995
9
6.171
68
4.471
48
5.789
28
6.007
8
6.165
67
4.580
47
5.806
27
6.022
7
6.146
66
4.677
46
5.818
26
6.038
6
6.108
65
4.762
45
5.827
25
6.051
5
6.042
64
4.837
44
5.834
24
6.063
4
5.920
63
4.905
43
5.840
23
6.074
3
5.763
62
4.963
42
5.846
22
6.083
2
5.477
61
5.018
41
5.854
21
6.090
1
5.160
60
5.073
40
5.865
20
6.096
0
4.521
59
5.145
39
5.881
19
6.101
58
5.226
33
5.898
18
6.105
57
5.310
37
5.914
17
6.108
56
5.390
36
5.929
16
6.112
55
5.462
35
5.944
15
6.119
54
5.527
34
5.956
14
6.128
53
5.584
33
5.963
13
6.138
Older Age Seventy-Three Yeare.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
73
3.631
53
5.325
33
5.673
13
5.829
72
3.764
52
5.374
32
5.681
12
5.838
71
3.908
51
5.418
31
5.687
11
5.847
70
4.054
50
5.458
30
5.692
10
5.855
69
4.182
49
5.489
29
5.698
9
5.859
6S
4.297
48
5.513
28
5.709
8
5.854
67
4.399
47
5.528
27
5.723
7
5.836
66
4.489
45
5.538
26
5.738
6
5,800
65
4.568
45
5.545
25
6.750
5
5.737
64
4.637
44
5.551
24
5.761
4
6.622
63
4.699
43
5.556
23
5.771
3
5.474
62
4.752
42
5.561
22
5.779
2
5.204
61
4.802
41
5.568
21
5.786
1
4.905
60
4.853
40
5.578
20
5.791
0
4.301
59
4.920
39
5.592
19
5.795
58
4.995
38
5.609
18
5.799
57
5.073
37
5.6*24
17
5.802
56
5.147
36
5.638
16
5.805
55
5.213
35
5.651
15
5.811
54
5.273
34
5.663
14
5.b20
Digitized by VjOOQ iC
TABLE XXI.
337
Value of iCl per Annum during the joint Continuance of Two Lives^
(Carlisle 3 per Cent)
Oldei
Age Seventy-Four Yean.
Ajc.
V.lw.
Aga
VldM.
Age.
Vmlae.
. Ag«.
Vakw.
74
3.400
54
5.048
34
5.403
14
5.547
73
3.512
53
5.097
33
5.412
13
5.556
72
3.639
52
5.141
32
5.419
12
5.564
71
3.776
51
5.181
31
5.424
11
5.572
70
3.914
50
5.218
30
5.429
10
5.580
69
4.035
49
5.247
29
5.434
9
5.583
68
4.143
48
5.267
28
5.445
8
5.578
67
4.238
47
5.280
27
5.458
7
5.560
66
4.322
46
5.289
26
5.471
6
5.5'26
65
4.395
45
5.295
25
5.483
5
5.467
64
4.459
44
5.299
24
5.493
4
5.357
63
4.515
43
5.304
23
5.502
3
5.217
62
4.564
42
5.308
22
5.510
2
4.961
61
4.610
41
5.314
21
5.516
1
4.680
6U
4.657
40
5.323
20
5.520
0
4.107
59
4.719
39
5.337
. 19
5.524
58
4.789
38
5.352
18
5.527
57
4.862
37
5.366
17
5.530
56
4.931 I
36
5.379
16
5.533
55
4.993 '
35
5.392
15
5.539
Older Age Seventy-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
75
3.231
55
4.813
35
5.179
15
5.315
74
3.313
54
4.865
34
5.189
14
5.322
73
3.421
53
4.910
33
5.198
13
5.330
72
3.541
52
4.951
32
5.204
12
5.338
71
3.672
51
4.988
31
5.209
11
5.345
70
3.804
50
5.022
30
5.213
10
5.353
69
3.919
49
5.047
29
5.218
9
5.356
68
4.021
48
5.066
28
5.227
8
5.351
67
4.110
47
5.077
27
5.240
7
5.334
66
4.189
46
5.084
26
5.253
6
5.301
65
4.257
45
5.089
25
5.263
5
5.244
64
4.315
44
5.093
24
5.273
4
5.140
63
4.368
43
5.097
23
5.281
3
5.006
62
4.412
42
5.100
22
5.288
2
4.762
61
4.454
41
5.106
21
5.294
1
4.495
60
4.498
40
5.115
20
5.298
0
3.947
59
4.556
39
5.127
19
5.301
58
4.622
3S
5.142
18
5.304
57
4.691
37
5.155
17
5.306
56
4.756
36
5.167
16
5.S09
Digitized?y Google
338
TABLBXXI.
Value of £1 per Anniini during the joint Continuance of Two lavei.*
(Carlisle 3 per Cent)
Older Age Seventy-Six Years.
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
Value.
76
3.068
56
4.581
36
4.959
16
5.090
75
3.147
55
4.635
35
4.970
15
5.094
74
3.225
64
4.683
34
4.979
14
5.102
73
3.328
53
4.725
33
4.987
13
5.109
72
3.443
52
4.762
32
4.993
12
5.117
71
3.568
51
4.797
31
4.997
11
5.124
70
3.693
50
4.828
30
5.001
10
5.131
69
3.802
49
4.851
29
5.005
9
5.133
68
3.898
48
4.867
28
5.014
8
5.128
67
3.982
47
4.877
27
5.026
7
5.112
66
4.055
46
4.883
26
5.038
6
5.080
65
4.117
45
4.887
25
5.048
5
5.026
64
4.172
44
4.890
24
5.057
4
4.926
63
4.220
43
4.893
23
5.064
3
4.800
62
4.261
42
4.896
22
5.071
2
4.567
61
4.299
41
4.901
21
5.076
1
4.313
60
4.339
40
4.909
20
5.079
0
3.791
59
4.394
39
4.921
19
5.082
58
4.456
38
4.935
18
5.085
57
4.^20
37
4.947
17
5.087
Older Age Seventy-Seven Yean.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
17
2.927
57
4.362
37
4.755
17
4.884
76
2.995
56
4.419
36
4.766
16
4.886
75
3.070
55
4.470
35
4.776
15
4.890
74
3.H5
54
4.514
34
4.784
14
4.897
73
3.243
53
4.553
33
4.792
13
4.905
72
3.353
52
4.587
32
4.797^
12
4.911
71
3.472
51
4.619
31
4.801
11
4.918
70
3.591
50
4.647
30
4.804
10
4.924
69
3.694
49
4.668
29
4.808
9
4.927
68
3.784
48
4.6S3
28
4.816
8
4.921
67
3.863
47
4.691
27
4.828
7
4.906
66
3.930
46
4.696 '
26
4.S39
6
4.875
65
3.988
45
4.699
25
4.848
5
4.824
64
4.038
44
4.701
24
4.856
4
4.728
63
4.082
43
4.703
23
4.863
3
4.608
62
4.120
42
4.706
22
4.869
2
4.386
61
4.155
41
4.711
21
4.874
1
4.145
60
4.192
40
4.719
20
4.877
0
3.647
59
4.243
39
4.730
19
4.879
58
4.301
38
4.743
18
4.882
Digitized by LjOOQ IC
TABLB XXl.
339
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 3 per Cent)
Older Age Seventy-Eight Years.
Age.
Value.
Age.
Vdue.
Age.
Value.
Age.
Value.
78
2.784
58
4.141
38
4.647
18
4.675
77
2.853
57
4.199
37
4.558
17
4.676
76
2.917
56
4.252
36
4.568
16
4.679;
75
2.989
55
4.299
35
4.578
15
4.683
74
3.059
54
4.840
34
4.586
14
4.689
73
3.152
53
4.375
33
4.592
13
4.696
72
3.257
52
4.407
32
4.597
12
4.702
71
3.370
51
4.435
31
4.600
11
4.708
70
3.483
50
4.461
30
4.603
10
4.n5
4.717
69
3.580
49
4.480
29
4.607
9
68
3.664
48
4.493
28
4.615
8
4.711
67
3.737
47
4.500
27
4.625
7
4.696
66
3.800
46
4.504
26
4.636
6
4.667
65
3.853
45
4.506
25
4.644
5
4.618
64
3.898
44
4.508
24
4.652
4
4.527
63
3.939
43
4.510
23
4.658
3
4.413
62
3.973
42
4.512
22
4.664
2
4.203
61
4.005
41
4.517
21
4.668
1
3.974
60
4.039
40
4.524
20
4.670
0
3.501
59
4.087
39
4.535
19
4.673
Older Age Seventy-Nine Years.
Age.
Value.
A«e.
Value.
Age.
Value.
Age.
Value.
79
2.610
59
3.905
39
4.815
19
4.441
78
2.694
58
3.956
38
4.326
18
4.443
77
2.759
57
4.010
37
4.836
17
4.444
76
2.819
56
4.059
36
4.346
16
4.446
75
2.886
55
4.102
35
4.854;
15
4.450
74
2.952
54
4.140
34
4.861
14
4.456
73
3.039
53
4.172
33
4.367
13
4.462
72
3.138
52
4.201
32
4.372
12
4.468
71
3.245
51
4.226
31
4.874
11
4.474
70
3.351
50
4.250
30
4.377
10
4.479
69
3.441
49
4.267
29
4.380
9
4.481
68
3.520
48
4.278
28
4.387
8
4.476
67
3.586
47
4.284
27
4.397
7
4.461
66
3.644
46
4.287
26
4.407
6
4.434
65
3.692
45
4.289
25
4.415
5
4.387
64
3.733
44
4.290
24
4.422
4
4.302
63
3.770
43
4.291
23
4.428
3
4.195
62
3.800
42
4.294
22
4.433
2
3.996
61
3.830
41
4.298
21
4.436
1
3.782
60
3.861
40
4.304
20
4.439
0
3.335
DigKze2byVjOOQlC
340 TABLE XXI.
Value of £1 per Annum during ihe joint Continuance of Two LiTC&
(GarUsLe 3 per Cent.)
Older Age Eighty Years.
Age.
Valae.
Age.
Valoe.
Age.
Value.
Age.
Valae.
80
2.459
59
3.737
38
4.122
17
4.229 ,
79
2.532
58
3.785
37
4-131
16
4.231
78
2.611
57
3.834
36
4.140
15
4.235
77
2.672
56
3.880
35
4.148
14
4.241
76
2.728
55
3.920
34
4.154
13
4.247
75
2.790
54
3.954
33
4.160
12
4.252
74
2.852
53
3.984
32
4.164
li
4.257
73
2.935
52
4.010
31
4.166
10
4.262
72
3.028
51
4.033
30
4.168
9
4.264
71
3.129
50
4.054
29
4.171
8
4.259
70
3.228
49
4.069
28
4.178
7
4.245
69
3.312
48
4.079
27
4.187
6
4.219
68
3.385
47
4.084
26
4.196
5
4.175
67
3.446
46
4.086
25
4.203
4
4.094
66
3.498
45
4.087
24
4.210
3
3.993
65
3.542
44
4.088
23
4.215
2
3.806
64
3.580
43
4.090
22
4.219
1
3.605
63
3.613
42
4.091
21
4.223
0
3.183
62
3.640
41
4.095
20
4.225
61
3.667
40
4.102
19
4.227
60
3.695
39
4.111
18
4.228
Older Age EightyOne Years.
:Age.
Valae.
Age.
Valna.
Age.
Value.
Age.
Value.
81
2.283
60
3.510
39
3.888
18
3.995
80
2.368
59
3.548
38
3.898
17
3.996
79
2.436
58
3.593
37
3.907
16
3.998
78
2.510
57
3.639
36
3.915
15
4.001
77
2.566
56
3.681
35
3.922
14
4.006
76
2.618
55
3.717
34
3.928
13
4.012
75
2.676
54
3.748
33
3.933
12
4.017
74
2.734
53
3.775
32
3.936
11
4.021
73
2.811
52
3.798
31
3.938
10
4.026
72
2.899
51
3.819
30
3.940
9
4.027
71
2.992
50
3.838
29
3.943
8
4.022
70
3.085
49
3.851
28
3.949
7
4.009
69
3.163
48
3.860
27
3.958
6
3.985
68
3.229
47
3.864
26
3.966
5
3.943
67
3.285
46
3.865
25
3-973
4
3.868
66
3.332
45
3.866
24
3.979
3
3.774
65
3.372
44
3.867
23
3.983
2
3.599
64
3.405
43
3.868
22
3.987
1
3.411
63
3.435
42
3.870
21
3.990
0
3.015
62
3.460
41
3.874
20
3.992
61
3.484
40
3.879
19
3.993
Digitized by LjOOQ IC
TABLE XXI.
341
Value of £1 per Annum daring the joint Gontinnance of Two liTOS.
(Garliale 3 per Cent.)
Older Age Eighty-Two Years.
Age.
Valne.
Age.
61
Valae.
Age.
Vftlue.
Age.
Value.
S2
2.135
3.318
40
3.679
19
3.783
81
2.207
60
3.342
39
3.688
18
3.784
80
2.286
59
3.378
38
3.697
17
3.786
79
2.350
58
3.419
37
3.705
16
3.787
78
2.419
57
3.462
36
3.712
15
3.790
77
2.471
56
3.501
35
3.719
14
3.795
76
2.518
55
3.534
31
3.724
13
3.800
75
2.573
54
3.562
33
3.728
12
3.805
74
2.626
53
3.586
32
3.731
11
3.809
73
2.699
52
3.607
31
3.733
10
3.813
72
2.781
51
3.626
30
3.735
9
3.815
71
2.869
50
3.643
29
3.737
8
3.810
70
2.955
49
3.655
28
3.743
7
3.797
69
3.027
48
3.662
27
3.751
6
3.774
68
3.088
47
3.665
26
3.759
5
3.735
67
3.138
46
3.667
25
3.765
4
3.664
66
3.181
45
3.667
24
3.770
3
3.576
65
3.217
44
3.668
23
3.775
2
3.412
64
3.247
43
3.669
22
3.778
1
3.238
63
3.274
42
3.670
21
3.781
0
2.865
62
3.297
41
3.674
20
3.782
Older Age Eighty-Three Years.
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
Value.
83
1.978
62
3.125
41
3.468 ,
20
3.567
82
2.053
61
3.145
40
3.473
19
3.568
81
2.120
60
3.167
39
3.481
18
3.569
80
2.195
59
3.200
38
3.489
17
3.570
79
2.254
58
3.238
37
3.497
16
3.571
78
2.318
57
3.277
36
3.504
15
3.574
71
2.365
56
3.313
35
3.509
14
3.579
76
2.4U9
55
3.343
34
3.514
13
3.583
75
2.459
54
3.369
33
3.518
12
3.588
74
2.509
53
3.390
32
3.521
11
3.592
73
2.577
52
3.409
31
3.522
10
3.596
72
2.6.53
51
3.426
30
3.524
9
3.597
71
2.735
50
3.441
29
"3.526
8
3.592
70
2.815
49
3.452
28
3.531
7
3.580
69
2.881
48
3.459
27
3.539
6
3.558
68
2.936
47
3.461
26
3.546
5
3.522
67
2.983
46
3.462
25
3.551
4
3.456
6G
3.021
45
3.462
24
3.556
3
3.374
65
3.054
44
3.463
23
3-560
2
3.221
64
3.081
43
3.464
22
3.563
1
3.059
63
3.106
42
3.465
21
3.566
0
2.710
Digitized
byV^UUyl
342 TABLB XXI.
Value of £1 per Annum during the joint Continuance of Two Lhes.
(Carlisle 3 per Cent.)
Older Age Eighty-Four Years.
Age.
Value.
Age.
Value.
Age.
iValue.
Age.
Value.
84
1.823
62
2.956
40
3.273
18
3.360
83
1.899
61
2.974
39
3.281
17
3.361
82
1.969
60
2.995
38
3.289
16
3.363
81
2.031
59
3.025
37
3.295
15
3.365
80
2.101
58
3.060
36
3.301
14
3.369
79
2.155
b1
3.097
35
3.307
13
3.374
78
2.214
56
3.130
34
3.311
12
3.378
11
2.258
55
3.157
33
3.314
11
3.381
76
2.298
54
3.180
32
3.317
10
3.385
75
2.345
53
3.199
31
3.318
9
3.386
74
2.391
52
3.216
30
3.319
8
3.381
73
2.454
51
3.231
29
3.321
7
3.370
72
2.525
50
3.245
28
3.326
6
3.350
71
2.601
49
3.255
27
3.333
5
3.316
70
2.675
48
3.261
26
3.339
4
3.254
69
2.736
47
3.262
25
3.345
3
3.178
68
2.786
46
3.263
24
3.349
2
3.036
67
2.828
45
3.263
23
3.353
1
2.886
66
2.863
44
3.264
22
3.355
0
2.560
65
2.892
43
3.264
21
3.358
64
2.916
42
3.266
20
3.359
63
2.938
41
3.269
19
3.360
Older Age Eighty-Five Years.
Age.
Valoo.
Ag*
Value.
Age.
Value.
Age.
Value.
85
1.657
63
2.761
41
3.061
19
3.143
84
1.738
62
2.777
40
3.065
18
3.144
83
1.806
61
2.794
39
3.072
17
3.145
82
1.871
60
2.812
38
3.079
16
3.146
81
1.929
59
2.840
37
3.085
15
3.149
80
1.993
58
2.873
36
3.091
14
3.153 '
79
2.043
t1
2.906
35
3.095
13
3,157
78
2.098
56
2.936
34
3.099
12
3.160
77
2.137
55
2.961
33
3.102
1]
3.163
76
2.174
54
2.982
32
3.104
10
3.167
75
2.217
53
2.999
31
3.106
9
3.167
74
2.259
52
3.014
30
3.107
8
3.163
73
2.318
51
3.028
29
3.108
7
3.152
72
2.384
50
3.040
28
3.113
6
3.134
. 71
2.454
49
3.049,
2J
3.119
5
3.102
70
2.522
48
3.054
26
3.126
4
3.045
69
2.577
47
3.055
25
3.130
3
2.975
68
2.623
46
3.056
24
3.134
2
2.843
67
2«661
45
3.056
23
3.137
1
2.705
66
2.692
44
3.056
22
3.140
0
2.402
65
2.719
43
3.057
21
3.142
64
2.741
42
3.058
20
3.143
c
^r»al(> .
_. . .
L.lUS^lL-w
TABLK XXL
343
Value of £1 per Annum daring the joint Continuance of Two Lives.
(Carlisle 3 per Cent)
Older Age Eighty- Six Years.
Aie.
Value.
Age.
Valne.
Age.
Value.
Age.
Value.
86
1.509
64
2.585
42
2.876
20
2.954
85
1.580
63
2.603
41
2.879
19
2.954
84
1.656
62
2.618
40
2.883
13
2.955
83
1.720
61
2.634
39
2.889
17
2.956
82
1.781
60
2.651
38
2.895
16
2.957
81
1.834
59
2.677
37
2.901
15
2.959
80
1.894
58
2.707
36
2.906
14
2.963
79
1.939
57
2.738
35
2.910
13
2.967
78
1.991
56
2.765
34
2.914
12
2.970
77
2.027
55
2.788
33
2.917
11
2.973
76
2.061
54
2.807
32
2.919
10
2.976
75
2*101
53
2.822
31
2.920
9
2.976
74
2.140
52
2.836
30
2.921
8
2.972
73
2.195
51
2.849
29
2.922
7
2.962
72
2.257
50
2.860
28
2.926
6
2.945
71
2.322
49
2.868
27
2.933
5
2.916
70
2.385
48
2.873
26
2.938
4
2.862
69
2.436
47
2.874
25
2.943
3
2.797
68
2.477
46
2.874
24
2.946
2
2.674
67
2.512
45
2.874
23
2.949
1
2.546
66
2.541
44
2.874
22
2.951
0
2.263
65
2.565
43
2.875
21
2.953
Older^Age Eighty-Seven Years.
Age.
ValiM
Age.
Value.
Age.
Value.
Age.
Value.
87
1.389
65
2.438
43
2.727
21
2.799
86
1.447
64
2.457
42
2.727
20
2.800
85
1.515
63
2.474
41
2.730
19
2.800
84
1.587
62
2.488
40
2.734
18
2.801
83
1.647
61
2.502
39
2.739
17
2.802
82
1.704
60
2.'518
38
2.746
16
2.803
81
1.753
59
2.543
37
2.751
15
2.806-
80
1.810
58
2.571
36
2.755
14
2.808
79
1.852
57
2.600
35
2.759
13
2.813
78
1.901
56
2.625
34
2.763
12
2.815
71
1.935
55
2.646
33
2.765
11
2.817
76
1.967
54
2.663
32
2.767
10
2.820
76
2.004
53
2.678
31
2.768
9
2.821
74
2.041
52
2.691
30
2.769
8
2.817
73
2.093
61
2.703
29
2.770
7
2.807
72
2.151
60
2.713
28
2.775
6
2.791
71
2.212
49
2.720
27
2.780
5
2.763
70
2.271
48
2.725
26
2.786
4
2.713
69
2.318
47
2.726
25
2.789
3
2.652
68
2.357
46
2.726
24
2.793
2
2.536
67
2.389
45
2.726
23
2.795
1
2.416
66
2.416
44
2,726
22
2.797
0
2.149
Digitized by ^^UUV
le
344
TABLK XXI.
Valoe of £1 per Ammin during the joint Continuanee of Two Litci.
(Carlisle 3 per Cent.)
Older Age Eighty-Eight Years.
Ag«.
Value.
Age.
Valoe.
Age.
Value.
Age.
Value.
88
1.328
65
2.362
42
2.638
19
2.707
87
1.358
64
2.380
41
2.640
18
2.707
86
1.414
63
2.397
40
2.643
17
2.708
85
1.479
62
2.410
39
2.649
16
2.709
84
1.548
61
2.424
38
2.655
15
2.711
83
1.606
60
2.439
37
2.660
14
2.714
82
1.660
59
2.462
36
2.664
13
2.717
81
1.707
58
2.489
35
2.668
12
2.720
80
1.761
57
2.516
34
2.671
11
2.723
79
1.803
56
2.540
33
2.673
10
2.726
78
1.849
55
2.560
32
2.675
9
2.726
n
1.881
54
2.577
31
2.676
8
2.722
76
1.912
53
2.591
30
2.677
7
2.713
75
1.948
52
2.603
29
2.678
6
2.697
74
1.983
51
2.614
28
2.682
5
2.671
73
2.033
50
2.624
27
2.688
4
2.623
72
2.088
49
2.631
26
2.693
3
2.564
71
2.147
48
2.635
25
2.696
2
2.453
70
2.203
47
2.636
24
2.700
1
2.338
69
2.248
46
2.636
23
2.702
0
2.081
68
2.285
45
2.636
22
2.704
*
67
2.315
44
2.636
21
2.705
66
2.341
43
2.637
20
2.706
Older Age Eighty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
89
1.248
66
2.252
43
2.533
20
2.599
88
1.287
65
2.273
42
2.534
19
2..^99
87
1.314
64
2.290
41
2.536
18
2.600
86
1.368
63
2.306
40
2.539
17
2.600
85
1.430
62
2.318
39
2.^44
16
2.601
84
1.496
61
2.331
38
2.550
15
2.603
83
1.551
60
2.345
37
2.554
14
2.606
82
1.603
59
2.368
36
2.559
13
2.609
81
1.648
58
2.393
35
2.562
12
2.612
80
1.699
67
2.419
34
2.565
11
2.615
79
1.739
56
2.442
33
2.568
10
2.617
78
1.783
55
2.460
32
2.569
9
2.617
77
1.814
54
2.476
31
2.570
8
2.614
76
1.843
53
2.490
30
2.571
7
2.605
75
1.877
52
2.501
29
2.572
6
2.590
74
1.911
51
2.512
28
2.576
5
2.565
73
1.959
50
2.522
27
2.581
4
2.519
72
2.012
49
2.528
26
2.586
3
2.464
71
2.067
48
2.532
25
2.589
2
2.357
70
2.121
47
2.533
24
2.592
1
2.248
69
2.163
46
2.533
23
2.595
0
2.002
68
2.199
45
2.532
22
2.596
67
2.228
44
2.532
21
2.598
Digitized by VjiOOQlC
TABLE XXI.
Value of £1 per Annam during the joint Conturaance of Two Idret,
(Carlisle 3 per Gent.)
Older Age Ninety Yean.
345
Age.
Value.
Age.
Value.
Age.
Value.
Ag«.
Value.
90
1.088
67
2.088
44
2.374
21
2.436
89
1.165
66
2.112
43
2.375
20
2.437
88
1.201
65
2.131
42
2.375
19
2.437
87
1.226
64
2.147
41
2.377
18
2.438
86
1.277
63
2.162
40
2.380
17
2.438
85
1.335
62
2.174
39
2.385
16
2.439
84
1.397
61
2.186
38
2.391
15
2.441
83
1.448
60
2.199
37
2.395
14
2.444
82
1.497
59
2.220
36
2.399
13
2.447
81
1.540
53
2.244
35
2.403
12
2.449
80
1.5S9
b7
2.268
34
2.405
11
2.451
79
1.626
56
2.289
33
2.408
10
2.454
78
1.668
55
2.307
32
2.409
9
2.454
77
1.698
54
2.322
31
2.410
8
2.451
76
1.725
53
2.335
30
2.411
7
2.443
75
1.758
52
2.346
29
2.412
6
2.429
74
1.789
51
2.356
28
2.416
5
2.405
73
1.834
50
2.365
27
2.420
4
2.362
72
1.884
49
2.371
26
2.425
3
2.310
71
1.936
48
2.374
25
2.428
2
2.210
70
1.987
47
2.375
24
2.431
1
2.107
69
2.027
46
2.375
23
2.433
0
1.876
68
2.061
45
2.375
22
2.435
Older Age Ninetj-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Vahio.
91
1.050
68
2.044
45
2.357
22
2.417
90
1.069
67
2.072 ;
44
2.357
21
2.418
89
1.144
66
2.096
43
2.357
20
2.419
88
1.179
65
2.115
42
2.358
19
2.419
87
1.205
64
2.131
41
2.359
18
2.420
86
1.255
63
2.146
40
2.363
17
2.420
85
1.314
62
2.158
39
2.367
16
2.421
84
1.376
61
2.169
38
2.373
15
2.423
83
1.427
60
2.182
37
2.377
14
2.426
82
1.477
59
2.203
36
2.381
13
2.429
81
1.520
58
2.226
35
2.385
12
2.431
80
1.570
57
2.251
34
2.388
11
2.434
79
1.607
56
2.272
33
2.390
10
2.436
78
1.649
55
2.290
32
2.391
9
2.436
77
1.679
54
2.305
31
2.392
8
2.433
76
1.707
53
2.318
30
2.393
7
2.425
75
1.740
52
2.329
29
2.394
6
2.411
74
1.771
51
2.339
28
2.398
5
2.387
73
1.816
50
2.348
27
2.402
4
2.344
72
1.866
49
2.354
26
2.407
3
2.292
71
1.919
48
2.3.S7
25
2.410
2
2.192
70
1.969
47
2.358
24
2.413.
1
2.089
69
2.010
46
2.357
23
2.415
0
1.859
Digitized by ^^UUV I
346
TABLB XXI.
Value of £1 per Annom durioff the joint Gontinaance of Two Livei*
(Carlisle 3 per Cent.)
Older Age Ninety-Two Years.
A«e.
Value.
Age.
Valae.
Age.
52
Value.
Age.
Value.
Age.
Value.
92
1.120
72
1.940
2.422
32
2.485
12
2.526
91
1.084
71
1.995
51
2.432
31
2.486
11
2.529
90
1.102
70
2.048
50
2.441
30
2.487
10
2.531
89
1.180
69
2.091
49
2.447
29
2.488
9
2.532
88
1.217
68
2.127
48
2.450
28
2.491
8
2.528
87
1.245
67
2.156
47
2.451
27
2.496
7
2.520
86
1.297
66
2.181
46
2.450
26
2.501
6
2.505
85
1.359
65
2.201
45
2.450
25
2.504
5
2.480
84
1.424
64
2.218
44
2.449
24
2.507
4
2.435
83
1.479
63
2.232
43
2.449
23
2.510
3
2.380
82
1.531
62
2.244
42
2.450
22
2.511
2
2.276
81
1.677
61
2.255
41
2.452
21
2.513
1
2.168
80
1.629
60
2.269
40
2.455
20
2.514
0
1.928
79
1.668
59
2.290
39
2.460
19
2.514
78
1.713
58
2.315
38
2.466
18
2.514
77
1.744
57
2.340
37
2.470
17
2.515
76
1.774
56
2.363
36
2.475
16
2.516
75
1.808
55
2.381
35
2.478
15
2.517
74
1.341
54
2.397
34
2.481
14
2.520
73
1.887
53
2.410
33
2.484
13
2.524
Older Age Ninety -Three Years.
Age.
Value.
Ag.».
Value.
Age.
Value.
Age.
Value.
Age.
Value.
93
1.226
73
1.977
53
2.518
33
3.592
13
2.632
92
1.171
72
2.032
52
2.530
32
2.593
12
2.635
91
1.133
71
2.090
51
2.540
•31
2.594
11
2.637
90
1.151
70
2.146
50
2.549
30
2.594
10
2.640
89
1.232
69
2.191
49
2.555
29
2.595
9
2.640
88
1.272
68
2.228
48
2.558
28
2.599
8
2.637
87
1.301
67
2.258
47
2.558
27
2.604
7
2.628
86
1.357
66
2.283
46
2.557
26
2.609
6
2.612
85
1.422
65
2.304
45
2.556
25
2.613
5
2.586
84
1.491
64
2.320
44
2.556
24
2.616
4
2. 539
83
1.549
63
2.335
43
2.556
23
2.620
3
2.482
82
1.605
62
2.346
42
2.556
22
2.620
2
2.373
81
1.653
61
2.358
41
2.558
21
2.621
1
2.260
80
1.707
60
2.371
40
2.562
20
2.622
0
2.010
79
1.749
59
2.393
39
2.567
19
2.622
78
1.795
58
2.419
38
2.573
18
2.623
77
1.828
57
2.445
37
2.578
17
2.623
76
1.859
56
2*469
36
2.582
16
2.624
75
1.894
55
2.489
35
2.586
15
2.636
74
1.929
54
2.505
34
2.589
14
2.629
Digitized by VjOOQ iC
TABLE XXI.
347
Value of £1 p€r Annum during the joint Continuance of Two Lives.
(Carlisle 3 per Cent)
Older Age Ninety-Four Years.
Age.
Value.
Ag«.
Valoe.
Age.
Value.
Age.
Value.
Age.
14
Value.
94
1.302
74
1.983
54
2.559
34
2.640
2.679
93
1.262
73
2.032
53
2.572
33
2.643
13
2.682
92
1.205
72
2.087
52
2.683
32
2.644
12
2.685
91
1.164
71
2.146
51
2.593
31
2.644
11
2.687
90
1.183
70
2.203
50
2.602
30
2.645
10
2.690
89
1.266
169
2.249
49
2.607
29
2.646
9
2.690
88
1.308
68
2.286
48
2.609
28
2.650
8
2.686
87
1.339
67
2.316
47
2.609
27
2.655
7
2.677
86
1.397
66
2.341
46
2.609
26
2.660
6
2.661
85
1.465
65
2.360
45
2.607
25
2.663
5
2.635
84
1.537
64
2.376
44
2.607
24
2.666
4
2.587
83
1.596
63
2.389
43
2.606
23
2.669
3
2.529
82
1.654
62
2.400
42
2.607
22
2.670
2
2.418
81
1.703
61
2.412
41
2.609
21
2.672
1
2.304
80
1.759
.60
2.425
40
2.612
20
2.672
0
2.050
79
1.802
59
2.447
39
2.618
19
2.672
78
1.848
58
2.473
38
2.624
18
2.673
n
1.882
bl
2.500
37
2.629
17
2.673
76
1.912
56
2.523
36
2.633
16
2.674
lb
1.948
55
2.543
35
a.637
15
2.676
Older Age Ninety-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
95
1.383
75
1.993
55
2.575
35
2.663
15
2.699
94
1.340
74
2.027
54
2.590
34
2.666
14
2.703
93
1.298
73
2.076
53
2.603
33
2.668
13
2.706
92
1.239
72
2.132
52
2.613
32
2.669
12
2.709
91
1.197
71
2.191
51
2.622
31
2.669
11
2.711
90
1.217
70
2.248
50
2.630
30
2.671
10
2.714
89
1.303
69
2.292
49
2.634
29
2.671
9
2.714
88
1.347
68
2.328
48
2.636
28
2.674
8
2.710
87
1.379
67
2.357
47
2.636
27
2.680
7
2.701
86
1.439
66
2.380
46
2.634
26
2.684
6
2.684
85
1.509
65
2.398
45
2.633
25
2.683
5
2. 658
84
1.582
64
2.412
44
2.632
24
2.691
4
2.610
83
1.643
63
2.425
43
2.632
23
2.693
3
2.551
82
1.701
62
2.435
42
2.633
22
2.695
2
2.441
81
1.750
61
2.446
41
2.635
21
2.696
1
2.327
80
1.806
60
2.458
40
2.639
20
2.696
0
2.072
79
1.848
59
2.480
39
2.644
19
2.696
78
1.895
58
2.506
38
2.650
18
2.697
77
1.927
57
2.533
37
2.655
17
2.697
76
1.957
b^
2.556
36
2.659
16
2.698
.G(
\r\r^\o
y v_j V.
;U^IL
343
TABLB XXI.
Value of £1 per Annum daring the joint Continuance of Two Livei.
(Carliile 3 per Cent)
Older Age Ninety-Six Years.
Age.
Valoe.
A^e.
Value.
Age.
56
Value.
Age.
36
Value.
Age.
rvalue.
96
1.424
76
1.960
2.523
2.615
16
2.649
95
1.401
75
1.993
55
2.540
35
2.618
15
2.651
94
1.354
74
2.026
54
2.554
34
2.621
14
2.654
93
1.311
73
2.073
53
2.564
33
2.622
13
2.657
92
1.251
72
2.127
52
2.573
32
2.623
12
2.660
91
1.210
71
2.184
51
2.581
31
2.624
11
2.662
90
1.231
70
2.239
50
2.588
30
2.624
10
2.665
89
1.319
69
2.281
49
2.592
29
2.625
9
2.665
88
1.364
68
2.314
48
2.593
28
2.628
8
2.660
87
1.397
67
2.339
47
2.592
27
2.633
7
2.651
86
1.458
66
2.359
46
2.591
26
2.638
6
2.635
85
1.527
65
2.375
45
2.590
25
2.641
5
2.610
84
1.599
64
2.387
44
2.589
24
2.644
4
2.563
83
1.659
63
2.398
43
2.589
23
2.646
3
2.507
82
1.715
62
2.407
42
2.589
22
2.647
2
2.400
81
1.763
61
2.417
41
2.592
21
2.648
1
2.290
80
1.817
60
2.429
40
2.595
20
2.648
0
2.043
79
1.857
59
2.451
39
2.601
19
2.648
78
1.901
58
2.475
38
2.606
18
2.648
77
1.932
57
2.501
37
2.611
17
2.649
Older Age Ninety-Seven Years.
'Age.
Valae.
Age.
Valae.
Age.
Value.
Age.
Value.
Age.
Velae.
97
1.395
77
1.875
57
2.384
37
2.478
17
2.510
96
1.405
76
1.900
56
2.404
36
2.482
16
2.511
95
1.377
75
1.930
55
2.419
35
2.484
15
2.513
94
1.330
74
1.960
54
2.430
34
2.486
14
2.516
,93
1.288
73
2.004
53
2.439
33
2.488
13
2.518
92
1.230
72
2.054
52
2.446
32
2.488
12
2.521
91
1.191
71
2.107
51
2.452
31
2.488
11
2.523
90
1.213
70
2.157
50
2.458
30
2.488
10
2.525
89
1.301
69
2.194
49
2.461
29
2.489
9
2.524
88
1.346
68
2.222
48
2.462
28
2.493
8
2.520
87
1.378
67
2.243
47
2.461
27
2.497
7
2.512
[86
1.436
66
2.259
46
2.460
26
2.502
6
2.497
85
1.502
65
2.272
45
2.458
25
2.504
5
2.473
84
1.571
64
2.282
44
2.458
24
2.507
4
2.430
"83
1.626
63
2.292
43
2.458
23
2.508
3
2.378
82
1.679
62
2.300
42
2.458
22
2.509
2
2.279
81
1.723
61
2.308
41
2.460
21
2.510
1
2.178
80
1.772
60
2.319
40
2.464
20
2.510
0
1.947
79
1.808
59
2.338
39
2.469
19
2.510
78
1.848
58
2.361
38
2.474
18
2.510
Digitized by VjUUVJIC
TABLE XXI.
349
Value of £1 per Annum during the joint Continuanee of Two LiTes.
(Carliile 3 per Cent.)
Older Age Ninety-Eigbt Years.
Al«.
' Valnfc
Age.
ValM.
Ag«.
Value.
Age.
Value.
Age.
Velue.
98
1.375
78
1.782
58
2.225
38
2.318
18
2.347
97
1.377
77
1.805
57
2.245
37
2.322
17
2.348
96
1.378
76
1.826
56
2.262
36
2.324
16
2.348
95
1.348
75
1.853
55
2.274
35
2.326
15
2.350
94
1.302
74
1.879
54
2.282
34
2.328
14
2.352
93
1.262
73
1.919
53
2.289
33
2.329
13
2.355
92
1.208
72
1.964
52
2.294
32
2.329
12i
2.357
91
1.172
71
2.011
51
2.300
31
2.329
n
2.359
90
1.196
70
2.055
50
2.305
30
2.329
10
2.360
89
1.285
69
2.086
49
2.307
29
2.330
9
2.360
88
1.329
68
2.108
48
2.308
28
2.333
8
2.356
87
1.358
67
2.124
47
2.306
27
2.337
7
2.348
86
1.412
66
2.137
46
2.305
26
2.341
6
2.334
85
1.473
65
2.147
45
2.303
'25
2.343
5
2.313
84
1.537
64
2.155
44
2.303
24
2.345
4
2.273
83
1.587
63
2.164
43
2.303
23
2.346
3
2.227
82
1.634
62
2.170
42
2.304
22
2.347
2
2.138
81
1.672
61
2.177
41
2.306
21
2.347
1
2.048 i
80
1.716
60
2.187
40
2.309
20
2.347
0
1.837
79
1.747
59
2.204
39
2.313
19
2.347
Older Age Ninety-Nine Yean.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
99
1.294
79
1.622
59
1.989
39
2.073
19
2.099
98
1.321
78
1.651
58
2.006
38
2.077
18
2.099
97
1.308
77
1.669
57
2.022
37
2.079
17
2.099
96
1.304
76
1.685
56
2.035
36
2.081
16
2.100
95
1.275
75
1.707
55
2.044
35
2.083
15
2.101
94
1.234
74
1.729
54
2.050
34
2.084
14
2.103
S3
1.200
73
1.764
53
2.054
33
2.085
13
2.105
92
1.151
72
1.802
52
2.058
32
2.085
12
2.107
91
1.121
71
1.840
51
2.062
31
2.085
11
2.108
90
1.147
70
1.875
50
2.066
30
2.085
10
2.109
89
1.233
69
1.898
49
2.068
29
2.085
9
2.109
88
1.272
68
1.914
48
2.068
28
2.088
8
2.105
87
1.295
67
1.926
47
2.066
27
2.092
7
2.098
86
1.341
66
1.935
46
2.065
26
2.095
6
2.086
85
1.395
65
1.943
45
2.064
25
2.096
5
2.068
84
1.450
64
1.949
44
2.064
24
2.098
4
2.033
83
1.492
63
1.955
43
2.064
23
2.098
3
1.997
82
1.530
62
1.960
42
2.065
22
2.099
2
1.920
81
1.561
61
. 1.966
41
2.067
21
2.099
1
1.847
80
1.597
60
1.974
40
2.069
20
2.099
0
1.664
Digitized by VjOOQ IC
360 TABLE XXI.
Value of £1 per Annum during the joint Continuance of Tvo LiTet.
(Carlisle 3 per Cent.)
Older Age One Hundred Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
100
0.991
79
1.333
58
1.600
37
1.648
16
1.661
99
1.117
78
1.354
57
1.611
36
1.649
15
1.663
98
1.118
77
1.365
56
1.620
35
1.650
14
1.664
97
1.098
76
1.376
55
1.625
34
1.651
13
1.666
96
1.094
75
1.393
54
1.628
33
1.651
12
1.667
95
1.072
74
1.408
53
1.631
32
1.651
11
1.667
94
1.039
73
1.434
52
1.634
31
1.651
10
1.668
93
1.013
72
1.462
51
1.637
30
1.651
9
1.667
92
0.975
71
1.489
50
1.639
29
1.652
8
1.665
91
0.953
70
1.513
49
1.640
28
1.654
7
1.659
JO
0.979
69
1.527
48
1.640
27
1.657
6
1.651
89
1.052
68
1.537
47
1.640
26
1.659
5
1.637
88
1.080
67
1.544
46
1.638
25
1.660
4
1.613
87
1.093
66
1.550
45
1.638
24
1.660
3
1.585
86
1.129
65
1.555
44
1.637
23
1.661
2
1.528
85
1.170
64
1.559
43
1.637
22
1.661
1
1.476
84
1.213
63
1.564
42
1.638
21
1.661
0
1.337
83
1.242
62
1.567
41
1.639
20
1.661
82
1.268
61
1.571
40
1.641
19
1.661
81
1.289
60
1.577
39
1.644
18
1.661
80
1.316
59
1.588
38
1.646
17
1.661
Older Age One Hundred and One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
101
0.687
80
1.002
59
1.172
38
1.207
17
1.215
100
0.807
79
1.012
58
1.180
37
1.207
16
1.215
99
0.884
78
1.026
57
1.186
36
1.208
15
1.216
98
0.870
77
1.032
56
1.191
435
1.209
14
1.217
97
0.852
76
1.039
bi
1.194
*34
1.209
13
1.218
96
0.851
75
1.050
54
1.196
33
1.209
•12
1.219
95
0.835
74
1.060
53
1.197
32
1.209
11
1.219
94
0.811
73
1.077
52
1.199
31
1.209
10
1.219
93
0.794
72
1.095
51
1.201
30
1.209
9
1.219
92
0.767
71
1.113
50
1.202
29
1.209
8
1.217
91
0.753
70
1.127
49
1.202
28
1.211
7
1.213
90
0.776
69
1.135
48
1.202
27
1.213
6
1.208
89
0.833
68
1.140
47
1.201
26
1.214
5
1.199
88
0.847
67
1.144
46
1.201
25
1.214
4
1.182
87
0.853
66
1.148
45
1.200
24
1.215
3
1.165
86
0.879
65
1.151
44
1.200
23
1.215
2
1.126
85
0.909
64
1.153
43
1.201
22
1.215
1
1.093
84
0.937
63
1.156
42
1.201
21
1.215
0
.996
83
0.954
62
1.158
41
1.202
20
1.215
82
0.971
61
1.160
40
1.203
19
1.215
81
0.984
60
1.164
39
1.205
18
1.215
Digitized by LjOOQ IC
TABLE XXI.
351
Value of £1 per Annom during the joint Continuance of Two Litrei.
(Carliale 3 per Gent.)
Older Age One Hundred and Two Years.
Age.
▼aloe.'
Af^
Value.
Age.
Value.;
Agi.
Valu©.
Ar«.
Value.
102
0.387
81
0.645
60
0.739
39
0.759
18
0.764
101
0.497
80
0.655
59
0.743
38
0.760
17
0.764
lUO
0.558
79
0.660
58
0.747
37
0.761
16
0.765
99
0.597
78
0.667
57
0.750
36
0.761
15
0.765
98
0.579
77
0.670
56
0.753
35
0.761
14
0.766
97
0.568
76
0.673
55
0.754
34
0.761
13
0.766
96
0.571
75
0.680
54
0.755
33
0.761
12
0.766
95
0.560
74
0.685
53
0.755
32
0.761
11
0.766
94
0.545
73
0.695
52
0.756
31
0.761
10
0.767
93
0.536
72
0.705
51
0.757
30
0.761
9
0.766
92
0.520
71
0.714
50
0.758
29
0.762
8
0.765
91
0.513
70
0.721
49
0.758
23
0.763
7
0.763
90
0.530
69
0.724
48
0.758
27
0.763
6
0.760
89
0.566
68
0.726
47
0.757
26
0.764
5
0.755
88
0.570
67
0.728
46
0.757
25
0.764
4
0.746
87
0.572
66
0.730
45
0.757
24
0.764
3
0.737
86
0.589
65
0.732
44
0.757
',23
0.764
2
0.714
85
0.606
64
0.733
43
0.757
22
0.764
1
0.698
84
0.621
63
0.734
42
0.757
21
0.764
0
0.640
83
0.629
62
0.735
41
0.758
20
0.764
82
0.638
61
0.737
40
0.758
19
0.764
Older Age One Hundred and Three Years.
Age.
vaue.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
163
0.108
82
0.278
61
0.312
40
0.319
19
0.321
102
0.194
81
0.280
60
0.313
39
0.320
IS
0.321
101
0.231
80
0.284
59
0.314
38
0.320
17
0.321
100
0.252
79
0.285
58
0.316
37
0.320
16
0.321
99
0.265
78
0.288
57
0.317
36
0.320
15
0.322
98
0.254
11
0.289
56
0.317
35
0,320
14
0.322
97
0.252
76
0.290
55
0.318
34
0.320
13
0.322
96
0.253
75
0.293
54
0.318
33
0.320
12
0.322
95
0.248
74
0.294
53
0.318
32
0.320
11
0.322
94
0.243
73
0.298
52
0.319
31
0.320
10
0.322
93
0.240
72
0.302
51
0.319
30
0,320
9
0.322
92
0.233
71
0.305
50
0.319
29
0.320
8
0.321
91
0.231
70
0.307
49
0.319
28
0,321
7
0.321
90
0.239
69
0.308
48
0.319
27
0.321
6
0.320
89
0.254
68
0.309
47
0.319
26
0.321
5
0.318
88
0.252
67
0.309
46
0.319
25
0.321
4
0.314
87
0,254
66
0.310
45
0.319
24
0.321
3
0.311
86
0.261
65
0.310
44
0.319
23
0.321
2
0.303
85
0.267
64
0.311
43
0.319
22
0.321
1
0.298
84
0.272
63
0.311
42
0.319
21
0.321
0
0.274
83
0.275
62
0.312
41
0.319
20
0.321
Digitized by LjOOQ IC
(
352
TABLE XXI.
Value of £1 per Annum dnring the joint Continuance of Two Lires.
(Carlisle 4 per Cent.)
Older Age 0 Yeara.
Older Age One Year.
Age.
Value.
Age.
1
0
Valtt«.
0
8.896
11.924
10.296
Older Age Two Years.
Older Age
Three Years.
• Age.
Value.
Age.
3
2
1
0
Valoe.
2
1
0
13.671
12.765
11.018
15.260
14.442
13.483
11.636
Older Age Four Years.
Older Age Five Years.
Age.
Valoe.
4
16.147
3
15.696
2
14.854
1
13.867
0
11.965
Value.
16.801
16.469
16.009
15.150
14.142
12.201
Older Age Six Years.
Older Age Seven Years.
Age.
Value.
Age.
Value.
Age.
Valne.
Age.
Value.
6
5
4
3
17.112
16.954
16.620
16.155
2
1
0
15.287
14.269
12.311
7
6
6
4
17.242
17.175
17.017
16.681
3
2
1
0
16.214
15.341
14.321
12.356
Digitized by LjOOQ iC
TABLB XXL
353
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 4 per Cent)
Older Age Eight Years.
Older Age Nine Years.
Ap.
ValM.
Ag«.
ValM.
Age.
Valu©.
Age.
Value.
8
7
6
5
4
17.251
17.244
17.178
17.019
16.683
3
2
1
0
16.214
15.343
14.322
12.356
9
8
7
6
5
17.179
17.213
17.207-
17.140
16.982
4
3
2
1
0
16.644
16.178
15.308
14.288
12.328
Older Age Ten Years.
Older Age Eleven Years.
A««.
ValM.
Age.
V«ln«.
Age.
Value.
Age.
Value.
10
9
8
7
6
5
17.049
17.112
17.147
17.140
17.073
16.913
4
3
2
1
0
16.578
16.112
15.245
14.230
12.278
H
10
9
8
7
6
16.891
16.968
17.031
17.065
17.058
16.989
5
4
3
2
1
0
16.831
16.496
16.032
15.169
14.160
12.216
Older Age Twelve Years.
Older Age Thirteen Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
12
11
10
9
8
7
6
16.737
16.813
16.8S9
16.951
16.984
16.975
16.908
5
4
3
2
1
0
16.749
16.415
15.9.)3
15.095
14.089
12.156
13
12
11
10
9
8
7
16.582
16.65S
16.733
16.809
16.870
16.900
16.892
6
5
4
3
2
1
0
16.824
16.665
16.332
15.«73
15.017
14.017
12.094
DigBz^to by Google
354
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Litres.
(Carlisle 4 per Cent)
Older Age Fourteen Years.
Older Age Fifteen Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
14
13
12
11
10
9
8
7
16.425
16.502
16.578
16.651
16.726
16.785
16.816
16.806
6
5
4
3
2
1
0
16.737
16.579
16.248
15.789
14.938
13.943
12.031
15
14
13
12
11
10
9
8
16.272
16.347
16.424
16.498
16.570
16.643
16.702
16.732
7
6
5
4
3
2
1
0
16.721
16.652
16.494
16.163
15.706
14.860
13.870
11.968
Older Age Sixteen Years.
Older Age Seventeen Years.
Age.
Value.
Age.
Value.
Age.
Valufli
Age.
Value.
16
15
14
13
12
11
10
9
8
16.134
16.202
16.277
16.351
16.425
16.495
16.568
16.625
16.654
7
6
5
4
3
2
1
0
16.643
16.573
16.414
16.085
15.630
14.787
13.802
11.910
17
16
15
14
13
12
11
10
9
16.097
16.070
16.137
16.209
16.283
16.354
16.425
16.496
16.552
8
7
6
5
4
3
2
1
0
16.580
16.568
16.498
16.339
16.011
15.557
14.718
13.738
11.854
Older Age Eighteen
Years.
Older Age Nineteen Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
18
15.880
8
16.50 >
19
15.748
9
16.400
17
15.943
7
16.492
18
15.813
8
16.425
16
16.004
6
16.421
17
15. 874
7
16.411
15
16.070
5
16.263
16
15.934
6
16.341
14
16.141
4
15.935
15
15.999
5
16.182
13
16.213
3
15.483
14
16.068
4
15.855
12
16.285
2
14.64S
13
16.140
3
15.406
11
16.353
1
13.672
12
16.209
2
14.574
10
16.423
0
11.798
11
16.177
I
13.604
9
16.478
10
16.346
0
11.739
■ Digitized by VjOOQ iC
TABLE XXI.
355
Value of £1 per Axmum during^ the joint Coatinuance of Two livei.
(Carlisle 4 per Cent.)
Older Age Twenty Yeare.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
20
19
18
17
16
16
15.610
15.677
15.742
15.801
15.861
15.922
14
13
12
11
10
9
15.993
16.062
16.130
16.197
16.264
16.316
8
7
6
5
4
3
16.341
16.327
16.255
16.097
15.771
15.324
2
1
0
14.497
13..'i31
11.677
Older Age Twenty-One Years.
A««.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
21
20
19
18
17
16
15.466
15.536
15.603
16.666
15.724
15.781
15
14
13
12
11
10
15.844
15.911
15.980
16.046
16.112
16.177
9
8
7
6
5
4
16.229
16.253
16.237
16.166
16.007
15.683
3
2
I
0
15.238
14.415
13.455
11.612
Older Age Twenty-Two Yean.
Aije.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
22
21
20
19
18
17
15.310
15.387
15.456
15.521
15.582
15.639
16
15
14
13
12
U
15.696
15.756
15.822
15.889
15.955
16.018
10
9
8
7
6
5
16.083
16.134
16.156
16.141
16.068
15.910
4
3
2
1
0
15.588
15.145
14.326
13.373
11.541
Older Age Twenty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
23
22
21
20
19
18
17
15.148
15.228
15.303
15.370
15.434
15.493
15.550
16
15
14
13
12
11
10
15.604
15.663
15.728
15.794
15.857
15.920
15.983
9
8
7
6
5
4
3
16.032
16.055
16.038
15.965
15.808
15.487
15.046
2
1
0
14.234
13.286
11.467
Digit?e^b?G00gle
356
TABLE XXI.
Value of £1 per Annttm during the joint Continuance of Two Lives.
(Carlisle 4 per Cent)
Older Age Twenty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age
Value.
24
14.978
17
15.454
10
15.878
3
14.943
23
15.061
16
15.507
9
15.927
2
14.136
22
15.140
15
15.565
8
15.947
1
13.195
21
15.213
14
15.628
7
15.930
(1
11.389
20
15.280
13
15.692
6
15.857
19
15.341
12
15.755
5
15.701
18
15.400
11
15.816
4
15.380
Older Age Twenty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
25
24
23
22
21
20
19
14.800
14.888
14.970
15.046
15.118
15.182
15.243
18
17
16
15
14
13
12
15.300
15.352
15.404
15.460
16.522
15.585
15.646
11
10
9
8
7
6
5
15.706
15.768
15.814
15.833
15.816
15.743
15.586
4
3
2
1
0
15.269
14.834
14.033
13.099
11.307
Older Age Twenty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
26
26
24
23
22
21
20
14.620
14.709
14.795
14.874
14.950
15.019
15.083
19
18
17
16
15
14
13
15.141
15.196
15.248
15.298
15.352
15.413
15.475
12
11
10
9
8
7
6
15.534
15.594
15.652
15.698
15.717
15.699
15.625
5
4
3
2
1
0
15.470
15.154
14.722
13.927
13.001
11.223
Older Age Twenty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
27
26
25
24
23
22
21
14.431
14.524
14.611
14.695
14.773
14.846
14.915
20
19
18
17
16
15
14
14.976
15.033
15.086
15.136
15.185
15.238
15.297
13
12
11
10
9
8
7
15.357
15.417
15.473
15.531
15.576
15.594
lb. 574
6
5
4
3
2
1
0
15.502
15.347
15.033
14.605
13.816
12.897
11.134
Digitized by VjOOQ IC
TABLE XXI.
357
Value of £1 per Annam during the joint Continuance df Two Lives*
(Carlisle 4 per Cent.)
Older Age Twenty-Eight Years.
Age.
Valae.
Age.
Value. •
Ago.
Value.
Age.
Value.
28
14.244
20
14.868
12
15.296
4
14.911
27
14.336
19
14.924
11
15.352
3
14.486
26
14.4-27
18
14.975
10
15.409
2
13.703
25
14.512
17
15.024
9
15.453
1
12.792
24
14.594
16
15.071
8
15.469
0
11.044
23
14.670
15
15.123
7
15.450
22
14.742
14
15.180
6
15.377
21
14.808
13
15.240
5
15.223
Older Age Twenty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
29
14.075
21
14.709
13
15.128
5
15.106
28
14.158
20
14.767
12
15.184
4
14.797
27
14.249
19
14.821
11
15.239
3
14.374
26
14.337
18
14.871
10
15.295
2
13.597
25
14.421
17
14.918
9
15.336
1
12.694
24
14.500
16
14.965
8
15.353
0
10.960
23
14.575
15
15.015
7
15.333
22
14.644
14
15.072
6
15.260
Older Age Thirty Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
30
13.930
22
14.557
14
14.973
6
15.154
29
14.001
21
14.621
13
15.029
5
15.001
28
U.083
20
14.677
12
15.083
4
14.693
27
14.171
19
14.729
11
15.137
3
14.273
26
14.258
18
14.778
10
15.190
2
13.502
25
14.339
17
14.824
9
15.233
1
12.605
24
14.417
16
14.868
8
15.248
0
10.883
23
14.490
15
14.918
7
15.227
Older Age Thirty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
31
13.784
23
14.402
15
14.818
7
15.119
30
13.856
22
14.468
14
14.872
6
15.046
29
13.925
21
14.530
13
14.926
5
14.893
28
14.004
20
14.584
12
14.980
4
14.587
27
14.091
19
14.635
11
15.031
3
14.170
26
14.176
18
14.683
10
15.085
2
13.404
25
14.255
17
14.726
9
15.126
1
12.514
24
14.331
16
14.771
8
15.140
0
10.806
Digitized by VjOOQ IC
358
TABLE XXI.
Value of £1 per Annum during the joint Gontinaance of Two Li?ei.
(Cftiliiil« 4 per Cent.)
Older Age Thirty-Two Yean.
Ajlt.
Value.
Aire.
Value.
Age.
Value.
A«e.
Value.
32
13.632
•23
14.309
14
14.765
5
14.780
31
13.707
22
14.374
13
14.819
4
14.476
30
13.777
21
14.433
12
14.870
3
14.062
•^9
13.844
20
14.496
11
14.922
2
13.301
28
13.921
19
14.536
10
14.974
1
12.419
27
14.006
18
14.581
9
15.013
0
10.725
26
14.088
17
14.625
6
15.027
25
14.166
16
14.666
7
15.006
24
14.240
15
14.713
6
14.932
Older Age thirty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
33
13.469
24
14.140
15
14.599
6
14.810
32
13.550
23
14.208
14
14.651
5
14.659
31
13.622
22
14.270
13
14.702
4
14.357
30
13.689
21
14.328
12
14.754
3
13.945
29
13.755
20
14.380
11
14.803
2
13.192
28
13.830
19
14.427
10
14.854
1
12.317
27
13.912
18
14.473
9
14.893
0
10.637
26
13.993
17
14.513
8
14.906
25
13.068
16
14.554
7
14.883
Older Age Thirty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value. 4
Age.
Value.
34
13.294
25
13.961
16
14.433
7
14.752
33
13.381
24
14.032
15
14.477
6.
14.679
32
13.459
23
14.097
14
14.526
5
14.523
31
13.528
22
14.157
13
14.578
4
14.228
30
13.594
21
14.214
12
14.627
3
13.821
29
13.657
20
14.263
11
14.676
2
13.074
28
13.730
19
14.311
10
14.726
1
12.208
27
13.809
18
14.353
9
14.763
0
10.544
26
13.888
17
14.393
8
14.775
»
Digitized by^^UUVlC
TABLE XXI.
359
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 4 per Cent.)
Older Age Thirty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
35
13.111
26
13.777
17
14.266
8
14.637
34 ,
13.202
25
13.848
16
14.305
7
14.615
33
13.285
24
13.916
15
14.347
6
14.541
32
13.360
23
13.980
14
14.396
5
14.391
31
13.428
22
14.039
13
14.446
4
14.094
30
13.491
21
14.093
12
14.494
3
13.690
29
13.552
20
14.142
11
14.542
2
12.951
28
13.622
19
14.186
10
14.590
I
12.093
27
13.700
18
14.228
9
14.626
0
10.446
Older Age Thirty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value. '
36
12.919
26
13.658
16
14.169
6
14.396
35
13.014
25
13.727
15
14.211
5
14.248
34
13.102
24
13.794
14
14.258
4
13.953
33
13.182
23
13.855
13
14.307
3
13.553
32
13.255
22
13.912
12
14.354 •
2
12.821
31
13.321
21
13.966
11
14.400
1
11.973
30
13.381
20
14.012
10
14.447
0
10.343
29
13.440
19
14.055
9
14.483
28
13.508
18
14.096
8
14,493
27
13.584
17
14.133
7
14.470
Older Age Thirty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
37
12.724
27
13.462
17
13.993
7
• 14.320
36
12.821
26
13.535
16
14.030
6
14.247
35
12.912
25
13.602
15
14.070
5
14.100
34
12.997
24
13.666
14
14.116
4
13.808
33
13.075
23
13.726
13
14.163
3
13.412
32
13.146
22
13.782
12
14.209
2
12.688
31
13.208
21
13.832
11
14.254
1
11.849
30
13.267
20
13.877
10
14.300
0
10.237
29
13.323
19
13.920
9
14.334
^
13.390
18
13.958
8
14.344
360
TABLE XXI.
Valae of £1 per Annum durini^f the joint Continuance of Tiro Lives*
(Carlisle 4 per Cent.)
Older Age Thirty-Eight Years.
A«e.
y^ue.
Age.
Value.
Age.
Value.
Age.
Valaa.
38
12.525
28
13.265
18
13.815
8
14.190
37
12.624
27
13.336
17
13.851
7
14.166
36
12.717
26
13.407
16
13.885
6
14.093
35
12.805
25
13.472
15
13.924
5
13.947
34
12.887
24
13.534
14
13.969
4
13.658
33.
12.964
23
13.593
13
14.015
3
13.266
32
13.031
22
13.645
12
14.059
2
12.550
31
13.091
21
13.650
11
14.103
1
11.721
30
13.147
20
13.739
10
14.148
0
10.127
29
13.201
19
13.779
9
14.181
Older Age Thirty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
39
12.322
29
13.074
19
13.632
9
14.023
38
12.423
28
13.136
18
13.669
8
14.031
37
12.617
27
13.205
17
13.702
7
14.007
36
12.607
26
13.273
16
13.736
6
13.934
35
12.693
25
13.336
15
13.773
5
13.789
34
12.773
24
13.398
14
13.817
4
13.503
33
12.845
23
13.452
13
13.861
3
13.116
32
12.910
22
13.504
12
13.905
2
12.408
31
12.969
21
13.552
11
13.947
1
11.589
30
13.022
20
13.594
10
13.991
0
10.014
Older Age Forty Ycani,
Ago.
Valae.
Age.
Value.
1
Age.
Value.
Age.
Value.
40
12.126
29
12.947
18
13.522
7
13.848
39
12.222
28
13.007
17
13.555
6
13.776
38,
12.319
27
13.074
16
13.587
5
13.632
37
12.411
26
13.140
15
13.623
4
13.349
36
12.498
25
13.202
14
13.665
3
12.966
35
12.581
24
13.269
13
13.708
3
12.266
34
12.657
23
13.313
12
13.751
1
11.457
33
12.727
22
13.363
11
13.792
0
9.902
32
12.790
21
13.410
10
13.835
31
12.846
20
13.449
9
13.866
30
12.897
19
13.488
8
13.873
Digitized by LjOOQ IC
TABLE XXI.
361
> Valae of £1 per Anmmi duriofi; the joint Contmoanee of Two Lives.
(Carlisle 4 per Cent;
Older Age Forty-One Years.
Age.
Talne.
Age.
Yftlae.
Ag...
Valae.
Age.
Value.
41
11.945
30
12.778
19
13.348
8
13.721
40
12.034
29
12.826
18
13.382
7
13.696
39
12.127
28
12.884
17
13.413
6
13.624
38
12.221
27
12.948
16
13.444
5
13.481
37
12.309
26
13.014
15
13.479
4
13.201
36
12.394
25
13.071
14
13.520
3
12.822
35
12.473
24
13.128
13
13.562
2
12.130
34
12.547
23
13.180
12
13.603
1
11.331
33
12.615
22
13.228
11
13.644
0
9.794
32
12.675
21
13.272
10
13.685
31
12.728
20
13.312
9
13.715
Older Age Forty-Two Years.
Ag«.
Value.
Age.
VslM.
Age.
Valae.
Age.
Value.
42
11.772
31
12.612
20
13.176
9
13.565
41
11.857
30
12.660
19
13.210
8
13.571
40
11.942
29
12.705
18
13.243
7
13.546
39
12.032
28
12.761
17
13.273
6
13.474
38
12.123
27
12.825
16
13.302
5
13.332
37
12.209
26
12.S85
15
13.336
4
13.056
36
12.290
25
12.942
14
13.376
3
12.680
35
12.367
24
12.9U7
13
13.417
2
11.996
34
12.438
23
13.048
12
13.4.^8
1
11.206
33
12.503
22
13.094
11
13.496
0
9.687
32
12.560
21
13.138
lU
13.536
Older Age Forty-Three Years.
Age.
Valae.
Age.
Value.
Age.
Value.
Age.
Value.
43
11.602
32
12.445
21
13.001
10
13.387
42
11.686
31
12.494
20
13.038
9
13.415
41
11.767
30
12.539
19
13.071
8
13.420
40
11.849
29
12.583
18
13.103
7
13-394
39
11.936
28
12.638
17
13.131
6
13.323
38
12.024
27
12.697
16
13.160
5
13.182
37
12.106
26
12.757
15
13.192
4
12.907
36
12.184
25
12.812
14
13.231
3
12.536
35
12.259
24
12.865
13
13.272
2
11.861
34
12.327
23
12.914
12
13.310
1
11.081
33
12.389
.24,
12.960
11
13.348
0
9.580
Digitized by LjOOQ IC
362
TABLE XXI.
Value of £1 per Annum duriof the joint Continuance of Two Lifei.
(Carlisle 4 per Cent.)
Older Age Forty-Four Years.
Age.
Value.
11.426
Age.
Value.
A^.
Value.
Age.
Value.
44
32
12.322
20
12.893
8
13.262
43
11.513
31
12.369
19
12.926
7
13.236
42
11.592
30
12.412
18
12.955
6
13.165
41
11.670
29
12.455
17
12.982
5
13.025
40
11.749
28
12.505
16
13.010
4
12.752
39
11.833
27
12.564
15
13.D41
3
12.387
38
11.917
26
12.622
14
13.080
2
11.720
37
11.996
25
12.675
13
13.117
1
10.949
36
12.072
24
12.726
12
13.155
0
9.468
35
12.143
23
12.774
11
13.192
34
12.208
22
12.817
10
13.230
33
12.269
21
12.858
9
13.257
Older Age Forty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
45
11.243
33
12.141
21
12.706
9
13.092
44
11.333
32
12.191
20
12.741
8
13.096
43
11.416
31
12.236
19
12.771
7
13.070
42
11.491
30
12.278
18
12.800
6
12.999
41
11.566
29
12.317
17
12.826
5
12.859
40
11.641
28
12.366
16
12.852
4
12.592
39
11.722
27
12.423
15
12.884
3
12.230
38
11.802
26
12.479
14
12.919
2
11.572
37
11.879
25
12.530
13
12.957
1
10.812
36
11.951
24
12.580
12
12.993
0
9.350
35
12.019
23
12.626
U
13.029
34
12.083
22
12.668
10
13.066
Older Age Forty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value
46
11.047
34
11.946
22
12.507
10
12.891
45
11.143
33
12.001
21
12.545
9
12.916
44
11.229
32
12.050
20
12.577
8
12.919
43
11.307
31
12.093
19
12.606
7
12.892
42
11.380
30
12.130
18
12.634
6
12.820
41
11.450
29
12.169
17
12.659
5
12.685
40
11.523
28
12.216
16
12.635
4
12.420
39
11.600
27
12.271
15
12.714
3
12.064
38
11.677
26
12.325
14
12.749
2
11.414
37
11.751
25
12.375
13
12.785
1
10.666
36
11.819
24
12.422
12
12.821
0
9.226
35
11.886
23
12.467
11
12.855
Digitized by LjOOQ IC
TABLE XXI.
363
Value of £1 per Annum during the Joint Continuance of Two Lifee.
(Carlisle 4 per Cent.)
Older Age Forty-Seven Yeaw.
Age.
Value.
Age.
Valne.
Age.
Valoe.
Age.
Value.
47
10.837
33
11,740
23
12.296
11
12.670
46
10.940
34
11.798
22
12.336
10
12.704
45
11.031
33
11.850
21
12.371
9
12.728
44
11.113
32
11,897
20
12.402
8
12.731
43
11.188
31
11.936
19
12.430
7
12,702
42
11,256
30
11.973
18
12.456
6
12.634
41
11.324
29
12.009
17
12.481
5
12.497
40
11.392
28
12.055
16
12.505
4
12.237
39
11.466
27
12.107
15
12.533
3
11.886
38
11,541
26
12.160
14
12.567
2
11.247
37
11.610
25
12.207
13
12.602
1
10.511
36
11.677
24
12.254
12
12.636
0
9.094
Older Age Forty-Eight Years.
Aii.
,Vela«.
Age.
Value.
Age.
Value.
Age.
Value.
48
10.607
35
11.579
22
12.148
9
12.278
47
10.720
34
11.634
21
12.182
8
12.525
46
10.818
33
11.685
20
12.212
7
12.500
45
10.905
32
11.728
19
12.239
6
12.430
44
10.983
31
11.766
18
12.264
5
12.297
43
11.053
30
11.801
17
12.287
4
12.040
42
11.118
29
11.834
16
12.310
3
11.694
41
11.182
28
11.878
15
12.337
2
11.067
40
11.247
27
11.929
14
12.370
1
10.344
39
11.318
26
11.979
13
12.403
0
8.952
38
11.388
25
12.025
12
12.436
37
11.456
24
12.069
U
12.469
36
11.519
23
12.111
10
12.502
Older Age Forty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
49
10.345
36
11.339
23
11.902
10
12.278
48
10.474
35
11.396
22
11.938
9
12.298
47
10.581
34
11.449
21
11.971
8
12.300
46
10.675
33
11.496
20
11.999
7
12.273
45
10.757
32
11.537
19
12.025
6
12.205
44
10.830
31
11.573
18
12.049
5
12.074
43
10.897
30
11.606
17
12.071
4
11.820
42
10.958
29
11.638
16
12.093
3
11.482
41
11.019
28
11.679
15
12.119
2
10.866
40
11.080
27
11.728
14
12.150
1
10.158
39
11.146
26
11.776
13
12.182
0
8.793
38
11.215
25
11.821
12
12.214
37
11.279
24
11.864
11
12.245
Digitized
byV^ooyi
364
TABLE XXI.
Value of £1 per Annum during the Joint Continuance of Two Lives.
(Carliftle 4 per Cent.)
Older Age Fifty Years.
Age.
VollM.
Age.
Valae.
Age.
Value.
Age.
Value. ^
50
10.059
37
11.084
24
11.639
11
12.004
49
10.200
36
11.141
23
11.677
10
12.034
48
10.322
35
11.196
22
11.711
9
12.056
47
10.425
34
11.245
21
11.743
6
12.056
46
10,513
33
11.290
20
11.769
7
12.029
45
10.591
32
11.329
19
11.794
6
11.961
44
10.661
31
11.362
18
11.816
5
11.832
43
10.723
30
11.393
17
11.837
4
11.585
42
10.781
29
11.423
16
11.858
3
11.253
41
10.837
28
11.463
1.^
11.882
2
10.650
40
10.894
27
11.509
14
11.912
1
9.958
39
10.959
26
11.556
13
11.944
0
8.621
38
11.023
25
11.599
12
11.974
Older Age Fifty-One Years.
Ag<i.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
51
9.748
38
10.812
25
11.357
12
11.715
50
9.901
37
10.809
24
11.396
11
11.743
49
10.035
36
10.924
23
11.432
10
11.774
48
10.152
35
10.975
22
11.465
9
11.793
47
10.249
34
11.022
21
11.494
8
11.793
46
10.332
33
11.064
20
11.520
7
11.766
45
10.407
32
11.101
19
11.543
6
11.699
44
10.471
31
11.132
18
11.565
5
11.573
43
10.530
30
11.161
17
11.584
4
11.330
42
10.583
29
11.190
16
11.603
3
11.007
41
10.635
28
11.227
15
11.627
2
10.418
40
10.691
27
11.272
14
11.656
1
9.741
39
10.751
26
11.317
13
11.686
0
8.439
Older Age Fifty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
52
9.434
39
10.537
26
11.071
13
11.423
51
9.589
38
10.594
25
11.110
12
11.450
50
9.735
37
10.649
24
11.147
11
11.478
49
9.863
36
10.700
23
11.182
10
11.506
48
9.974
35
10.748
22
11.212
9
11.525
47
10.065
34
10.792
21
11.241
8
11.524
46
10.145
33
10.832
20
11.265
7
11.497
45
10.214
32
10.866
19
11.287
6
11.432
44
10.274
31
10.896
18
11.307
5
11.308
43
10.329
30
10.923
17
11.325
4
'11.071
42
10.378
29
10.950
16
11.344
3
10.755
41
10.429
28
10.986
15
11.367
2
10.179
40
10.480
27
t
11.029
14
11.394
1
0
9.523
8.251
Digitized by VjUU V IC "
TABLE XXI.
3G5
Value of £1 per Annum during the joint Continnance of Two liives.
(Carlisle 4 per Cent)
Older Age Fifty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Valoe.
53
9.117
42
10.167
31
10.653
20
11.004
9
11.251
52
9.273
41
10.213
30
10.678
19
11.025
8
11.249
51
9.420
40
10.261
29
10.703
18
11.043
7
11.223
50
9.560
39
10.314
28
10.738
17
11.061
6
11.158
49
9.682
38
10.369
27
10.778
16
11.078
5
11.037
48
9.787
37
10.420
26
10.819
15
11.100
4
10.806
47
9.875
36
10.468
25
10.856
14
11.126
3
10.496
46
9.949
35
10.514
24
10.892
13
11.153
2
9.939
45
10.013
34
10.555
23
10.924
12
11.180
1
9.299
44
10.070
33
10.593
22
10.954
11
11.206
0
8.060
43
10.120
32
10.625
21
10.981
10
11.233
Older Age Fifty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
10
Value.
54
8.796
43
9.904
32
10.377
21
10.715
10.954
53
8.953
42
9.947
31
10.403
20
10.736
9
10.970
52
9.102
41
9.989
30
10.426
19
10.755
8
10.968
51
9.243
40
10.034
29
10.450
18
10.774
7
10.942
50
9.376
39
10.084
28
10.483
17
10.790
6
10.878
49
9.492
38
10.135
27
10.522
16
10.806
5
10.760
48
9.593
37
10.183
26
10.560
15
:0.826
4
10.533
47
9.674
36
10.229
25
10.596
14
10.851
3
10.235
46
9.744
35
10.272
24
10.629
13
10.878
2
9.691
45
9.804
34
10.311
23
10.661
12
10.903
1
9.069
44
9.856
33
10.347
22
10.689
11
10.928
0
7.864
Older Age Fifty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
55
8.465
43
9.676
31
10.142
19
10.477
7
10.651
54
8.627
42
9.715
30
10.164
18
10.494
6
10.589
53
8.777
41
9.754
29
10.187
17
10.509
5
10.472
52
8.920
40
9.796
28
10.218
16
10.524
4
10.255
51
9.054
39
9.843
27
10.254
15
10.543
3
9.964
50
9.181
38
9.891
26
10.292
14
10.567
2
9.435
49
9.291
37
9.937
25
10.325
13
10.592
1
8.832
48
9.386
36
9.979
24
10.358
12
10.616
0
7.661
47
9.463
35
10.020
23
10.387
11
10.640
46
9.527
34
10.057
22
10.414
10
10.664
45
9.583
33
10.090
21
10.438
9
10.680
44
9.632
32
10.119
20
10.458
^ 8
10.678
Digitized by LjOOQ IC
TABLE Xn.
Value of £ I per Annum during the joint Continuance of Two Lirei.
(Carlisle 4 per Cent.)
Older Age Fifty-Six Yean.
A«e.
Value.
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
8
Value.
56
8.128
44
9.398
32
9,851
20
10.173
10,379
55
8*293
43
9,438
31
9.873
19
10.190
;
10.353
54
8.448
42
9.474
30
9.894
18
10.20G
6
10.291
53
8.592
41
9.510
29
9.915
17
10.220
5
10.180
52
8.727
40
9.549
28
9.944
16
10.234
4
9,967
51
8.855
39
9.593
27
9.980
15
10,252
3
9.685
50
8.976
38
9.638
26
10.015
14
10.275
2
9.173
49
9.080
37
9.681
25
10.047
13
10.299
1
8.589
48
9.169
36
9.721
24
10.078
12
10.322
0
7.454
47
9.241
35
9.759
23
10.106
11
10.344
46
9.301
34
9.794
22
10.131
10
10.368
45
9.353
33
9.825
21
10.154
9
10.382
Older Age Fifty-Seven Years.
Age.
Valee.
Age
Value.
Age.
Value.
Age.
Value.
Age.
9
Value.
57
7.783
45
9.113
33
9.551
21
9.862
10.076
56
7.952
44
9.154
32
9.575
20
9.880
8
10.073
55
8.110
43
9.190
31
9.597
19
9.896
7
10.046
54
8.258
42
9.223
30
9.616
18
9.910
6
9.988
53
8.395
41
9.256
29
9,635
17
9.923
5
9.879
52
8.524
40
9.292
28
9.663
16
9.937
4
9.673
51
8.64.')
39
9.333
27
9.696
15
9.953
3
9.400
50
8.760
38
9.375
26
9.730
14
9.975
2
8.904
49
8.858
37
9.416
25
9.761
13
9.998
1
8,339
48
8.942
36
9.453
24
9.790
12
10.019
0
7.240
47
9.009
35
9.489
23
9.816
11
10.041
46
9.065
34
9.522
22
9.840
10
10.063
Older Age Fifty-Eight
Years.
Age.
Value.
Age.
46
Value.
Age.
Value.
Age.
22
Value.
Age.
Value.
58
7.444
8.825
34
9.248
9.548
10
9.758
57
7.610
45
8.869
33
9.275
21
9.569
9
9.771
56
7.771
44
8.906
32
9.299
20
9.585
8
9.766
55
7.922
43
8.940
3t
9.318
19
9.600
7
9.742
54
8.063
42
8.969
30
9.336
18
9.614
6
9.684
53
8.194
41
9.000
29
9.354
17
9.626
5
9.578
52
8.316
40
9.033
28
9.380
16
9.638
4
9.379
51
8.431
39
9.071
27
9.412
15
9.654
3
9.114
50
8.540
38
9.111
26
9.444
14
9.675
2
8.635
49
8.633
37
9.148
25
9.473
13
9.696
1
8.089
48
8.711
36
9.184
24
9.501
12
9.717
0
7.026
47
8.774
35
9.217
23
9.526
11
9,737
Digitized by LjOOQ iC
TABLE XXL 36/
Valoe of £1 per Annum daring the joint Continuance of Two Life>^\^ - .
(Carliile 4 per Cent)
Older Age Fifty-Nine Years.
Age
Value.
Age.
Valufi.
Age.
35
Value.
Age.
Valoe.
Age.
Value.
59
7.131
47
8.547
8.957
23
9.248
11
9.447
58
7.284
46
8.595
34
8.986
22
9.270
10
9.467
57
7.443
45
8.635
33
9.012
21
9.2»9
9
9.478
56
7.597
44
8.669
32
9.0S4
20
9.304
8
9.476
55
7.7^1
43
8.699
31
9.051
19
9.318
7
9.450
54
7.876
42
8.726
30
9.068
18
9.331
6
9«394
53
8.000
41
8.754
29
9.085
17
9.342
5
9.291
52
8.116
40
8.784
28
9.110
16
9.351
4
9.097
51
8.225
39
8.820
27
9.140
15
9.369
3
8.842
50
8.328
38
8.857
26
9.171
14
9.388
2
8.378
49
8.416
37
8.892
25
9.198
13
0.408
1
7.851
48
8.490
36
8.926
24
9.225
12
9.428
0
6.822
Older Age Sixty Years.
Ag».
Value.
Age.
Value.
Age.
Value.
Age.
21
Value.
Age.
Value.
60
6.854
47
8.337
84
8.743
9.029
8
9.203
59
6.989
46
8.381
33
8.767
20
9.043
7
9.179
58
7.136
45
8.417
32
8,787
19
9.056
6
9.124
57
7.289
44
8.448
31
8.804
18
9.068
5
9.024
56
7.437
43
8.475
30
8.820
17
9.078
4
8.836
55
7.574
42
8.500
29
8.835
16
9.089
3
8.589
54
7.703
41
8.525
28
8.859
15
9.103
2
8.1.39
53
7.821
40
8.553
27
8.888
14
9.122
1
7.629
52
7.931
39
8.587
26
8.917
13
9.141
0
6.632
51
8.035
38
8.622
25
8.943
12
9.159
50
8.132
37
8.655
24
8.968
11
9.178
49
8.214
36
8.686
23
8.991
10
9.196
48
8.283
35
8.716
22
9.011
9
9.207
Older Age 1
Sixty-One Years.
Age.
Value.
Age.
Value.
Age.
35
Value.
Aire.
Value.
Age.
Value.
61
6.630
48
8.104
8.504
22
8.783
9
8.969
60
6.739
47
8.153
34
8.530
21
8.800
8
8.964
59
6.869
46
8.193
33
8.552
20
8.814
7
8.940
58
7.010
45
8.227
32
8.572
19
8.826
6
8.887
57
7.157
44
8.255
31
8.587
18
8.837
5
8.789
56
7.299
43
8.279
30
8.602
17
8.847
4
8.606
55
7.431
42
8.302
29
8.616
16
8.857
3
8.366
54
7.553
41
8.325
28
8.639
15
8.870
2
7.929
53
7.666
40
8.350
27
8.666
14
8.887
1
7.434
52
7.771
39
8.382
26
8.694
13
8.905
0
6.465
51
7.869
38
8.415
25
8.719
12
8.9Z3
50
7.962
37
8.446
24
8.743
11
8.940
49
8.039
36
8.476
23
8.764
10
8.958
Digitized by VjOOQ IC
368
TABLE XXL
Vodue of £1 per Annum during the joint Continuuice of Two Lives.
(Carlisle 4 per Cent)
Older Age Sixty-Two Years.
Ag«.
Value.
Age.
Valiw.
Age.
Value. J Afe.
Value.
62
6.417
42
8.104
22
8.558 2
7.721
61
6.521
41
8.125
21
8.574 1
7.242
60
6.625 .
40
8.149
20
8.587 U
6.301
59
6.749
39
8.179
19
8.598
58
6.884
38
8.210
18
8.608
67
7.025
37
8.239
17
8.617
56
7.161
36
8.268
16
8.626
65
7.287
35
8.294
15
8.639
54
7.404
34
8.318
14
b.655
53
7.511
33
8.340
13
8.673
52
7.611
32
8.358
12
8.690
51
7.704
31
8.372
11
8.706
50
7.791
30
8. 386
10
8.723
49
7.864
29
8.400
9
8.733
48
7.925
28
8.421
8
8.728
47
7.970
27
8.447
7
8.704
46
8.007
26
8.474
6
8.652
45
8.037
25
8.498
6
8.557
44
8.062
24
8.520
4
8.379
43
8.085
23
8.540
3
8.146
Older Age Sixty-Three Years.
Age,
Value.
Age.
Value.
Ape.
Value.
Ag«.
Value.
63
6 202
43
7.884
23
8.311
3
'.822
62
6.307
42
7.901
22
8.328
2
7.510
61
6.405
41
7.921
21
8.343
I
7.046
60
6.504
40
7.943
20
8.355
0
6.134
59
6.622
39
7.970
.19
8.366
68
6.752
38
8. 000
18
8.375
57
6.887
37
8.028
17
8.383
56
7.017
36
8.054
16
8.392
55
7.137
35
8.079
15
8.403
54
7.248
34
8.102
14
8.419
53
7.350
33
8.122
13
8.436
52
7.444
32
8.139
12
8.452
51
7.533
31
8.153
n
8.467
50
7.615
30
8.165
10
8.483
49
7.683
29
8.178
9
8.493
48
7.739
28
8.198
8
8.488
47
7.781
27
8.223
7
8.464
46
7.814
26
8.249
6
8.413
45
7.842
25
8.271
5
8.341
44
7.864
24
8.293
4
8.148
Digitized by VjOOQ IC
TABLE XXI.
369
Valoe of £1 per Annum during the Joint Continuance of Two Lives.
(Carliile 4 per Cent)
Older Age Sixty-Four Years.
Af«.
ValM.
Af«.
ValM.
Age.
Value.
Age.
Value.
64
5.974
44
7.651
24
8.051
4
7.904
63
6.085
43
7.669
23
8.069
3
7.685
62
6.184
42
7.685
22
8.085
2
7.288
61
6.277
41
7.702
21
8.099
1
6.840
60
6.370
40
7.723
20
8.110
0
5.958
59
6.482
39
7.748
19
8.120
58
6.606
38
7.776
18
8.128
57
6.735
37
7.802
17
8.136
56
6.858
36
7.827
16
8.144
65
6.973
35
7.851
15
8.155
54
7.078
34
7.872
14
8.169
53
7.174
33
7.891
13
8.185
52
7.264
32
7.907
12
8.200
51
7.346
31
7.919
11
8.215
50
7.423
30
7.931
10
8.231
49
7.487
29
7.943
9
8.239
48
7.539
28
7.962
8
8.234
47
7.577
27
7.986
7
8.210
46
7.607
26
8.010
6
8.161
45
7.6S1
25
8.031
5
8.071
Older Age Sixty-Five Years.
Age.
Value.
Age.
Vttloe.
Age.
V»Ioa.
Age.
Value.
65
5.738
45
7.411
25
7.783
5
7.<514
64
5.853
44
7.429
24
7.802
4
7.652
63
5.958
43
7.445
23
7.819
3
7.441
62
6.050
42
7.459
22
7.833
2
7.053
61
6.138
41
7.474
21
7.846
1
6.627
60
6.225
40
7.493
20
7.856
0
5.777
59
6.332
39
7.517
19
7.865
58
6.450
38
7.543
18
7.873
57
6.672
37
7.568
17
7.880
56
6.690
36
7.591
16
7.857
55
6.798
35
7.614
16
7.897
54
6.898
34
7.634
14
7.911
63
6.988
33
7.651
13
7.926
52
7.072
32
7.666
12
7,941
51
7.149
31
7.677
11
7.954
50
7.221
30
7.688
10
7.969
49
7.280
•29
7.699
9
7.977
48
7.328
2d
7.717
8
7.971
47
7.363
•27
7.740
7
7.948
46
7.390
26
7.762
6
7.900
DigLd by Google
370
TABLE XXI.
Value of £1 per Annum daring the joint Continuance of Two Livei.
(Carliile 4 per Cent.)
Older Age Sixty-Six Years.
Age.
Value.
Age.
Value.
Agi*.
Value.
Age.
Value.
66
5.490
46
7.159
26
7.503
6
7.628
65
5.611
45
7.178
25
7.522
5
7.544
64
5.718
44
7.194
24
7.540
4
7.389
63
6.817
43
7.207
23
7.556
3
7.186
62
5.904
42
7.219
22
7.569
2
6.818
61
5.986
41
7.234
21
7.581
1
6.405
60
6.068
40
7.251
20
7.591
0
5.587
69
6.1G9
39
7.273
19
7.599
58
6.280
38
7.298
18
7.606
57
6.396
37
7.321
17
7.612
56
6.508
36
7.343
16
7.618
55
6.610
35
7.364
15
7.628
54
6.704
34
7.383
14
7.641
53
6.788
33
7.399
13
7.655
52
6.866
32
7.412
12
7.669
51
6.939
31
7.423
11
7.682
50
7.005
30
7.433
10
7.695
49
7.060
29
7.443
9
7.703
43
7.104
28
7.460
8
7.697
47
7.135
27
7.481
7
7.675
Older Age Sixty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.-
Value.
67
5.228
47
6.893
27
7.210
7
7.388
66
5.355
46
6.914
26
7.230
6
7.343
65
5.468
45
6.931
25
7.248
5
7.263
64
5.570
44
6.944
24
7.265
4
7.113
63
5.662
43
6.956
23
7.280
3
6.919
62
5.743
42
6.967
22
7.292
2
6.567
61
5.819
41
6.979
21
7.363
1
6.172
60
5.895
40
6.995
20
7.312
0
5.388
59
5.990
39
7.016
19
7.319
58
6.095
38
7.039
18
7.325
57
6.205
37
7.061
17
7.331
56
6.310
36
7.081
16
7.337
55
6.406
35
7.101
15
7.346
54
6.494
34
7.118
14
7.358
53
6.573
33
7.134
13
7.371
■■i
0.6 Ifi
32
7.146
12
7.384
.,1
U 713
31
7.156
11
7.396
:->{)
eu77'o
30
7.164
10
7.409
A9
e.'^-i'j
29
7.174
9
7.416
4«
6.HG.1
L'8
7.190
8
7.410
Digitized by LjOOQ iC
TABLE XXI.
371
Valiia of £1 per Aoanai during the joint Coatinaaace of Two Litea,
(Carliile 4 per Cent)
Older Age Sixty-Eight Years.
Axe.
V«lu«.
Age.
Value.
Age.
Value.
Age.
Value.
68
4.954
48
6.612
28
6.908
8
7.112
67
5.087
47
6.638
27
6.927
7
7.091
66
5.206
46
6.656
26
6.946
6
7.047
65
5.312
45
6.671
25
6.963
5
6.970
64
5.407
44
6.682
24
6.979
4
6.827
63
5.493
43
6.692
23
6.992
3
6.643
62
5.567
42
6.702
22
7.004
2
6.306
61
5.638
41
6.713
21
7.014
1
6.930
60
5.709
40
6.728
20
7.021
0
5.181
59
5.79S
39
6.747
19
7.028
58
5.897
38
6.769
18
7.034
57
6.001
37
6.789
17
7.039
56
6.099
36
6.808
16
7.044
55
6.189
35
6.826
15
7.052
54
6.271
34
6.842
14
7.064
53
6.344
33
6.857
13
7.077
52
6.411
32
6.868
12
7.088
51
6.473
31
6.877
11
7.100
50
6.531
30
6.885
10
7.112
49
6.576
29
6.893
9
7.118
Older Age Sixty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
69
4.666
49
6.314
29
6.600
9
6.808
68
4.806
48
6.347
28
6.614
8
6.802
67
4.930
47
6.369
27
6.632
7
6.782
66
5.042
46
6.385
26
6.650
6
6.740
65
5.141
45
6.397
25
6.666
5
6.667
64
5.229
44
6.407
24
6.680
4
6.531
63
5.306
43
6.416
23
6.693
3
6.355
62
5.377
42
6.424
22
6.703
2
6.035
61
5.442
41
6.434
21
6.712
1
5.679
60
5.508
40
6.447
20
6.719
0
4.967
59
5.591
39
6.466
19
6.725
58
5.684
38
6.486
IS
6.730
57
5.781
37
6.504
17
6.735
56
5.873
36
6.522
16
6.740
55
5.937
35
6.539
15
6.747
54
6.033
34
6.554
14
6.75
53
6.100
33
6.567
13
6.770
52
6.162
32
6.578
12
6.781
51
6.219
31
6.585
11
6.791
50
6.272
30
6.593
10
6.803
Digitized by VjOOQ IC
372
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Livea.
(Carlisle 4 per Cent.)
Older Age Seventy
Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
70
4.367
50
6.001
30
6.291
10
6.484
69
4.512
49
6.039
29
6. 298
9
6.489
68
4.643
48
6.069
2S
6.311
8
6.483
67
4.760
47
6.088
27
6.327
7
6.463
66
4.864
46
6.102
26
6.344
6
6.424
65
4.956
45
6.113
25
6.358
5
6.354
64
5.036
44
6.121
24
6.372
4
6.225
63
5.110
43
6.129
23
6.383
3
6.059
62
5.173
42
6.136
22
6.393
2
5.756
61
5.233
41
6.145
21
6.401
1
5.420
60
5.293
40
6.157
20
6.407
0
4.744
59
5.371
39
6.174
19
6.413
58
5.438
38
6.192
18
6.417
57
5.548
37
6.210
17
6.421
56
5.634
36
6.226
16
6.426
f>5
5.712
35
6.242
15
6.433
54
5.782
34
6.255
14
6.443
53
5.844
33
6.268
13
6.454
52
5.901
34
6.277
12
6.464
51
5.953
31
6.284
11
6.474
Older Age Seventy-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
71
4.030
51
6.671
31
5.969
11
6.143
70
4.204
50
5.715
30
5.975
10
6.152
69
4.340
49
5.749
29
5.981
9
6.157
08
4.462
48
5.776
28
5.993
8
6.151
67
4.571
47
3.792
27
6.009
7
6.132
66
4.667
46
5.804
26
6.024
6
6.094
65
4.732
45
5.813
25
6.037
5
6.028
64
4.826
44
5.820
24
6.050
4
5.907
63
4.894
43
5.827
23
6.060
3
5.750
62
4.952
42
5.832
22
6.069
2
5.465
61
5.006
41
5.841
21
6.076
1
5.149
60
5.062
40
5.852
20
6.082
0
4.311
59
5.134
39
5.867
19
6.087
58
5.214
,18
5.884
18
6.091
o7
5.298
37
5.901
17
6.094
56
5.378
36
5.916
16
6.093
55
5.449
35
5.930
15
6.105
54
5.514
34
5.943
14
6.114
53
5.571
33
5.954
13
6.124
52
5.623
32
5.'J62
12
6.134
Digitized by LjOOQ IC
TABLE XXI.
373
Value of £1 per Anntixn daring the joint Contintiance of Two Lives.
(Carlisle 4 per Cent.)
Older Age Seventy-Two Years.
Ag«.
Valn«.
Age.
Value.
Age.
Value.
A(fe.
Value.
72
3.755
52
5.357
32
5.664
12
5.821
71
3.898
51
5.401
31
5.670
11
5.829
70
4.043
50
5.441
30
5.675
10
5.838
69
4.171
49
5.473
29
5.681
9
5.842
68
4.285
48
5.496'
28
5.692
8
5.836
67
4.386
47
5.510
27
5.706
7
5.818
66
4.476
46
5.521
26
5.720
6
5.782
63
4.554
45
5.528
25
5.733
5
5.720
64
4.623
44
5.534
24
5.744
4
5.605
63
4.684
43
5.539
23
5.754
3
5.458
62
4.737
42
5.544
22
5.762
2
5.189
61
4.787
41
5.551
21
5.768
1
4.892
60
4.838
40
5.561
20
5.773
0
4.290
59
4.905
39
5.576
19
6.778
58
4.980
38
5.592
18
5.781
57
5.058
37
5.607
17
5.784
56
5.132
36
5.621
16
5.788
55
5.193
35
5.634
15
5.794
54
5.257
34
5.646
14
5.803
53
5.310
33
5.656
13
5.812
Older Age Seventy-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
73
3.497
53
5.071
33
5.386
13
5.529
72
3.622
52
5.115
32
5.3«3
12
5.537
71
3.758
51
5.155*
31
5.398
11
5.545
70
3.895
50
5.192
30
5.403
10
5.553
69
4.016
49
5.220
29
5.408
9
5.556
68
4.123
48
5.241
28
5.418
8
5.551
67
4.217
47
5.254
27
5.432
7
5.533
66
4.300
46
5.262
26
5.445
6
5.499
65
4.373
45
5.2H9
23
5.456
5
5.440
64
4.436
44
5.273
24
5.467
4
5.331
63
4.492
43
5.-278
23
5.475
3
5.193
62
4.541
42
5.252
22
5.483
2
4.938
61
4.586
41
5. 288
21
5.489
1
4.658
60
4.633
40
ft.-i98
2C
5.493
0
4.088
59
4.695
39
5.311
19
5.497
58
4.765
38
5.326
18
5.500
57
4.838
37
5.340
17
5.503
56
4.907
36
5.3')3
16
5.506
55
4.968
35
5.366
15
5.512
54
5.023
34
5.376
14
5.520
Digitized by VjOOQIC
874
TABLE nCI.
Value of £1 per Annum during the Joint Continuance of Two lifM.
(Carlisle 4 per Cent.)
Older Age Seventy-Four Years.
Age.
Valiw.
Age.
Valne.
Afe.
Valve.
Ag«.
Value.
74
3.279
54
4.815
34
5.137
14
5.270
73
3.385
53
4.860
33
5.146
13
5.278
72
3.505
52
4.900
32
5.152
12
5.286
71
3.634
51
4.937
31
5.157
U
5.293
70
3.764
50
4.971
30
5.161
10
5.300
69
3.878
49
4.996
29
5.166
9
5.303
68
3.978
48
5.015
28
5.175
8
5.293
67
4.067
47
5.026
27
5.188
7
5.281
66
4.144
46
5.033
26
5.201
6
5.1149
65
4.211
45
5.038
25
5.211
5
5.192
64
4.269
44
5.042
24
5.221
4
5.089
63
4.322
43
5.046
23
5.229
3
4.958
62
4.366
42
5.049
22
5.236
2
4.716
61
4.408
41
5.055
21
5.241
1
4.451
60
4.451
40
5.064
20
5.245
0
3.910
59
4.509
39
5.076
19
5.249
58
4.574
38
5.090
18
5.251
57
4.643
37
5.104
17
5.254
56
4.707
36
5.116
16
5.257
55
4.764
35
5.128
15
5.262
Older Age Seventy-Five Years.
Age.
Value.
Age.
Value.
Age.
Valoe.
Ar.
Yalm.
75
3.119
55
4.598
35
4.933
15
5.057
74
3.197
54
4.646
34
4.942
14
5.064
73
3.299
53
4.688
*33
4.950
13
5.072
72
3.413
52
4.725
32
4.956
12
5.079
71
3.537
51
4.759
31
4.960
11
5.086
70
3.661
50
4.790
30
4.964
10
5.093
69
3.769
49
4.813
29
4.968
9
5.096
68
3.864
48
4.830
28
4.977
8
5.090
67
3.947
47
4.840
27
4.989
7
5.074
66
4.020
46
4.846
26
5.001
6
5.043
65
4.082
4"!
4.850
25
5.010
5
4.989
64
4.136
44
4.853
24
5.019
4
4.890
63
4.185
43
4.856
23
5.027
3
4.765
62
4.225
42
4.859
22
5.033
2
4.534
61
4.264
41
4.864
21
5.038
1
4.282
60
4.304
40
4.872
20
5.042
0
3.764
r)9
4.358
39
4.884
19
5.045
58
4.420
3s
4.898
18
5.047
57
4. 484
37
4.910
17
5.050
56
4.545
36
4.922
16
5.052
Digitized by
Uoogic"
TABLE XXI.
375
Value of £1 per Annum during the joint Couiinuance of Two Lives.
(Carlisle 4 per Cent.)
Older Age Seventy -Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
76
2.966
56
4.384
36
4.730
16
4.851
75
3.041
55
4.434
35
4.741
15
4.856
74
3.114
54
4.478
34
4.749
14
4.862
73
3.212
53
4.517
33
4.756
13
4.869
72
3.321
52
4.551
32
4.762
12
4.876
71
3.439
51
4.583
31
4.766
11
4.883
70
3.558
50
4.611
30
4.769
10
4.889
69
3.660
49
4.632
29
4.773
9
4.892
68
3.750
48
4.647
2S
4.781
8
4.886
67
3.828
47
4.655
27
4.793
7
4.871
66
3.895
46
4.660
26
4.804
6
4.841
65
4.953
45
4.664
25
4.813
5
4.789
64
4.003
44
4.666
24
4.821
4
4.695
63
4.047
43
4.669
23
4.828
3
4.575
62
4.035
42
4.671
22
4.834
2
4.355
61
4.120
41
4.676
21
4.839
1
4.115
60
4.157
40
4.684
20
4.842
0
3.621
59
4.208
39
4.695
19
4.844
58
4.266
38
4.708
18
4.847
57
4.327
37
4.720
17
4.849
Older Age Seventy-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
77
2.833
57
4.181
37
4.543
17
4.662
76
2.897
56
4.234
36
4.553
16
4.664
75
2.969
55
4.281
35
4.563
15
4.669
74
3.039
54
4.323
34
4.571
14
4.675
73
3.132
53
4.358
33
4.577
13
4.682
72
3.237
52
4.390
32
4.582
12
4.688
71
3.349
51
4.419
31
4.585
11
4.694
70
3.462
50
4.445
30
4.588
10
4.700
69
3.559
49
4.464
29
4.592
9
4.703
68
3.644
48
4.477
28
4.600
8
4.697
67
3.716
47
4.484
27
4.610
7
4.682
66
3.779
46
4.489
26
4.621
6
4.653
65
3.833
45
4.491
25
4.630
5
4.604
64
3.879
44
4.493
24
4.637
4
4.514
63
3.920
43
4.495
23
4.644
3
4.400
62
3.954
42
4.497
22
4.649
2
4.190
61
3.987
41
4.502
21
4.653
1
3.962
60
4.021
40
4.509
20
4.656
0
3.489
59
4.069
39
4.520
19
4.6.58
58
4.124
38
4.532
18
4.660
Digitized by LjOOQ IC
376
TABLE XXI.
Value of £1 per Annam during the joint Continotnce of Tvo Livet.
(Carlisle 4 per Cent)
Older Age Seventy-Eight Yean.
Aff.-.
Value.
Age.
Value.
A«e.
Value.
A«e.
Value.
78
2.698
fVS
3.976
38
4.351
18
4.470
17
2.764
57
4.029
37
4.362
17
4.472
76
2.824
56
4.080
36
4.371
16
4.474
75
2.892
55
4.123
35
4.380
15
4.477
74
2.938
54
4.161
34
4.387
14
4.484
73
3.047
53
4.194
33
4.394
13
4.490
7->
3.146
52
4.223
32
4.398
12
4.496
71
3.254
51
4.250
31
4.401
11
4.501
70
3.361
50
4.274
30
4.403
10
4.507
69
3.45-2
49
4.291
29
4.407
9
4.509
68
3.531
43
4.303
28
4.414
8
4.504
67
3.599
47
4.309
27
4.424
7
4.489
66
3.658
46
4.312
26
4.434
6
4.462
65
3.707
45
4.314
25
4.442
5
4.415
64
3.749
44
4.315
24
4.449
4
4.329
63
3.786
43
4.317
23
4.455
3
4.221
62
3.818
42
4.319
22
4.460
2
4.021
61
3.b47
41
4.323
21
4.464
1
3.804
60
3.879
40
4.330
20
4.466
0
3.354
59
3.924
39
4.340
19
4.468
Older Age Seventy-Nine Years.
Age.
Value.
Age.
Value.
Acfli
Value.
Age.
Valae.
79
2.538
59
3.755
39
4.135
19
4.253
78
2.613
58
3.803
38
4.146
18
4.255
77
2.674
57
3.8.53
37
4.156
17
4.256
76
2.731
56
3.899
36
4.165
16
4.258
75
2.795
55
3.940
35
4.173
15
4.261
74
2.857
54
3.975
84
4.179
14
4.267
73
2.940
53
4.005
33
4.185
13
4.273
72
3.035
52
4.031
32
4.189
12
4.279
71
3.136
51
4.055
31
4.191
11
4.284
70
3.237
50
4.077
30
4.194
10
4.289
69
3.322
49
4.092
29
4.196
9
4.291
68
3.395
48
4.103
28
4.203
8
4.286
67
3.458
47
4.107
27
4.213
7
4.272
66
3.51)
46
4.110
26
4.222
6
4.245
65
3.556
45
4.111
25
4.229
5
4.201
64
3.594
44
4.112
24
4.236
4
4.120
63
3.628
43
4.114
23
4.241
3
4.018
62
3.657
42
4. 115
•^2
4.246
8
3.829
61
3.684
41
4.119
21
4.249
1
3.626
60
3.713
40
4.126
20
4.251
0
3.200
Digitized by VjOOQ IC
TABLE XXI-
377
Valne of £1 per Annum during the joint Continuance of Tvo Livci
(CarHsle 4 per Cent.)
Older Age Eighty Years.
Age.
Valae.
Age.
Value.
Age.
Value.
Age.
Value.
80
2.390
59
3.597
38
3.956
17
4.057
79
2.459
58
3.642
37
3-965
16
4.058
78
2.535
^1
3.689
36
3.973
15
4.062
n
2.592
56
3.732
35
3.981
14
4.067
76
2.645
55
3.770
34
3.987
13
4.073
75
2.704
54
3.802
33
3.912
12
4.078
74
2.763
53
3.829
32
3.995
11
4.083
73
2.842
52
3.853
31
3.998
10
4.088
n
2.931
51
3.875
30
3.999
9
4.089
71
3.026
50
3.894
29
4.002
8
4.084
70
3.121
49
3.908
28
4.009
7
4.071
69
3.201
48
3.917
27
4.017
6
4.046
68
3.269
47
3.921
26
4.026
5
4.004
67
3.326
46
3.923
25
4.033
4
3.927
66
3.375
45
3.924
24
4.039
3
3.831
65
3.416
44
3.925
23
4.044
2
3.653
64
3.450
43
3.926
22
4.048
1
3.462
63
3.481
42
3.928
21
4.051
0
3.059
62
3.507
41
3.931
20
4.053
61
3.531
40
3.937
19
4.054
60
3.558
39
3.946
18
4.056
,
Older Age Eighty-One Years.
Age.
Valne.
Ag..
Valoe.
Age.
Value.
Age.
Valua.
81
2.222
60
3.384
39
3.738
18
3.837
80
2.303
59
3.420
38
3.747
17
3.838
79
2.368
58
3.462
37
3.756
16
3.840
78
2.438
57
3.505
36
3.768
15
3.843
77
2.491
56
3.545
35
3.769
14
3.848
76
2.540
55
3.579
34
3.775
13
3.853
75
2.596
54
3.609
33
3.780
12
3.858
74
2.650
53
3.633
32
3.782
11
3.862
73
2.724
52
3.655
31
3.784
10
3.867
72
2.808
51
3.674
30
3.786
9
3.868
71
2.897
50
3.692
29
3.788
8
3.863
70
2.986
49
3.704
28
3.794
7
3.850
69
3.059
48
3.712
27
3.803
6
3.827
68
3.121
47
3.715
26
3.810
5
3.787
67
3.174
46
3.716
25
3.816
4
3.715
66
3.218
45
3.717
24
3.822
3
3.625
65
3.255
44
3.717
23
3.827
2
3.458
64
3.286
43
3.719
22
3.830
1
3.280
63
3.314
42
3.720
21
3.833
0
2.902
62
3.337
41
3.723
20
3.835
61
3.359
40
3.729
19
3.836
Digitized by VjOOQ IC
378
TABLK XXl.
Value of £1 per Annum during the joint Continuance of Two Lives
(Carlisle 4 per Cent.)
Older Age Eighty-Two Years.
Age.
Valae.
Age.
Value.
Age.
Value.
Age.
Value.
82
2.079
61
3.203
40
8.542
19
3.639
81
2.H8
60
3.226
39
3.550
IS
3.640
80
2.225
59
3.260
38
3.558
17
3.641
79
2.283
53
3.299
37
3.566
16
3.643
78
2.351
57
3.339
36
3.573
15
3.646
77
2.400
56
3.376
35
3.579
14
3.650
76
2.446
55
3.407
34
3.584
13
3.655
75
2.497
54
3.434
33
3.588
12
3.660
74
2.548
53
3.456
32
3.590
11
3.663
73
2.617
52
3.475
31
3.592
10
3.668
72
2.696
51
3.493
30
3.594
9
3.669
71
2.780
50
3.509
29
3.596
8
3.664
70
2.862
49
3.520
28
3.601
7
3.652
69
2.930
48
3.527
27
3.609
6
3.630
68
2.987
47
3.529
26
3.616
5
3.592
67
3.035
46
3.530
25
3.622
4
3.525
66
3.075
45
3.530
24
3.627
3
3.441
65
3.109
44
3.531
23
3.631
2
3.284
64
3.137
43
3.532
22
3.634
1
3.118
63
3.162
42
3.533
21
3.637
0
2.761
62
3.183
41
3.536
20
3.638
Older Age Eighty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
83
1.929
62
3.021
41
3.343
20
3.436
82
2.0U2
61
3.039
40
3.348
19
3.437
81
2.066
60
3.060
39
3.354
18
3.437
80
2.137
59
3.091
38
3.363
17
3.438
79
2.193
58
3.127
37
3.370
16
3.440
78
2.255
57
3.165
36
3.376
15
3.442
77
2.300
56
3.199
35
3.382
14
3.447
76
2.341
55
3.227
34
3.386
13
3.451
75
2.389
54
3.251
33
3.390
12
3.455
74
2.436
53
3.271
32
3.392
11
3.459
73
2.501
52
3.289
31
3.394
10
3.463
72
2.575
51
3.304
30
3.395
9
3.463
71
2.653
50
3.319
29
3.397
8
3.459
70
2.729
49
3.328
28
3.402
7
3.447
69
2.792
43
3.334
27
3.409
6
3.427
68
2.844
47
3.336
26
3.416
5
3.392
67
2.887
46
3.337
25
3.421
4
3.328
66
2.924
45
3.337
24
3.426
3
3.250
65
2.954
44
3.338
23
3.430
2
3.104
64
2.979
43
3.338
22
3.432
1
2.949
63
3.002
42
3,340
21
3 435
0
2.615
Digitized by VjOOQ IC
TABLE XXI.
Value of £1 per Adiiqiii during^ the joint Continuance of Two LiTei.
(Carlisle 4 per Cent.)
Older Age Eighty-Four Years.
379
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
Value.
84
1.782
62
2.860
40
3.159
18
3.241
83
1.853
61
2.877
39
3.165
17
3.241
82
1.921
60
2.896
38
3.173
16
3.242
81
1.980
59
2.925
37
3.179
15
3.245
80
2.047
58
2.959
36
3.185
14
3.249
79
2.099
57
2.994
35
3.190
13
3.253
78
2.156
56
3.0-25
34
3.194
12
3.257
77
2.197
55
3.050
33
3.197
11
3.260
76
2.235
54
3.072
32
3.199
10
3.264
75
2.280
53
3.090
31
3.201
9
3.264
74
2.323
52
3.105
30
3.202
8
3.260
73
2.384
51
3.120
29
3.204
7
3.249
72
2.453
50
3.133
28
3.208
6
3.230
71
2.525
49
3.142
27
3.215
5
3.197
70
2.596
48
3.147
26
3.221
4
3.138
69
2.653
47
3.140
25
3.226
3
3.066
68
2.701
46
3.149
24
3.230
2
2.929
67
2.740
45
3.149
23
3.234
1
2.786
66
2.773
44
3.149
22
3.236
0
2.473
65
2.800
43
3.150
21
3.238
64
2.823
42
3.151
20
3.239
63
2.843
41
3.154
19
3.240
Oldei
■ Age Eighty-Five Years.
Age.
Value.
Age.
Value,
Age.
Value.
Age.
Value.
85
1.619
63
2.674
41
2.956
19
3.034
84
1.698
62
2.689
40
2.961
18
3.035
83
1.763
61
2,705
39
2.967
17
3.086
82
1.826
60
2.722
38
2.974
16
3.037
81
1.881
59
2.749
37
2.980
15
3.039
80
1.943
58
2.780
36
2.985
14
3.043
79
1.990
57
2.812
35
2.989
13
3.047
78
2.043
56
2.840
34
2.993
12
3.050
77
2.081
55
2.863
33
2.996
n
3.053
76
2.116
54
2.883
32
2.998
10
3.056
75
2.157
53
2.899
31
2.999
9
3.057
74
2.197
52
2.913
30
3.000
8
3.053
73
2.254
51
2.926
29
3.001
7
3.043
72
2.317
50
2.938
28
3.006
6
3.024
71
2.384
49
2.946
27
3.012
5
2.994
70
2.449
48
2.950
26
3.018
4
2.940
69
2.501
47
2.952
25
3.022
3
2.873
68
2.545
46
2.952
24
3.026
2
2.746
67
2.580
45
2.952
23
3.029
1
2.G14
66
2.610
44
2.952
22
3.031
0
2.323
65
2.635
43
2.953
21
3.033
64
2.655
42
2.954
20
3.034
Digitized by LjOOQ IC
880
TABLE XXI.
Value of £1 per AnQiun daring the joint Conttnuuice of Tvo Lifei.
(Carlislo 4 per Gent)
Older Age Eighty- Six Years.
Age.
Valaa.
Age.
Value.
Age.
Value.
Age.
Value.
86
1.476
64
2.506
42
2.780
20
2.854
85
1.545
63
2.523
41
2.783
19
2.854
84
1.619
62
2.537
40
2.786
18
2.855
83
1.680
61
2.55^
39
2.792
17
2.855
82
1.739
60
2.568
38
2.799
16
2.857
81
1.790
59
2.593
37
2.804
15
2.859
80
1.847
58
2.621
36
2.809
14
2.862
79
1.891
57
2.651
35
2.813
13
2.866
78
1.940
56
2.677
34
2.816
12
2.869
77
1.975
55
2.698
33
2.819
11
2.872
76
2.007
54
2.716
32
2.821
10
2.874
75
2.045
53
2.731
31
2.821
9
2.875
74
2.083
52
2.744
30
2.822
8
2.871
73
2.135
51
2.755
29
2.824
7
2.861
72
2.194
50
2.766
28
2.828
6
2.844
71
2.257
49
2.773
27.
2.834
5
2.816
70
2.317
48
2.777
26
2.839
4
2.765
69
2.365
47
2.779
25
2.843
3
2.703
68
2.405
46
2.779
24
2.847
2
2.585
67
2.437
45
2.779
23
2.849
1
2.462
66
2,465
44
2.779
22
2.851
0
2.190
65
2.487
43
2.779
21
2.853
Older Age Eighty-Seven Yean.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
87
1.359
65
2.365
43
2.637
21
2.706
86
1.416
64
2.383
42
2.638
20
2.706
85
1.481
63
2.399
41
2.640
19
2.707
84
1.551
62
2.412
40
2.644
18
2.708
83
1.609
61
2.425
39
2.649
17
2.708
82
1.664
60
2.440
38
2.655
16
2.709
81
1.712
59
2.464
37
2.660
15
2.711
80
1.766
58
2.491
36
2.665
14
2.715
79
1.807
57
2.518
35
2.669
13
2.718
78
1.853
56
2.542
34
2.672
12
2.721
77
1.885
55
2.562
33
2.674
11
2.723
76
1.916
54
2.579
32
2.676
10
2.726
75
1.952
53
2.592
31
2.677
9
2.726
74
1.987
52
2.604
30
2.677
8
2.722
73
2.036
51
2.615
29
2.679
7
2.713
72
2.092
50
2.625
23
2.683
6
2.697
71
2.151
49
2.632
27
2.688
5
2.671
70
2.207
48
2.636
26
2.693
4
'2.623
69
2.252
47
2.637
25
2.697
3
2.564
68
2.289
46
2.637
24
2.700
2
2.453
67
2.319
45
2.637
23
2.702
1
2.338
66
2.344
44
2.637
22
2.704
0
2 081
Digitized by LjOOQ IC
TABLE XXI.
Value of £1 per Amuim during the joint Contisnaaee of Two Lives.
(Carlisle 4 per Cent)
Older Age Eighty-Eight Yean.
381
Age.
Value.
Age.
Value:
Age.
Value.
Age,
Value.
88
1.301
65
2.293
42
2.552
19
2.618
»7
1.329
64
2.310
41
2.554
18
2,619
86
1.334
63
2.325
40
2.558
17
2.619
85
1..447
62
2.338
39
2.563
16
2.620
84
1.514
61
2.350
38
2.569
15
2.622
83
1.569
60
2.365
37
2.574
14
2.625
82
1.622
59
2.387
36
2.578
13
2.628
81
1.667
58
2.413
35
2.581
12
2.631
80
1.719
57
2.439
34
2.584
11
2.633
79
1.759
56
2.462
33
2.587
10
2.636
7S
1.803
55
2.480
32
2.588
9
2.636
77
1.834
54
2.496
31
2.589
8
2.632
76
1.863
53
2.509
30
2.590
7
2.624
75
1.897
52
2.521
29
2.591
6
2.608
74
1.931
51
2.631
28
2.595
5
2.583
73
1.979
50
2.541
27
2.600
4
2.537
72
2.032
49
2.547
26
2.605
3
2.481
71
2.089
48
2.551
25
2.608
2
2.374
70
2.143
47
2.551
24
2.611
1
2.264
69
2.185
46
2.551
23
2.614
0
2.017
68
2.220
45
2.551
22
2.615
67
2.249
44
2.551
21
2.617
66
2.273
43
2.552
20
2.617
Older Age EightyNine Years.
Age.
Value:
Age.
Value.
Age.
Value.
Age.
Value.
89
1.223
66
2.187
43
2.452
20
2.514
88
1.260
65
2.207
42
2.453
19
2.515
87
1.287
64
2.223
4)
2.455
18
2.516
86
1.339
63
2.237
40
2.458
17
2.516
85
1.400
62
2.249
39
2.463
16
2.517
84
1.464
61
2.261
38
2.468
15
2.519
83
1.516
60
2.276
37
2.473
14
2.522
82
1.566
59
2.296
36
2.477
13
2.525
81
1.610
58
2.320
35
2.480
12
2.527
80
1.659
57
2.345
34
2.483
11
2.530
79
1.697
56
2.367
33
2.485
10
2.532
78
1.739
55
2.385
32
2.487
9
2.532
77
1.769
54
2.400
31
2.487
8
2.529
76
1.797
53
2.412
30
2.488
7
2.520
75
1.829
52
2.423
29
2.490
6
2.506
74
1.862
51
2.423
28
2.493
5
2.482
73
1.907
50
2.442
27
2.498
4
2.438
72
1.958
49
2.448
26
2.503
3
2.384
71
2.012
48
2.4:)1
25
2.506
2
2.282
70
2.063
47
2.452
24
2.509
1
2.177
69
2.103
46
2.452
23
2.511
0
1.941
68
2.137
45
2.452
22
2.513
67
2.164
44
2.452
21
2.514
Digitized by ^^OOQ IC
382
tABLB Xn.
ValiM of £1 per Annum during the joint Contiannnei oCTiro LitM.
(CarUsle 4 p«r Cent.)
Older Age Ninety Years.
Age.
Value.
Age.
Valae.
Age.
Valoe.
Age.
Valae.
90
1.066
67
2.028
44
2.299
21
2.357
89
1.142
66
2.050
43
2.299
20
2.358
88
1.176
65
2.069
42
2.299
19
2.358
87
1.201
64
2.084
41
2.301
18
2.359
86
1.250
63
2.098
40
2.304
17
2.359
85
1.307
62
2.109
39
2.309
16
2.360
84
1.367
61
2.120
38
2.314
15
2.361
83
1.416
60
2.132
37
2.318
14
2.364
82
1.463
59
2.152
36
2.322
13
2.367
81
1.504
53
2.175
35
2.325
12
2.369
80
1.551
57
2.198
34
2.328
11
2.372
79
1.587
56
2.219
33
2.330
10
2.374
78
1.C27
55
2.236
32
2.331
9
2.374
n
1.655
54
2.250
31
2.332
8
2.371
76
1.681
53
2.262
30
2.333
7
2.363
75
1.712
52
2.272
29
2.334
6
2.349
74
1.743
51
2.281
28
2.338
5
2.327
73
1.786
50
2.290
27
2.342
4
2.285
72
1.834
49
2.296
26
2.346
3
2.235
71
1.884
48
2.299
25
2.349
2
2.139
70
1.932
47
2.299
24
2.352
1
2.040
69
1.970
46
2.299
23
2.354
0
1.818
68
2.002
45
2.299
22
2.3^
Older Age Ninety-One Yean.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Yalne.
91
1.028
68
1.985
45
2.281
22
2.338
90
1.047
67
2.012
44
2.281
21
2.339
89
1.120
66
2.034
43
2.281
20
2.340
88
1.155
65
2.032
42
2.282
19
2.340
87
1.180
64
2.068
41
2.284
IS
2.341
86
1.229
63
2.081
40
2.287
17
2.341
85
1.285
62
2.092
39
2.291
16
2.342
84
1.345
61
2.103
38
2.296
15
2.344
83
1.395
60
2.115
37
2,301
14
2.347
82
1.443
59
2.135
36
2.304
13
2.349
81
1.484
58
2.158
35
2.308
12
2.352
60
1.532
57
2.181
34
2.311
11
2.354
79
1.567
56
2.202
33
2.313
10
2.356
78
1.608
55
2.219
32
2.314
9
2.357
n
1.636
54
2.233
31
2.315
8
2.353
76
1.663
53
2.245
30
2.316
7
2.346
75
1.694
52
2.255
29
2.317
6
2.332
74
1.724
51
2.265
28
2.320
5
2.309
73
1.767
50
2.273
27
2.325
4
2.268
72
1.815
49
2.279
26
2.329
3
2.217
71
1.866
48
2.282
25
2.332
2
2.121
70
i.914
47
2.282
24
2.334
1
2.023
60
1.9:)3
46
2.L>82
'?3
2.33G
0
1.801
Digitized by VjUUVIC
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 4 per Cent)
Older Age Ninety-Two Years.
382
Age.
Value.
Age.
Valtte.
Age.
52
Value.
Age.
Value.
Age.
Value.
92
1.096
72
1.886
2.345
32
2.405
12
2.444
91
1.061
71
1.939
51
2.355
.31
2.406
11
2.446
90
1.079
70
1.991
50
2.3<J4
30
2.406
10
2.449
89
1.155
69
2.031
49
2.369
29
2.407
9
2.449
88
1.191
68
2.065
48
2.372
28
2.411
8
2.445
87
1.218
67
2.093
47
2.372
27
2.416
7
2.437
86
1.269
66
2.116
46
2.372
26
2.420
6
2.423
85
1.329
65
2.135
45
2.371
25
2.423
5
2.399
84
1.392
64
2.151
44
2.371
24
2.426
4
2.356
83
1.445
63
2.165
43
2.371
23
2.428
3
2.303
82
1.495
62
2.176
42
2.374
22
2.430
2
2.203
81
1.539
61
2.187
41
2.373
21
2.431
1
2.099
80
1.589
60
2.199
40
2.376
20
2.432
0
1.869
79
1.627
59
2.220
39
2.381
19
2.432
78
1.669
58
2.243
38
2.386
18
2.433
77
1.699
57
2.268
37
2.391
17
2.433
76
1.727
56
2.289
36
2.395
16
2.434
75
1.760
55
2.307
35
2.399
15
2.436
74
1.791
54
2.322
34
2.401
14
2.438
73
1.836
63
2.334
33
2.404
13
2.441
Older Age Ninety-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
93
1.199
73
1.924
53
2.440
33
2.509
13
2.548
92
1.146
72
1.976
52
2.451
32
2.511
12
2.550
91
1.108
71
2.032
51
2.461
31
2.511
11
2.553
90
1.127
70
2.086
50
2.469
30
2.512
10
2.555
89
1.206
69
2.128
49
2.474
29
2.513
«
2.556
88
1.245
68
2.164
48
2.477
28
2.517
8
2.552
87
1.273
67
2.192
47
2.477
27
2.521
7
2.544
86
1.327
66
2.216
46
2.476
26
2.526
6
2.529
85
1.390
65
2.235
45
2.476
25
2.529
5
2.504
84
1.457
64
2.251
44
2.475
24
2.532
4
2.458
83
1.513
63
2.265
43
2.475
23
2.535
3
2.403
82
1.566
62
2.276
42
2.476
22
2.536
2
2.298
81
1.613
61
2.287
41
2.477
21
2.538
1
2.190
80
1.665
60
2.300
40
2.481
20
2.538
0
1.949
79
1.7U5
59
2.321
39
2.486
19
2.538
78
1.750
58
2.345
38
2.492
18
2.539
77
1.7«1
57
2.371
37
2.496
17
2.539
76
1.810
56
2-393
36
2.501
16
2.540
75
1.844
55
2.412
3.)
2.504
15
2.542
74
1.877
54
2.427
34
2.507
14
2.543
Digitized by LjOOQ iC
384
TABLE XXI.
Value of £1 per Annum during the joint GontinuMHoa of Two Lifes.
(Carlisle 4 per Cent)
Older Age Ninety-Four Years.
Ag«.
V«lu«.
Ag«.
Value.
A««.
V«llM.
A«e.
ValiMb
Af..
14
Valiw.
94
1.273
74
1.930
54
2.482
34
2.559
2.596
93
1.234
73
1.978
53
2.494
33
2.561
13
2.599
92
1.179
72
2.031
52
2.505
32
2.562
12
2.602
91
1.139
71
2.088
51
2.514
31
2.563
11
2.604
90
1.158
70
2.142
50
2.522
30
2.563
10
2.606
89
1.240
69
2.186
49
2.527
29
2.564
9
2.607
88
1.280
68
2.221
48
2.529
28
2.568
8
2.603
87
1.310
67
2.250
47
2.529
27
2.573
7
2.594
86
1.367
66
2.273
46
2.528
26
2.577
6
2.579
85
1.432
65
2.291
45
2.527
25
2.581
5
2.553
84
1.502
64
2.306
44
2.526
24
2.585
4
2.507
83
1.5'>9
63
2.319
43
2.526
23
2.586
3
2.451
82
1.614
62
2.330
42
2.527
22
2.588
2
2.342
81
1.662
61
2.340
41
2.529
21
2.589
1
2.234
80
1.716
60
2.353
40
2.532
20
2.589
0
1.989
79
1.756
59
2.375
39
2.538
19
2.569
78
1.801
58
2.400
38
2.543
18
2.590
n
1.833
57
2.425
37
2.548
17
2.590
76
1.862
56
2.448
36
2.552
16
2.591
75
1.897
55
2.466
35
2.556
15
2.593
Older Age Ninety-Five Yean.
Age.
Value.
Ace.
Value.
Age.
55
Value.
2.501
Age.
Value.
Age.
Valoe.
95
1.353
75
1.941
35
2.585
15
2.619
94
1.311
74
1.975
54
2.515
34
2.587
14
2.622
93
1.270
73
2.022
53
2.527
33
2.589
13
2.626
92
1.212
72
2.076
52
2.536
32
2.590
12
2.628
91
1.172
71
2.132
51
2.545
31
2.590
11
2.631
90
1.191
70
2.187
50
2.552
30
2.591
10
2.633
89
1.276
69
2.230
49
2.557
29
2.592
9
2.633
88
1.318
68
2.264
48
2.559
28
2.595
8
2.629
87
1.350
67
2.292
47
2.558
27
2.600
7
2.620
86
1.408
66
2.313
46
2.557
26
2.605
6
2.605
85
1.475
65
2.330
45
2.556
25
2.608
5
2.Ji79
84
1.546
64
2.344
44
2.555
24
2.611
4
2.532
83
1.605
63
2.356
43
2.555
23
2.613
3
2.476
82
1.661
62
2.366
42
2.556
22
2.615
2
2.370
81
1.709
61
2.376
41
2.558
2i
2.616
1
2.260
80
1.762
60
2.389
40
2.561
20
2.616
0
2.014
79
1.803
59
2.410
39
2.567
19
2.616
78
1.848
58
2.435
38
2.572
18
2.617
77
1.879
f)7
2.4C0
37
2.5,7
17
2.617
76
1.908
56
2.482
3G
2.581
16
2.617
Digitized by LjOOQ IC
TABLE XXI.
365
Value of £1 per Annum during the joint Continnanee of Two Lives.
(Carlisle 4 per Cent.)
Older Age-Ninety-Six Years.
A«e.
Value.
Age.
76
Value.
Age.
56
Value.
Age.
Value.
Age.
Value.
96
1.394
1.912
2.454
36
2.542
16
2.575
95
1.371
75
1.944
55
2.471
35
2.546
15
2.577
94
1.32i
74
1.975
54
2.484
34
2.548
14
2.580
93
1.283
73
2.022
53
2.494
33
2.549
13
2.583
92
1.225
72
2.074
52
2.502
32
2.550
12
2.586
91
1.185
71
2.129
51
2.510
31
2.553
11
2.588
90
1.206
70
2.181
50
2.516
30
2.551
10
2.590
89
1 .292
69
2.221
49
2.520
29
2.552
9
2.590
88
1.336
68
2.253
48
2.522
28
2.555
8
2.586
87
1.368
67
2.378
47
2.521
27
2.560
7
2.577
86
1.427
66
2.297
46
2.519
26
2.564
6
2.562
85
1.494
65
2.311
45
2.518
25
2.568
5
2.537
84
1.564
64
2.323
44
2.517
24
2.570
4
2.492
83
1.621
63
2.334
43
2.517
23
2.572
3
2.438
82
1.676
62
2.343
42
2.518
22
2.573
2
2.334
81
1.722
61
2.352
41
2.520
21
2.574
1
2. 228
80
1.774
60
2.364
40
2.523
20
2.574
0
1.989
79
1.813
59
2.384
39
2.529
19
2.574
78
1.856
58
2.408
38
2.534
18
2.574.
77
1.885
57
2.433
37
2.539
17
2.575
Older Age Ninety-Seven Years.
Ageu
Valu«.
Ag...
Value.
Age.
Value.
Age.
Value.
2.415
Age.
17
Value.
97
1.366
77
1.832
57
2.324
37
2.445
9G
1.376
76
1.856
56
2.343
36
2.418
16
2.446
95
1.348
75
1.885
55
2.357
35
2.421
15
2.448
94
1.302
74
1.914
54
2.368
34
2.422
14
2.451
93
1.261
73
1.957
53
2.376
33
2.424
13
2.453
92
1.205
72
2.005
52
2.383
32
2.424
12
2.456
91
1.167
71
2.056
51
2.389
31
2.424
11
2. 458
90
1.189
70
2.104
50
2.395
30
2.424
10
2.459
89
1.276
69
2.140
49
2.398
29
2.425
9
2.459
88
1.319
68
2.167
48
2.399
28
2.428
8
2.455
87
1.350
67
2.187
47
2.398
27
2.433
7
2.447
86
1.407
66
2.203
46
2.397
26
2.437
6
2.43-3
85
1.471
65
2.215
45
2.395
26
2.440
5
2.409
84
1.537
64
2.225
44
2.394
24
2.442
4
2.367
.83
1.591
63
2.234
43
2.395
23
2.444
3
2.317
82
1.642
62
2.242
42
2.395
22
2.444
2
2.221
81
1.684
61
2.250
41
2.397
21
2.445
1
2.124
80
1.732
60
2-261
40
2.401
20
2.445
0
1.899
79
1.767
59
2.280
39
2.406
19
2.445
78
1.806
53
2.302
38
2.411
18
2.445
Di^izi^i by Google
986
TABLV XXI.
Value of £1 per Annum auriog the joint Continuuee oC Two Li? e«.
(Carlisle 4 per Cent.)
Older Age Ninety-Eight Years.
Age.
Vala«.
Age.
Value.
Age.
Value.
A««.
Valne.
Ag^
Value.
98
1.349
78
1.745
59
2,174
38
1
2.264
18
2.293
97
1.350
77
1.767
57
2.194
37
2.268
17
2.293
96
1.351
76
1.787
56
2.210
36
2.270
16
2.293
95
1.321
75
1.813
55
2.221
35
2.272
15
2.295
94
1.276
74
1.838
54
2.230
34
2.274
14
2.298
93
K238
73
1.878
53
2.236
33
2.275
13
2.300
93
1.185
79
1.922
52
2.241
32
2.275
12
2.309
91
1.150
71
1.967
51
2.246
31
2.275
11
2.303
90
1.174
70
2.009
50
2.251
30
2.275
10
2.305
89
1.261
69
2.039
49
2.254
99
2.276
9
2.305
88
1.304
68
2.061
48
2.254
28
2.279
8
2.301
87
1.332
67
2.076
47
2.253
27
2.283
7
2.293
86
1.384
66
2.089
46
2.251
26
2.287
6
2.280
85
1.444
65
2.098
45
2.250
25
2.289
5
2.2^9
84
1.506
64
2.106
44
2.249
24
2.291
4
2.220
83
1.555
63
2.114
43
2.250
23
2.292
3
2.176
89
1.600
62
2.121
42
2.250
22
2.292
2
2.088
81
1.637
61
2.128
41
2.252
21
2.293
1
2.001
80
1.680
60
2.137
40
2.255
20
2.292
0
1.79Q
79
1.710
59
2.154
39
2.260
;i«
2.292
Older Age Ninety-Nine Years.
Age.
Valne.
AKe.
Vahie.
Age.
Value.
Age.
Value.
Age.
Value.
99
1.272
79
1.591
59
1.949
39
2.031
19
2.056
98
1.298
78
1.620
58
1.966
38
2.034
18
2.056
97
1.285
n
1.637
57
1.981
37
2.037
17
2.056
96
1.281
76
1.653
56
1.994
36
2.039
16
2.057
95
1.253
75
1.673
55
2.002
35
2.040
15
2.058
94
1.212
74
1.696
54
2.008
34
2.041
14
2.060
93
1.179
73
1.729
53
2.012
33
2.042
13
2 062
92
1.131
72
1.767
52
2.016
32
2.042
12
2.064
91
1.101
71
1.804
51
2.0-20
31
2.042
U
2.065
90
1.128
70
1.83S
50
2.024
30
2.042
10
2.066
89
1.212
69
1.861
49
2.026
29
2.043
9
2.065
88
1.250
68
1.876
48
2.0-26
28
2.045
8
2.062
87
1.272
67
1.887
47
2.024
27
2.049
7
2.055
86
1.317
66
1.896
46
2.029
26
2.052
6
2.044
85
1.370
65
1.904
45
2.022
25
2.054
5
2.02a
84
1.424
64
1.910
44
2.022
24
2.055
4
1.993
83
1.465
63
1.916
43
2.022
23
2.055
3
1.950
82
1.502
62
1.921
42
2.023
22
2.056
2
1.881
81
1.532
61
1.927
41
2.024
21
2.056
1
1.810
80
1.567
60
1.934
40
2.027
SO
2.056
0
1.631
Digitized by VjOOQ IC
TABLB XXI.
$67
Value of jCl per Annum during the joiat Caniiouanee of Two Lives..
(Carlisle 4 per Cent.)
Older Age One Handred Yeafs.
Ag..
VaUw.
Aga
VrflM.
A«t^
Value.
Age.
37
Value.
Age.
Vdue.
100
.976
79
l.Sll
58
1.672
1.619
16
1.682
99
1.099
78
1.831
57
1.583
30
1.6iO
15
1.639
98
1.100
77
1.342
56
1.591
35
1.621
14
.1.636
97
1.081
76
1.353
55
1.596
34
1.622
13
1.636
96
1.077
75
1.369
54
1.600
33
1.622
12
.1.637
95
1.055
74
1.385
53
1.603
32
1.622
11
1.638
94
1.023
73
1.410
52
1.605
31
1.622
10
1.639
93
0.997
72
1.437
51
1.608
30
1.622
9
1.638
92
0.960
71
1.464
50
1.611
29
1.623
8
1.635
91
0.938
70
1.487
49
1.611
28
1.625
7
1.630
90
0.964
69
1.501
48
1.611
27
1.628
6
1.622
89
1.036
68
1.611
47
1.610
26
1.629
5
1.609
88
1.063
67
1.518
46
1.609
25
1.630
4
1.584
87
1.076
66
1.623
45
1.608
24
.1.631
3
1.558
86
1.111
65
1.528
44
1.608
23
1.631
2
1.602
85
1.152
64
1.532
43
1.609
22
1 .632
1
1.451
84
1.198
63
1.537
42
1.609
21
1.632
0
1.314
83
J .222
62
1.540
41
1.610
20
1.632
82
1.247
61
1.544
40
1.612
19
1.632
81
1.268
60
1.549
39
1.615
18
1.632
80
1.294
59
1.560
38
1.618
17
1.632
Oldet Age One HnndTcd tmA One Years.
Ag*.
ValMt.
80
Value.
Age.
Valae.
Age.
Va1a«.
Age.
Value.
101
.679
.988
59
1.155
38
1.189
17
1.19/
100
.797
79
.998
58
1.162
37
1.190
16
1.198(
99
.872
78
I.OII
57
1.16S^
36
1.190
15
1.198
98
.858
77
i.oir
56
1.173
.35
1.191
14
1.199
97
.840
76
1.024
59
1.176
34
1.191
13
1.200
96
.8Z9
76
1.035
54
1.178
33
1.191
12
1.201
95
.824
74
1.043
53
1.180
32
1.191
11
1.20t
94
.800
73
1.062
5^
1.181
31
1.191
10
1.202
93
.783
72
1.080
51
1.183
30
1.191
9
1.201
92
.757
71
1.097
50
1.185
2Sf
1.192
8
1.1^9
91
.743f
70
1.111
49
1.185
28
1.193
7
1.195
90
.765
69
1.118
48
1.185
27
1.195
6
1.19«)
89
.821
68
a. 123
47
1.184
26
1.196
5
1.181
88
.836
67
1.127
46
1.183
25
1.196
4
1.165
87
.842
66
1.131
45
1.183
24
1.197
3
1.148
86
.867
65
1.134
44
1.183
23
1.197
2
1.110
85
.8(6
64
1.136
43
1.183
22
1.197
1
1.077
84
.924
63
1.139
42
1.183
21
1.197
0
.982
83
.941
62
l.Hl
41
1.184
20
1.197
82
.9$7
61
1.143
40
1.185
19
1.197
81
.970
60
1.147
39
' 1.187
18
1.197
n2ti^
Ed2/i
^ooqI
TABLE XXI.
Value of £t per Annuiii during the joint ContinuAnee of Two Livet.
(Carlisle 4 per Gent)
Older Age One Hundred and Two Years.
Af^
ValiM.
Age.
ValiM.
Ac«.
Valofl.
Age.
ValiM.*
Ace.
18
Value.
102
.383
81
.637
60
.730
39
.750
.755
lOi
.491
80
.647
59
.734
38
.751
17
.755
100
•552
79
.652
58
.738
37
.752
16
.756
99
.590
78
.659
57
.742
36
.752
15
.756
98
.572
n
.662
56
.744
35
.752
14
.757
97
.562
76
.666
55
.745
34
.752
13
.757
96
.564
75
.672
54
.746
33
.752
12
.757
95
.553
74
.677
53
.747
32
.752
11
.757
94
.539
73
.687
52
.747
31
.752
10
.758
93
.530
72
.696
51
,748
30
.752
9
.757
92
.514
71
.705
50
.749
29
.753
8
.756
91
.507
70
.712.
49
.749
28
.753
7
.754
90
.524
69
.715
48
.749
27
.754
6
.751
89
.560
68
.718
47
.748
26
.755
5
.746
88
.563
67
.720
46
.748
25
.755
4
.737
87
.5Gr>
66
.722
45
.748
24
.755
3
.728
86
.582
65
.723
44
.748
23
.755
2
.706
85
.599
64
.724
43
.748
22
.755
1
.689
84
.614
63
.726
42
.748
21
.755
0
.632
83
.622
62
.727
41
.749
20
.755
82
,631
61
.728
40
.749
19
.755
Older Age One Hundred and Three Years.
Age.
Valoa.
Age.
Value.
Age.
61
Valae.
Age.
Value.
Age.
Value.
103
.107
82
.275
.309
40
.316
19
.318
102
.192
81
.278
60
.310
39
.317
18
.318
101
.229
80
.282
59
.312
38
.317
17
.318
100
.249
79
.283
58
.313
37
.317
16
.318
99
.262
78
.286
57
.314
36
.317
15
.319
98
.252
77
.286
56
.314
35
.317
14
.319
97
.249
76
.288
55
.315
34
.317
13
.319
96
.251
75
.290
54
.315
33
.317
12
.319
95
.246
74
.292
53
.315
32
.317
11
.319
94
.240
73
.295
52
.316
31
.317
10
.319
93
.237
72
.299
51
.316
30
.317
9
.319
92
.231
71
.302
50
.316
29
.317
8
.318
91
.229
70
.304
49
•316
28
.313
7
.318
90
.237
69
.305
48
.316
27
.318
6
.317
89
.252
68
.306
47
.316
26
.318
5
.315
88
.250
67
.306
46
.316
25
.318
4
.311
87
.251
66
.307
45
.316
24
.318
3
.308
|86
.259
65
.307
44
.316
23
.318
2
.300
85
.264
64
.308
43
.316
22
.318
1
.295
84
.270
63
.308
42
.316
21
.318
0
.271
83
.272
62
.309
41
.316
20
.318
Digitized by LjOOQ IC
TABLE XXL
389
Valae of £1 per Annum daring the joint Continuance of Two Lives.
(Carlisle 5 per Cent)
Older Age 0 Years.
Older Age One Year.
Ajce.
ValiM.
Age.
Valne.
0
7.704
1
0
10.299
8.493
Older Age Two Years.
Older Age Three Years.
Age.
Value.
Age.
Value.
2
1
0
11.793
10.772
9.173
3
2
1
0
13.162
12.217
11.362
9.742
Older Age Four Years.
Older Age Five Years.
Ag*.
Value.
Age.
Value.
4
3
2
1
0
13.932
13.422
12.675
11.769
10.202
5
. 4
3
2
1
0
14.507
14.087
13.638
12.838
12.092
10.551
Older Age Six Years.
Older Age Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
6
5
4
3
14.789
14.574
14.212
13.809
2
1
0
13.096
12.331
10.597
7
6
5
4
14.917
14.798
14.619
14.306
3
2
1
0
13.936
13.258
12.336
10.629
Digitized by LjOOQ IC
m
TAB Ul XXI.
Value of £1 per Annum during the joint Continuance of Two Lim*
(Carlisle f per Cent.)
Older Age Eight Years.
Older Age Nine Years.
Age.
V«lne.
Ag».
Value.
Age.
Valne.
Age.
Value.
8
9
6
5
4
14.942
14.891
14.796
14.647
14.369
3
2
1
0
14.019
13.232
12.333
10.649
9
8
7
6
5
14.898
14.895
14.859
14.785
14.659
4
d
2
1
0
14.402
13.972
13.202
12.322
10.656
Older Age Ten Years.
Older Age Eleven ^
rears.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
10
9
8
7
6
5
14.803
14.839
14.846
14.823
14.763
14.649
4
3
1
0
14.342
13.923
13.168
12.303
10.649
11
10
9
8
7
6
14.684
14.741
14.786
14.795
14.782
14.731
5
4
3
2
1
Q
14.584
14.282
18.873
13.130
12.275
. 10.602
Older Age Twelve Years.
Older Age Thirteen Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
12
11
10
9
8
7
6
14.568
14.611
14.649
14.683
14.712
14.736
14.667
5
4
3
2
1
0
14.519
14.223
13.822
13.087
12.221
10.555
13
12
11
10
9
8
7
14.450
14.500
14.550
14.597
14.644
14.6g9
14.676
6
5
4
8
2
1
0
14.604
14.456
14.164
13.769
13.033
12.168
10.510
Digitized by VjOOQ IC
tABLK XKl.
39!
Valne of £1 per Anaam during the Joint Gontlnuatice of Two Live«.
(Oarlitle & per Gent.)
Older Age Fourteen Years.
Older Age Fifteen Years.
14
13
12
11
10
9
8
7.
Valoe.
14.331
14»385
14*439
14«494
14.550
14.606
14.633
14.615
Age.
Value.
14.542
14.395
14*106
13.716
12.978
12.116
10.465
Ag«.
15
14
13
12
11
10
9
8
Value.
14.215
14.270
14.326
14.383
14.441
14.500
14.554
14,576
Ago.
Value.
14.554
14.480
14.334
14.055
13.660
12.923
12.064
10.421
Older Ag^ Sixteen Years.
Older Age Seventeen Years.
Age.
Value.
Age.
Value,
A^.
Value.
Age.
Value.
16
14«112
7
14.4S3
17
14.018
8
14.412
15
14.166
6
14.419
16
14.072
7
14.438
14
14.221
5
14.284
15
14.125
6
14.369
13
14.276
4
14.001
14
14.178
.')
14.231
12
14.332
8
13.604
18
14.231
4
13.944
11
14.389
2
12.868
12
14.284
3
13.546
10
14.452
1
12.013
11
14.323
2
12.812
9
14.500
0
10.385
10
14.357
1 .
11.971
8
14.517
9
14.387
0
10.346
Older Age Eighteen
Years.
Older Age Niueteen Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
18
13.925
8
14.395
19
13.827
9
14.321
17
13.979
7
14.379
18
13.881
8
14,338
16
14.031
6
14.315
17
13.932
7
14.322
15
14.081
5
14.174
16
13.980
6
14.256
14
14.130
4
13.885
15
14.026
5
14.113
13
14.178
3
13.487
14
14.069
4
13.823
12
14.224
2
12.76-1
13
14.119
3
13.432
11
14.269
1
11.U25
U
14.169
2
12.712
10
14.313
0
10.305
n
14.219
I
11.876
9
14.355
10
14.270
0
10.261
Digitized by VjOOQ IC
892
TABLE XXI
Value of £1 per Annum daring tli« joint Continuance of Tiro Livcf.
(Carlisle 5 per Cent.)
Older Age Twenty '
yeam.
Age.
Valoe.
A««.
Valoe.
A«e.
Value.
Age.
ValM.
20
19
18
17
16
15
13.724
13,7;8
13.829
13.876
13.919
13.959
14
13
12
11
10
9
14.009
14.061
14.113
14.166
14.2-21
14.259
8
7
6
5
4
3
14.276
14.260
14.193
14.049
13.761
13.373
2
1
0
12.656
11.823
10.214
Older Age Twenty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Valne.
21
20
19
18
17
16
13.616
13.672
13.724
13.771
13.814
13.853
14
13
12
11
10
13.902
13.952
14.003
14.054
14.106
14.152
9
8
7
6
5
4
14.193
14.210
14.193
14.126
13.979
13.696
3
2
1
0
13.310
12.596
11.766
10.163
Older Age Twenty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
22
21
20
19
18
17
13.497
13.556
13.610
13.660
13.705
13.746
16
15
14
13
12
11
13.795
13.843
13.892
13.939
13.987
14.023
10
9
8
7
6
5
14.054
14.081
14.104
14.122
14.048
13.906
4
3
2
1
0
13.626
13.242
12.531
11.700
10.110
Older Age Twenty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
23
13.372
16
13.732
9
14.027
2
12.454
22
13.433
15
13.777
8
14.065
1
11.633
21
13.491
14
13.821
7
14.037
0
10.055
20
13.543
13
13.864
6
13.969
19
13.592
12
13.906
5
13.831
18
13.636
11
13.948
4
13.553
17
13.685
10
13.988
3
13.170
Digitized by LjOOQ IC
TABLE XXI.
d9S
Volae of £1 per Annum during^ the joint Continuance of Two Lifes.
(Carlisle 5 per Cent)
Older Age Twenty-Four Years.
A«e.
Value.
Age.
Value.
Age.
Value.
A«e.
Value.
24
13.240
17
13.614
10
13.923
3
13.083
23
13.303
16
13.658
9
13.971
2
12.376
22
13.363
15
13.699
8
13.975
1
11.565
21
13.419
14
13.737
7
13.952
0
9.998
20
13.471
13
13.782
6
13.888
19
13.520
12
13.829
5
13.753
18
13.568
11
13.875
4
13.476
Older Age Twenty-Five Years.
An^
Value.
Age.
Value.
Age.
Value.
Age.
Value.
25
24
23
22
21
20
19
13.101
13.165
13.227
13.287
13.344
13.398
13.447
18
17
16
15
14
13
12
13.492
13.534
13.573
13.608
13.654
13.701
13.749
11
10
9
8
7
6
5
13.799
13.850
13.880
13.886
13.967
13.806
13.672
4
3
2
1
0
13.386
12.997
12.299
11.496
9.940
Older Age Twenty-Six Years.
Age.
, Value.
Age.
Value.
Age.
Value.
Age.
Value.
26
25
24
23
22
21
20
12.960
13.025
13.089
13.151
13.212
13.272
13.322
19
18
17
16
15
14
13
13.369
13.411
13.449
13.483
13.528
13.574
13.620
12
11
10
9
8
7
6
13.668
13.716
13.765
13.791
13.797
13.782
13.723
5
4
3
2
1
0
13.584
13.296
12.913
12.223
11.426
9.877
Older Age Twenty-Seven Years.
Affe.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
27
12.811
20
13.238
13
13.535
6
13.640
26
12.876
19
13.283
12
13.579
5
13.496
25
12.942
18
13.323
11
13.611
4
13.207
24
13.007
17
13.359
10
13.638
3
12.829
23
13.072
16
13.403
9
13.662
2
12.14C
22
13.137
15
13.447
8
•13.682
1
11.357
21
13.190
14
13.491
7
13.697
0
9.814
Digitized by LjOOQ IC
394
TABLE XXI.
Vftlno of £1 f%t Annom during the joint Continiiaace of Two livet.
(C«r]itlt5perCent.)
Older Age Twenty-Eight Years,
Age.
27
26
25
24
21
Valne.
19.663
12.729
12.796
12.863
12.931
13.000
13.055
13.106
Ag«.
20
19
18
17
16
15
14
13
Valae.
13.153
13.196
13.235
13.279
13.321
13.363
13.403
13.442
Age.
12
11
10
9
8
7
6
5
Valoe.
13.480
13.518
13.554
13.589
13.623
13.619
13.555
13.408
Age.
Value.
13.120
12.746
12.077
11.287
9.751
Older Age Twenty-Nine Years.
Age.
Velae.
Age.
Value.
Age.
Value.
Age.
Value.
29
12.530
21
13.027
13
13.353
5
13.319
28
12.596
20
13.074
12
13.395
4
13.033
27
12.663
19
13,117
11
13.438
3
12.676
26
12.730
18
13.160
10
13.481
2
12.004
25
12.798
17
13.202
9
13.525
1
11.214
24
12.867
16
13.241
8
13.549
0
9.687
23
12.924
15
13.277
7
13.538
22
12,977
14
13.312
6
13.468
Older Age Thirty Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value,
30
12.419
22
12.908
14
13.237
6
13.378
29
12.485
21
12.959
13
13.279
5
13.229
28
I2.5r)0
20
13.008
12
13.3-24
4
12.960
27
12.615
19
13.052
11
13.369
3
12.601
26
12.679
18
13.092
10
13.416
2
11.928
25
12.742
17
13.130
9
13.451
1
11.140
24
12.800
16
13.164
8
13.470
0
9.623
23
12.855
15
13.195
7
13.453
Older Age Thirty-One Years,
Age.
Value.
Age.
Value.
Age.
15
Value.
Age.
Value..
31
12.308
23
12.787
13.123
7
13.864
30
12.374
22
12.842
14
13.165
6
13.287
29
12.438
21
12.896
13
13.207
5
13.149
28
12.499
20
12.941
12
13.251
4
12.882
27
12.558
19
12.982
1)
13.295
3
12.521
26
12.615
18
13.020
10
13.336
2
11.849
25
12.673
17
13.053
9
13.370
1
11.064
24
12.731
16
13.083
8
13.386
0
9.565
» Digitized by LjOOQ IC
TAPU XJU.
S96
Value of £1 per Annum during tlie joint Cpntinoance of Two LiTes.
(CaiUsle 5 per Cent)
Oldpf Age Thirty-Twp Yeaw.
Age.
V^ue.
A,e.
Value.
Age.
Value.
Age.
Value.
32
12,191*
23
12.717
14
13.092
5
13.068
31
12.257
22
12.776
18
13.132
4
12.798
30
12.319
21
12.823
12
13.172
8
12.437
29
12.377
20
12.866
U
13.200
2
11.766
98
12.431
19
12,906
10
13f224
I
10.989
V
12.488
18
12,941
9
13.248
0
9:503
26
12.541
17
12.973
8
13.259
a&
12.599
16
13.013
7
13.271
24
12.658
1^
13.052
6
13.198
Older Age Thirty-Three Yeare.
Agf.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
33
12.064
24
12.585
15
12.971
6
13.104
32
12.130
23
12.648
14
13.007
5
12.973
31
12.191
22
12.697
13
13.042
4
12.708
30
12.247
21
12.743
12
13.076
3
12.347
29
12.298
20
12.785
11
13.109
2
11.678
28
12.344
19
12.823
10
13.141
\
10.911
27
12.403
18
12.857
9
13.172
0
9.438
26
12.463
17
12.896
8
13.202
25
12.524
la
12.934
7
13.173
Older Age Thirty-Four Years.
Agr.
Vtlut.
Agi.
Value,
Age.
Value.
Age.
Value.
34
11.926
25
12.448
16
12.842
7
13.072
33
11.993
24
12.510
15
12.875
6
13.007
32
12.055
23
12.561
14
12.905
5
12.876
31
12.112
22
12.609
13
12.942
4
12.613
30
12.163
21
12.653
12
12.979
3
12.246
29
12,208
20
12.695
11
13.017
2
11.587
28
12,267
19
12.733
10
13.056
1
10.830
27
12,326
18
12.772
9
13.096
0
9.369
26
12.387
17
12.808
8
13.096
Digitized byVjOOQlC
396
TABLE XXI.
Value of £1 per Aanum during; the joint Continuance of Two Livet.
(Carlisle 5 per Cent.)
Older Age Thirty-Five Years.
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
Voloa.
35
11.780
26
12.309
17
12.709
8
12.988
34
11.850
25
12.365
16
12.738
7
12.968
33
11.915
24
12.416
15
12.765
6
12.904
32
11.974
23
12.4G6
14
12.802
5
12. 77.'>
31
12.029
22
12.513
13
12.840
4
12.503
30
12.078
21
12.559
12
12.880
3
12.144
29
12.136
20
12.602
11
12.921
2
11.494
28
12.194
19
12.641
10
12.963
1
10.745
27
12.252
18
12.676
9
12.984
0
9.296
Older Age Thirty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
36
11.627
26
12.214
16
12.626
6
12.798
35
11.699
2.')
12.266
15
12.662
5
12.658
34
11.767
24
12.316
14
12.698
4
12.392
33
11.830
23
12.366
13
12.736
3
12.040
32
11.889
22
12.416
12
12,774
2
11.398
31
11.944
21
12.464
11
12.814
1
10.656
30
12.002
20
12.503
10
12.847
0
9.213
29
12.058
19
12.539
9
12.871
28
12.112
18
12.572
8
12.879
27
12.164
17
12.601
7
12.860
Older Age Thirty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
37
11.470
27
12.058
17
12.489
7
12.750
36
11.543
26
12.110
16
12.524
6
12.681
35
11.614
25
12.161
15
12.558
5
12.541
34
11.681
24
12.214
14
12.593
4
12.280
33
11.745
23
12.266
13
12.629
3
11.934
32
11.806
22
12.319
12
12.664
2
11.299
31
11.863
21
12.360
11
12.683
1
10.558
30
11.917
20
12.398
10
12.709
0
9.129
29
11.967
19
12.432
9
12.726
28
12.014
18
12.462
8
12.740
Digitized by LjOOQ IC
TABLB XXI.
897
Value of £1 per Aanam during the joint Continuance of Two Lives.
(Carlisle 5 per Cent.)
Older Age Thirty-Eight Years.
Age.
Value.
Age.
Volae.
Age.
Valoe.
Age.
Value.
38
11.309
2»
11.900
18
12.350
8
12.654
37
11.383
27
11.951
17
12.384
7
12.635
36
11.456
26
12.004
16
12.417
6
12.562
35
11.526
25
12.058
15
12.449
5
12.424
34
11.595
24
12.113
14
12.480
4
12.167
33
11.661
23
12.169
13
12.511
3
11.827
32
11.718
22
12.212
12
12.541
2
11.196
31
11.770
21
12.252
11
12.570
1
10.460
30
11.818
20
12.288
10
12.599
0
9.045
29
11.861
19
12.321
9
12,627
Older Age Thirty-Nine Years.
Age.
Valne.
Age.
Value.
Age.
Value.
Age.
Value.
39
11.144
29
11.747
19
12.206
9
12.526
38
11.219
28
11.798
18
12.239
8
12.544
37
11.293
27
11.850
17
12.271
7
12.518
36
11.366
26
11.903
16
12.300
6
12.443
35
11,437
25
11.958
15
12.328
5
12.306
34
11.508
24
12.013
14
12.354
4
12.054
33
11.566
23
12.057
13
12.387
3
11.723
32
11.619
22
12.099
12
12.420
2
11.092
31
11.666
21
12.133
11
12.454
1
10.361
30
11.709
20
12.173
10
12.490
0
8.961
Older Age Forty Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
40
10.984
29
11.657
18
12.126
7
12.399
39
11.059
28
11.707
17
12.153
6
12.323
38
11.134
27
11.757
16
12.179
5
12.188
37
11.208
26
ll.fi07
15
12.201
4
11.952
36
11.281
25
11.856
14
12.233
3
11.614
35
11.354
24
11,901
13
12.267
2
10.985
34
11.414
23
11.944
12
12.303
1
10.261
33
11,469
22
11.985
11
12.340
0
8.876
32
11,520
21
12.024
10
12.378
31
11.566
20
12.062
9
12.422
30
11.607
19
12.095
8
12.430
Digitized by LjOOQ iC
3f8
TABLIXXI. .
Valae of £1 per Annum during the joint Contmnance of Two lifos.
(Carlisle 5 per Cent;
Older Age Forty-One Yean.
Ag...
Value.
Age.
Value.
Ag«.
Valoft
Age.
Value.
41
10.839
30
11.523
19
iU988
8
12.311
40
10.914
29
11«571
18
12»016
7
12,277
39
10.989
28
11.618
17
12.040
6
12.20t
38
11.062
27
li.663
16
12.061
5
12.087
37
11.133
26
11.706
15
12.092
4
11 .843
36
11.204
25
11.751
14
12,124
3
11.501
35
11.266
24
11.795
13
12.156
2
10.876
34
11.323
23
11.838
18
12.192
1
10.160
33
11.377
22
11.881
11
12.228
0
8.804
32
11.428
21
11.923
10
12*279
31
11.474
20
11,957
9
12.310
Older Age Forty-Two Years.
Age.
Value.
Age.
Value.
Age.
> Vaiuo.
Age.
Value.
42
10.701
31
11.391
20
11.851
12.134
41
10.777
30
11.436
19
11.880
12.145
40
10.856
29
11.479
18
11.906
12.152
39
10.921
28
11.519
17
11.928
12.100
38
10.990
27
11.556
16
11.956
11.976
37
11.056
26
11.600
1ft
11.989
11.727
36
11.119
25
11.645
14
12.019
11.385
35
11.179
24
11.691
13
12,051
10.765
34
11.236
28
11.737
12
12.082
10.076
33
11.290
22
11.783
11
12.103
8«726
32
11.342
21
11.819
10
12^120
Older Age Forty-Three Ydurs.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Va^ie.
43
10.566
32
11.255
21
11.713
10
12.01f
42
10.643
31
11.299
20
11.744
12.037
41
10.715
30
11.339
11.771
12.060
4%
10.783
29
11.375
11.796
12-047
39
10.847
28
11.407
11.825
11.987
38
10.907
27
11.451
11.854
11.858
37
10.970
26
11.497
11.882
11.605
36
11.032
26
11.543
11.909
11.264
35
11.092
24
11.59«
11.936
10.671
34
11.150
23
11.641
11.962
9^982
33
11.207
22
11.678
11.988
84640
Digitized by VjUUVIC
TABUS XXI.
Value of £\ per Aanum duriog the joint Continuanee of Two LWei*
(Carlisle 5 per Cent.)
Older Age Forty-Four Years.
Age.
Value.
Age.
Vftliie.
A^.
Value.
Age.
Value.
44
10.425
32
11.156
20
11.629
8
11.947
43
10.503
31
11.195
19
11.657
7
11.929
4a
10.575
30
11.230
18
11.686
6
11.862
41
10.641
29
11.261
1>
11.713
5
11.730
40
10.700
28
11.305
16
11.738
4
11.476
39
10.753
27
11.349
15
11.762
a
11.157
38
10.816
26
11.396
14
11.785
9
10.566
37
10,879
25
11.443
13
11.813
1
9.879
36
10,941
24
11,492
12
11.842
0
8.548
35
11.002
23
11.530
11
11.872
34
11.063
2i
11.566
10
11.903
33
11.113
21
11.599
9
11.935
Older Agt Forty-Five Years.
Age.
Value.
AJT.
Value.
Age.
Value.
Age.
Value.
45
10.278
33
11.008
21
11.479
11.810
44
10.360
32
ll.O'iO
20
11.511
11.821
43
10.433
31
11.088
19
11,539
11.79/
42
10.497
30
11.121
18
11.565
11.726
41
10.552
29
11.163
17
11.589
11.592
40
10.598
28
11.206
16
ll.CU
11.354
39
10.661
27
11,249
15
11.630
11.038
38
10,724
26
11.292
14
11.658
11.449
37
10.787
25
11,335
13
11,688
9.766
36
10.850
24
11,373
12
11.719
8.450
35
10.912
23
11,410
11
11,751
34
10.962
22
11.445
10
11.785
Older Age Forty-Six Years.
Age.
Value.
Age.
Value.
Age.
Valtui.
11.319
Age.
Value.
46
10.119
U
10.849
22
10
11.644
45
10.206
33
10.894
21
11.355
9
11.671
44
10.282
32
10.936
20
11.3^4
8
11.680
43
10.347
31
10.974
19
11.410
7
11.652
42
10.401
30
11.015
18
11.433
6
11.578
41
10.444
29
11.056
17
11.454
5
11.4.51
40
10.507
28
11.095
16
11.472
4
11.218
39
10.569
27
11.133
15
11.499
3
10.905
38
10.630
26
11.170
14
11.527
2
10.320
37
10.690
25
11.208
13
11.556
1
9.644
36
10.750
24
11.245
12
11.586
0
8.351
35
10,801
23
11.282
11
11.617
Digitized by VjOOQ IC
400
TABLE XXI.
Valae of £1 per Annum during^ the joint Continuance of Tiro Livei.
(Carlisle 5 per Cent.)
Older Age Forty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Ag*.
Value.
47
9.947
35
10.681
23
11.147
11
11.458
46
10.040
34
10.729
22
11.187
10
11.471
45
10.121
33
10.774
21
11.217
9
11.482
44
10.189
32
10.817
20
11.244
8
11.489
43
10.244
31
10.857
19
11.269
7
11.493
42
10.287
30
10.895
18
11.290
6
11.417
41
10.349
29
10.930
17
11.309
5
11.298
40
10.410
28
10.963
16
11.335
4
11.069
39
10.468
27
10.993
15
11.361
3
10.759
38
10.524
26
11.035
14
11.387
2
10.180
37
10.579
23
11.U68
13
11.414
I
9.512
36
10.631
24
11.107
12
11.441
0
8.243
Older Age Forty-Eight Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
48
9.756
35
10.548
22
11.036
9
11.3.36
47
9.856
34
10.597
21
11.064
8
11.355
46
9.942
33
10.644
20
11.090
7
11.314
45
10.015
32
10.683
19
1M14
6
11.245
44
10.075
31
10.719
18
11.134
5
11.132
43
10.121
30
10.751
17
11.159
4
10.907
42
10.183
29
10.780
16
11.183
3
10.600
41
10.242
28
10.805
15
11.206
2
10.022
40
10.297
27
10.842
14
11.229
1
9.371
39
10.348
26
10.880
13
11.252
0
8.126
38
10.396
25
10.920
12
11.274
37
10.448
24
10.961
11
11.295
36
10.498
23
11.004
10
11.316
Older Age Forty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
49
9.535
36
10.348
23
10.833
10
11.144
48
9.642
35
10.399
22
10.863
9
11.171
47
9.736
34
10.449
21
10.891
8
11.160
46
9.816
33
10.488
20
10.916
7
11.125
45
9.883
32
10.524
19
10.939
6
11.062
44
9.937
31
10.555
18
10.963
5
10.954
43
10.000
30
10.583
17
10.985
4
10.732
42
10.058
29
10.607
16
11.006
3
10.417
41
10.109
28
10.643
15
11.026
2
9.855
40
10.155
27
10.680
14
11.044
1
9.221
39
10.195
26
10.719
13
11.068
0
8.000
38
10.246
25
10.759
12
11.092
37
10.297
24
10.801
11
11.118
Digitized by VjOOQ IC
TABLE XXI.
Valuo of £1 per A&num daring the joint ContinYuinoe of Tiro Lives.
(CarlisU) 5 per Cent.)
Older Age Fifty Years.
401
Age.
Vftliw.
Ag0.
Valaa.
Age.
ValiM.
Age.
Veloe.
50
9.291
37
10.136
24
10.613
11
10.924
49
9.406
36
10.187
23
10.643
10
10.953
48
9.507
35
10.238
22
10.672
9
10.963
47
9.597
34
10.278
21
10.700
8
10.956
46
9.673
33
10.315
20
10.727
7
10.926
45
9.737
32
10.348
19
10.750
6
10.868
44
9.802
31
10.378
18
10.771
5
10.763
43
9.860
30
10.404
17
10.790
4
10.531
42
9.909
29
10.439
16
10.807
3
10.227
41
9.951
28
10.474
15
10.822
2
9.680
40
9.984
27
10.509
14
10.845
1
9.061
39
10.034
26
10.545
13
10.870
0
7.865
38
10.085
25
10.581
12
10.896
Older Age Fifty-One
Years.
Age.
Velne.
Age.
Value.
Age.
Value.
Age.
Valoe.
51
9.023
38
9.912
25
10.375
12
10.683
50
9.145
37
9.961
24
10.406
11
10.710
49
9.256
36
10.009
23
10.437
10
10.731
48
9.355
35
10.050
22
10.468
9
10.748
47
9.443
M
10.088
21
10.498
8
10.744
46
9.519
33
10.123
20
10.521
7
10.718
45
9.5S8
32
10.156
19
10.542
6
10.663
44
9.648
31
10.186
18
10.560
5
10.544
43
9.G97
30
10.219
17
10.576
4
10.323
42
9.737
29
10.252
16
10.589
3
10.029
41
9.766
28
10.283
15
10.611
2
9.496
40
9.815
27
10.314
14
10.634
1
8.893
39
9.864
26
10.344
13
10.658
0
7.710
Older Age Fifty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
52
8.751
39
. 9.688
26
10.130
13
10.441
51
8.880
38
9.733
25
10.162
12
10.464
50
8.999
37
9.776
24
10.194
11
10.477
49
9.107
36
9.817
23
10.227
10
10.487
48
9.205
35
9.855
22
10.261
9
10.494
47
9.292
34
9.893
21
10.2ii5
8
10.499
46
9.366
33
9.928
20
10.307
7
10.500
45
9.429
32
9.962
19
10.326
6
10.427
44
9.480
31
9.993
18
10.342
5
10.320
43
9.520
30
10.023
17
10.356
4
10.108
42
9.548
29
10.051
16
10.377
3
9.823
41
9.596
28
10.076
15
10.398
2
9.304
40
9.643
27
10.100
14
10.419
1
0
8.699
7.551
Digitized by LjOOQ IC
TA9HJ XXI.
Valoe of £1 per Annum dariof^ the jcunt Continuance of Two Liyet.
(Carlisle 5 per Cent)
Older Age Fifty-Three Years.
Age.
V»1q0.
Age.
V«lae.
Age.
31
Value.
Age-
Value.
Age.
ValM.
53
8.474
42
9.376
9.788
20
10.086
9
10.280
52
8,609
41
9.421
30
9.812
19
10.104
8
10.295
51
8.738
40
9.462
29
9.834
18
10.119
7
10.247
50
8,854
39
9.502
28
9.853
17
10.133
6
10.190
49
8.957
38
9.538
27
9.883
16
10.113
5
10.091
48
9,054
37
9.678
26
9.914
15
10.176
4
9.887
47
9.133
36
0.617
25
9.947
14
10.195
3
9.609
46
9.201
35
9.655
24
9.981
13
10.213
ft
9.081
43
9.256
34
9.693
23
10.017
12
10.230
I
8.506
44.
9,298
33
9.730
22
10.042
11
10.247
0
7.389
43
9.329
32
9.760
21
10.065
10
10.264
Older Age Fi%-Four Yean.
Age.
Valiu.
Age.
Value.
Age.
Value.
Af*
Value.
Age.
Value.
54
8.192
43
9.151
32
9.547
21
9.837
10
10.037
53
8.330
42
9.194
31
9.570
20
9.857
9
10.060
52
8.460
41
9.232
30
9.591
19
9.875
8
10.028
51
8.581
40
9.265
29
0.608
18
9.893
7
9.997
50
8.694
39
9.294
28
9.636
17
9.9U
6
9.952
49
8.799
38
9.333
27
9.666
16
9.927
5
9.868
48
8.884
37
9.372
26
9.698
15
9.942 <
4
9.659
47
8.957
36
9.411
25
9.731
14
9.956
3
9.360
46
9.018
35
9.450
24
9.766
13
9.976
2
8.861
45
9.067
34
9.490
23
9.792
12
9.99.^
1
8,309
44
9.104
33
9.520
22
9.816
11
lt).016
0
7.224
Older Age Fifty-Five Years,
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
.Age.
Value,
65
7.900
43
6.960
31
9.345
19
9.639
7
9.750
64
8.039
42
8.096
30
9.364
18
9.655
6
9.713
63
8.171
41
9.024
29
9.391
17
9.669
6
9.621
62
8.297
40
9.044
28
9.418
16
9.681
4
9.395
51 .
8.416
39
9.083
27
9.447
15
9.692
3
9.116
50
8.528
38
9.121
26
9.475
14
9.711
2
8.643
49
8.619
37
9.160
25
0.505
13
9.731
1
8.113
48
8.699
36
9.200
24
9.530
12
9.762
0
7.056
47
8.768
35
9.240
23
0.554
11
9.775
46
8.826
34
9.270
22
9.578
10
9.799
45
8.870
33
9.298
21
9.600
9
9.786
44
8.919
32
9.323
20
9.621
8
9.767
Digitized by LjOOQ iC
TABI,B JWJ.
m>
Value ef £1 per Aimam dwinff the joint Continuance of Tvo Lives.
(Garlitle 5 per Cent.)
Older Age Fifty-8ix Yean.
Al^
V.llM.
Ag..
VmliM.
Age.
32
Vriat.
Age.
20
VftltM.
Age
8
Vtloa.
56
7.600
44
8.721
9.091
9.877
9.^3
55
7.736
43
8.755
31
9.114
19
9.393
7
9.506
54
7.869
42
8.781
30
9.139
18
9.406
6
9.473
58
7.997
41
8.799
29
9.164
17
9.418
5
9.854
b2
8.121
40
8.835
28
9.189
16
9.427
4
9.139
51
8.*^48
39
8.871
27
9.^13
15
9.444
3
8.^79
SO
8.889
38
8.907
26
9.237
14
9.468
2
8.428
49
8.427
37
8.944
2)
9.262
13
9.482
1
7.916
48
8.503
36
8.981
24
9.286
12
9..'>02
0
6.866
47
8.570
35
9.012
23
9.310
11
9.^24
46
8.626
34
9.040
22
9.335
10
9.529
45
8.678
33
9.067
21
9.359
9
9.^20
Older Age Fifty «Seven Years.
Age.
V^oe.
Agt.
Value.
Ag*
Valne,
Age.
Valpe.
JVM.
9
Val,ie.
57
7.298
45
8.472
33
8.829
21
9.106
9.^64
56
7.426
44
8.508
32
8.8J^
20
9.122
8
9.?66
55
7.558
43
8.533
31
8.879
19
9.136
7
9.V6$
54
7.690
42
8.549
30
8.901
18
9.148
6
9.$2P
53
7.820
41
8.583
29
8.922
17
9.158
5
9.p96
52
7.950
40
8.617
28
8.942
1^
9.174
4
8.«9^
51
8.P53
39
8.650
27
8.060
15
9.190
3
8.M8
50
8.147
38
8.683
26
8.984
14
9.207
?
8.«10
49
8.231
37
8.716
25
9.008
13
9.225
1
7-708
48
8.306
36
8.746
24
9.034
12
9.243
0
6.682
47
8.872
35
8.775
23
9.060
11
9.252
46
8.4:^7
34
8.803
22
9.087
10
9.?59
Older Age Fifty^Eight Years.
Age.
Vshie.
6.U86
Age.
46
Value.
Age.
Value.
Age.
22
Value.
A^ce.
Value.
58
8.219
34
8.565
8.834
10
9.000
57
7.118
45
8.257
33
8.594
21
8.851
9
9.012
9.024
56
1.250
44
8.285
32
8.616
20
8.866
8
55
7.m
48
8.302
31
8.637
19
8.879
7
9.632
54
7.519
42
8.335
30
8.656
18
8.fc90
6
8.972
53
7.657
41
8.^66
29
8.670
17
8.905
5
8.84$
52?
7.f65
40
8.896
28
8.684
16
8.919
4
8.659
51
7.8G4
39
8.423
27
8.707
15
8.934
9
8.423
50
9.J55
38
8.449
26
8.731
14
8.948
2
8.011
49
8.137
37
8.478
25
8.757
13
8.962
1
7.^04
48
8.ni
36
8.507
24
8.785
12
8.975
0
6.5U4
47
8.}70
35
8.536
23
8.814
11
8.988
Dig?iz5bS? Google
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Lifts.
(Corlittia 5 per Cent.)
Older Age Fifty-Nine Years*
Ag«.
Value.
Ag...
Value.
Age.
Value.
A«e.
Value.
11
Value.
59
6.705
47
7.968
35
8.310
23
8.571
8.740
58
6.832
46
8.011
34
8.341
22
8.589
10
8.757
57
6.962
45
8.044
33
8.363
21
8.605
9
8.774
50
7.096
44
8.0f56
32
8.3S3
20
8.620
8
8.811
55
7.234
43
8.0S9
31
8.400
19
8.633
7
8.799
54
7.375
42
8.128
30
8.415
18
8.647
6
8.729
53
7.486
41
8.153
29
8.427
17
8.660
6
8.608
52
7.589
40
8.175
28
8.449
16
8.672
4
8.421
51
7.684
39
8.194
27
8.472
15
8.6S4
3
8.224
50
7.771
38
8.2-22
26
8.497
14
8.694
2
7.806
49
7.851
37
8.251
25
8.523
13
8.709
1
7.305
48
7.915
36
8.2t0
24
8.551
12
8.724
0
6.332
Older
Age Sixty Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
8
Value.
60
6.456
47
7.778
34
8.127
21
8.378
8.594
59
6.579
46
7.817
33
8.148
20
8.394
7
8.567
58
6.705
45
7.846
32
8.166
19
8.407
6
8.490
57
6.835
44
7.879
31
8.182
18
8.419
5
8.368
56
6.969
43
7.908
30
8.196
17
8.430
4
8.229
55
7.106
42
7.931
29
8.217
16
8.439
3
8.022
54
7.217
41
7.948
28
8.238
15
8.446
2
7.601
53
7.323
40
7.961
27
8.260
14
8.460
1
7.109
52
7.422
39
7.988
26
8.283
13
8.476
0
6.166
51
7.514
38
8.015
25
8.306
12
8.493
50
7.601
37
8.044
24
8.325
11
8.511
49
7.670
36
8.074
23
8.344
10
8.530
48
7.729
35
8.105
22
8.361
9
8.575
Older .
Age Sixty-One Years.
Age.
Value.
Age.
Value.
Age.
35
Value.
Age,
Value.
Age.
Value.
61
6.257
48
7.567
7.920 ;
22
8.165
9
8.3G9
60
6.376
47
7.614
34
7.941
21
8.1S4
8
8.372
59
6.495
46
7.652
33
7.960
20
8,197
1
8.334
58
6.616
45
7.688
32
7.978
19
8.209
6
8.256
57
6.738
44
7.717
31
7.995
18
8.219
5
8.178
56
6.860
43
7.739
30
8.014
17
8.226
4
8.030
55
6.969
42
7.755
29
8.033
16
8.233
3
7.815
54
7.075
41
7.763
28
8.052
15
8.246
2
7.397
53
7.177
40
7.788
27
8.071
14
8.260
1
6.917
52
7.275
39
7.814
26
8.090
13
8.275
0
6.032
51
7.370
38
7.841
25
8.109
12
8.291
50
7.445
37
7.868
24
8.128
11
8.308
49
7.510
36
7.897
23
8.147
10
8.338
Digitized by LjOOQ IC
TABLE XXL
405
Value of £1 per Annum during the joint Continuance of Two Lifeib
(Carlisle 6 per Cent.)
Older Age Sixty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
A«e.
Valoe.
62
6.067
42
7.571
22
7.975
2
7.193
61
6.182
41
7.594
21
7.989
1
6.756
60
6.294
40
7.618
20
8.001
0
5.891
59
6.403
39
7.642
19
8.012
58
6.510
38
7.6G6
18
8.020
57
6.615
37
7.691
17
8.026
56
6.722
36
7.713
16
8.038
55
6.828
3J
7.735
15
8.050
54
6.934
34
7.756
14
8.063
53
7.03:J
33
7.776
13
8.077
52
7.142
32
7.796
12
8.091
51
7.222
31
7.814
11
8.09J
50
7.294
30
7.831
10
8.102
49
7.357
29
7 847
9
8.104
48
7.412
28
7.861
8
8.104
47
7.458
27
7.875
7
8.102
46
7.497
25
7.893
6
8.059
45
7.528
25
7.913
5
7.978
44
7.550
24
7.933
4
7.823
43
7.565
23
7.953
3
7.604
Older Age Sixty-Three Years.
Ag#.
Value.
Age.
Value.
Age.
Value.
Age.
Valoft.
63
5 875
43
7.379
23
7.760
3
7.390
62
5.986
42
7.401
22
7.775
2
7.009
61
6.091
41
7.422
21
7.788
1
6.586
60
6.190
40
7.443
20
7.799
0
5.742
59
6.283
39
7.462
19
7.809
58
6.370
38
7.481
18
7.816
57
6.475
37
7.502
17
7.827
56
6.581
36
7.524
16
7.838
55
6.689
35
7.546
15
7.849
54
6.799
34
7.568
14
7.859
53
6.911
33
7.591
13
7.870
52
6.996
32
7.608
12
7.880
51
7.073
31
7.623
11
7.889
50
7.142
30
7.636
10
7.899
49
7.203
29
7.648
9
7.907
48
7.256
28
7.658
8
7.916
47
7.298
27
7.676
7
7.892
46
7.332
26
7.695
6
7.850
45
7.356
25
7.715
6
7.768
44
7.372
24
7.737
4
7.6U9
Digitized by LjOOQ iC
TABLSXXL
Value of £l per Annum durmg the Joml ConiinuaDoe of tVo LiimL
(Carlisle 6 per Cent)
Older Age Sixty-Four Years.
Age.
Valua.
Age.
Valae.
Age.
Value.
Age.
Valin.
64
5.669
44
7.175
24
7.532
4
7.387
63
5.778
43
7.197
23
7.547
3
7.179
62
5.879
42
7.216
• 22
7.5fil
8
6.815
61
5.971
41
7.233
21
7.573
1
6.406
60
6.053
40
7. 243
20
7.584
0
5.586
59
6.127
39
7.260
7.593
58
6.229
38
7.280
7.603
57
6.334
37
7.302
7.613
56
6.442
36
7.324
7.621
55
6.554
35
7.347.
7.630
54
6.669
34i
7.372
7.637
53
6.756
33
7.388
7.648
52
6.836
32
7.403
7.660
51
6.909
31
7.415
7.673
50
6.975
30
7.426
7.686
49
7.034
29
7.434
7.700
48
7.080
28
7.451
7.6{*9
47
7.117
27
7.469
7.671
46
7.146
26
7.489
7.630
45
7.165
45
7.510
7.547
Older Age Sixty-Five Years.
Ag^.
Value*
Age.
Value.
Age.
Value.
Age.
ValttB.
65
5.456
45
6.964
25
7.295
7.316
64
5.566
44
6.986
24
7.310
7.150
63
5.665
43
7.003
23
7.324
6.961
62
5.7:)3
42
7.017
32
7.337
6.613
61
ai.830
41
7.028
21
7.349
6.217
60
5.895
40
7.034
20
7.361
0
5.438
59
5.993
39
7.053
19
7.371
58
6.094
38
7.073
18
7.379
57
6.199
37
7.095
17
7.387
56
6.307
36
7.118
16
7,393
55
6.418
35
7.143
15
7.398
54
6.506
34
7.160
14
7.409
53
6.587
33
7.175
13
7.421
52
6.664
33
7.1'^8
18
7.434
51
6.734
31
7.200
U
7.448
50
6.799
30
7.210
10
7.463
49
6.849
29
7.226
0
7.453
48
6.891
28
7.242
8
7.454
47
6.924
27
7.259
7
7.440
46
6.948
26
7.277
6
7.390
Digitized by LjOOQ IC
TAMJB XXI.
40f
Vikw 4lf £1 per Aninim dtiring the Joiiit Contiattaaee of Two Lit«l.
(Carlitle S per CentO
Older Age Sixty^Six
Yeara.
Ag^
ValM.
Age.
Value.
Age.
Value.
Age.
Value.
66
5.230
46
6.740
26
7.047
6
7.156
65
5.345
45
6.763
25
7.061
5
7.050
64
5.447
44
6.781
24
7.076
4
6.909
63
5.536
43
6.794
23
7.090
3
6.734
62
5.613
42
6.802
22
7.104
2
6.400
61
6.678
41
6.804
21
7.118
1
6.018
60
5.771
40
6.821
20
7.128
0
5.235
59
5.866
39
6.839
19
7.136
58
5.961
38
6.859
18
7.142
57
6.058
37
6.860
17
7.147
56
6.156
36
6.903
16
7.1^1
55
6.241
35
6.920
15
7.161
54
6.323
34
6,935
14
7.171
53
6.401
33
6.949
13
7.182
52
6.475
32
6.963
12
7.195
51
6.546
31
6.975
11
7.208
50
6.601
30
6.989
10
7.192
49
6.647
29
7.004
9
7.202
43
6.686
28
7.018
8
7.211
47
6.717
27
7.033
7
7.198
Older Age Sixty-Seven Year*.
Age.
Value.
Age.
Value.
A«e.
Value.
Age.
Value.
67
4.990
47
6.503
27
6.785
7
6.945
66
5.109
46
6.528
26
6.799
6
6.861
65
5.215
45
6.547
25
6.813
5
6.786
64
5.309
44 .
6.559
24
6.828
4
6.665
63
5.390
43
6.565
23
6.844
3
6.501
62
5.458
42
6.565
22
6.8B0
2
6.178
61
5.546
41
6.580
21
6.870
1.
5.787
60
5.633
40
6.597
20
6.879
0
5.049
59
5.717
39
6.614
19
6.885
58
5.800
38
6.632
18
6.891
57
5.881
37
6.651
17
6.894
56
5.963
36
6.667
16
6.903
*
55
6.044
35
6.683
15
6.912
54
6.124
34
6.698
14
6.922
53
6.204
33
6.713
13
6.932
52
6.282
32
6.728
12
6.943
51
6.341
31
6.741
11
6.947
50
6.392
30
6.753
10
6.949
49
6.436
29
6.765
9
6.950
48
6.473
28
6.7f5
8
6.948
Digitized by LjOOQ IC
f»
TABLE XXI.
Valae of £1 per Ammm daring the jolot Ccmttiitiaiiee of Two Livei.
(CarUtle 5 per Cent)
Older Age Sixty-Eight Yean.
Ab«.
V«lne.
Age,
Value.
Ag«.
V.lw.
A«^
Valtte.
68
4.737
48
6.251
28
6.514
8
6.699
67
4.858
47
6.279
27
6.527
7
6.630
66
4.968
46
6.299
26
6.541
6
6.574
65
5.067
45
6.313
25
6.557
5
6.525
64
5.154
44
6.319
24
6.573
4
6.416
63
5.230
43
6.319
23
6.591
3
6.259
62
5.314
42
6.333
22
6.602
2
5.901
61
5.393
41
6.347
21
6.611
1
5.542
60
5.4fi7
40
6.360
20
6.618
0
4.B64
59
5.536
39
6.374
19
6.624
6^
5.600
38 ,
6.383
18
6.628
67
5.679
37 '
6.403
17
6.636
56
5.759
36
6.419
16
6.G43
55
5.841
3:>
6.435
15
6.651
54
5.924
34
6.451
14
6.659
53
6.009
33
6.468
13
6.667
52
6.071
32
6.480
12
6.674
51
6.126
31
6.491
11
6.681
50
6.174
30
6.500
10
6.687
49
6.216
29
6.508
9
6.693
Older Age l^xty-Nine Years.
Ag«.
Valor.
Ag«.
49
Value.
As*.
Value.
Aft.
Value.
69
4.471
5.980
29
6.236
9
6.425
68
4.592
48
O.OiO
28
6.248
8
6.377
67
4.705
47
6.033
27
6.262
7
6.329
66
4.808
46
6.050
26
6.276
6
6.298
65
4.9U2
45
6.059
25
6.292
5
6.265
64
4.988
44
6.061
24
6.309
4
6.164
63
5.069
43
6.074
23
6.320
3
5.960
62
5.143
42
6.085
22
6.329
2
5.637
61
5.209
41
6.096
21
6.337
1
5,316
60
5.268
40
6.105
20
6.344
0
4.679
59
5.319
39
6.113
19
6.350
58
5.394
38
6.127
18
6.357
57
5.472
37
6.142
17
6.363
56
5.554
36
6.158
16
6.369
55
5.638
35
6.176
15
6.375
54
5.725
34
6.194
14
6.380
r>3
5.788
31
6.206
13
6.388
52
5.845
32
6.216
12
6.396
51
5.896
31
6.224
11
6.405
50
5.941
30
6.231
10
6.415
Digitized by VjOOQ iC
TABLE XXI.
4e»
Value of XI per Annniii diirini^ the joint Gontiniuuce of Two Liref.
(Carlisle 5 per Cent.)
Older Age Seventy
Years.
Agit
Value.
Ag«.
VdM.
Age.
Value.
Age.
Value.
70
4.191
50
5.695
30
5.954
10
6.131
69
4.310
49
5.728
29
5.9U5
9
6.114
68
4.423
48
6.754
28
5.977
8
6.074
67
4.533
47
5.774
27
5.990
7
6.044
66
4.637
46
5.787.
26
6.003
6
6.030
65
4.737
45
5.793
25
6.017
5
6.008
64
4.81S
44
5.806
24
6.027
4
5.866
63
4.889
43
.'j.816
23
6.037
3
5.678
62
4.950
42
5.824
22
6.046
2
5.387
61
5.002
41
5.8ii9
21
6.054
I
5.096
60
5.044
40
5.832
20
6.061
0
4.496
59
5.1)5
39
5.845
19
6.067
58
5.189
38
5.859
18
6.073
57
5.267
37
5.874
17
6.077
56
5.347
36
5.891
16
6.081
55
5.431
35
5.910
15
6.084
54
5.494
34
5.922
14
6.092
53
5.551
33
5.932
13
6.100
52
5.604
32
5.941
12
6.109
51
5.652
31
5.948
11
6.12U
Older Age Seventy-One Years.
Age.
Value.
Age.
Value.
Age.
V.lue.
Age.
Value.
71
3.893
51
5.391
31
5.660
11
5.819
70
4.00S
.')0
5.427
30
5.670
10
5.848
69
4.123
49
5.457
29
5.680
9
5.820
68
4.238
48
5.480
28
5.690
8
5.789
67
4.354
47
5.498
27
5.7U0
7
* 5.775
66
4.469
46
5.510
26
5.710
6
5.772
65
4.552
45
5.523
25
5.720
5
5.730
64
4.625
44
5.533
24
5.729
4
5.585
63
4.687
43
5.540
23
5.739
3
5.414
62
4.738
42
5.543
22
5.749
2
5.150
61
4.779
41
5.542
21
5.7.'>8
1
4.884
60
4.846
40
5.. 553
20
5.764
0
4.296
59
4.914
39
5.565
19
5.769
58
4.982
38
5.579
18
5.773
57
5.052
37
5.594
17
5.776
56
5.123
36
5.611
16
5.778
55
5.183
35
5.622
15
5.785
54
5.2J9
34
5.633
14
5.792
53
5.293
33
5.643
13
5.800
52
5.344
32
5.652
12
5.809
Digitized by LjOOQ IC
410
TABLE XXI.
Valtt0 of £1 per Annum daring tbe joint Conlinuaiieo of TVo Jairm*
(Garliile 5 per Gent.)
Older Age Seventy-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
72
3.615
52
5.102
32
5.379
12
5.523
71
3.725
51
5,141
31
5.388
11
5.525
70
3.839
50
5.174
30
5.396
10
5.526
69
3.958
49
5.201
29
5.404
9
5.526
68
4.080
48
6.223
28
5.411
8
5,5-24
67
4.307
47
5.240
27
5.418
7
5.520
66
4.J293
i|6
5.255
26
5.427
6
5.525
65
4.368
45
5.265
25
5.437
5
5.466
64
4.433
44
5.271
24
5.447
4
5.321
63
4.486
43
5.272
23
5.453
3
5.166
62
4.529
42
6.269
22
5.469
2
4.926
61
4.590
41
5.278
21
5.476
1
4.680
60
4.651
40
5.289
20
5.481
0
4.106
59
4.710
39
6.300
19
5.485
58
4.769
38
5.313
18
5.488
57
4.826
37
5.327
17
5.490
56
4.883
36
5.338
16
5.496
55
4.939
35
5.349
15
5.502
54
4.994
34
5.359
14
6.508
53
5.049
33
5.369
13
5.515
Older Age Seventy-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
73
3.371
53
4.837
33
5.123
13
5.255
72
3.476
52
4.878
32
5.131
12
5.260
71
3.587
51
4.915
31
5.138
11
5.264
70
3.705
50
4.946
30
5.144
10
5.268
69
3.830
49
4.971
29
5.149
9
5.272
6S
3.961
48
4.992
28
5.153
8
5.275
67
4.049
47
5.008
27
5.162
7
5.305
66
4.127
46
5.019
26
5.171
6
5.286
65
4.196
45
5.026
23
5.182
5
5.216
64
4.254
44
5.027
24
5.194
4
5.074
63
4.302
43
5.023
23
5.206
3
4.936
62
4.359
42
5.031
22
5.213
2
4.737
61
4.413
41
5.039
21
5.219
1
4.483
60
4.463
40
5.048
20
5.223
0
3.926
59
4.910
39
5.058
19
5.226
58
4.553
38
5.068
18
5.228
57
4.607
37
5.078
17
5.233
56
4.663
36
5.089
16
5.238
55
4.719
35
6.100
15
5.244
54
4.778
34
5.111
14
5.249
Digitized by VjOOQiC
TABLB XXI.
4U
Value «f £1 per Aiiniim during thi josnl Gontmuaiiee of T#o liftt.
(Culitle 5 per Cent)
Older
Age SeTcnty-Four Years.
Age.
TaliM.
Agt.
Value.
Age.
Valee.
Age.
Value.
74
3.165
54
4.600
34
4.894
14
5.016
73
3.265
53
4.643
33
4.902
13
5.021
72
3.371
52
4.681
32
4.908
12
5*027
71
3.484
51
4.714
31
4.913
11
5.033
70
3.604
50
^ 4.742
30
4.917
10
5.040
69
3.731
49
4.766
29
4.920
9
5.047
68
3.820
48
4.784
28
4.928
8
5.084
67
3.901
47
4.797
27
4.937
7
5.092
66
3.978
46
4.805
26
4.948
6
5.056
65
4.038
45
4.808
25
4.959
5
4.979
64
4.094
44
4.806
24
4.971
4
4.844
63
4.150
43
4.813
23
4.978
8
4.759
62
4.199
42
4.820
22
4.984
2
4.550
61
4.244
41
4.826
21
4.990
1
4.293
60
4.282
40
4.832
20
4.994
0
3.756
59
4.315
39
4.838
. 19
4.997
58
4.367
38
4.847
18
5.001
57
4.421
37
4.858
17
5.005
56
4.478
36
4.869
16
5.009'
55
4.538
35
4.881
15
5^013
Older Agii Seventy-Five Yeftts.
=■ ■--••■ - — - --- ■ — - - -
Agi.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
75
3.015
55
4.400
35
4.706
15
4.821
74
3.108 .
54
4.443
34
4.714
14
4.826
73
3.206
53
4.483
33
4.721
13
4.832
7i
3.308
52
4.518
32
4.7lf
12
4.839
71
3.416
51
4.549
31
4,731 '
11
4.847
70
3.528
50
4.577
30
4.735
10
4.855
69
3.616
49
4.598
29
4.743
9
4.853
68
3.700
48
4^613
28
4.751
8
4.892
67
3.778
47
4.624
27
4.759
7
4.884
66
3.852
46
4.629
26
4.768
6
4.834
63
3.92i
49
4.630
25
4.778
5
4.756
64
3.97f
44
4.637
24
4.785
4
4.668
tl
4.025
43
4.642
23
4.791
3
4.581
4.066
42
4.646
22
4.797
2
4.366
61
4.099
41
44649
21
4.802
1
4aio
60
4.125
40
4.650
20
4.807
4.811
0
3.59b
59
4.174
39
4.658
19
58
4.22^
38
4.668
18
4.814
57
4.282
37
4.679
17
4.817
56
4.339
36
4.699
16
4.819
Digitized by VjOOQ iC
m
TABLB XXI.
Value of £1 per Annam during the joint Coutinuanee pf Two Lives.
(Carlisle 5 per Cent.)
Older Age Seventy-Six Years.
Age.
Value.
Age.
Valua.
Age.
Value.
Ai^.
Value.
76
2.870
56
4.201
36
4.520
16
4.632
75
2.956
55
4.243
35
4.51^8
15
4.636
74
3.044
54
4.282
34
4..'i35
14
4.642
73
3.134
53
4.319
33
4.542
13
4.647
72
3.226
52
4.3o3
32
4.548
12
4.654
71
3.319
51
4.3^5
31
4.553
11
4.661
70
3.406
50
4.408
30
4.560
10
4.672
69
3.492
49
4.427
29
4.567
9
4.677
68
3.578
48
4.441
2S
4.574
8
4.699
67
3.661
47
4.431
27
4.581
7
4.678
66
3.746
46
4.4')6
26
4.588
6
4.621
65
3.805
45
4.463
25
4.595
5
4.577
64
3.856
44
4.468
24
4.601
4
4.4911
63
3.897
43
4.471
23
4.608
3
4.402
62
3.930
42
4.472
22
4.614
2
4.186
61
3.954
41
4.470
21
4.620
I
3.934
60
4.000
40
4.477
20
4.6i4
0
3.465
59
4.048
39
4.486
19
4.627
53
4.01)8
33
4.496
18
4.630
57
4.149
37
4.507
17
4.631
Older
Age Seventy-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Ar.
Value.
77
2.744
57
4.013
37
4.348
17
4.458
76
2.823
53
4.053
36
4.3)6
16
4.462
75
2.901
55
4.093
35
4.363
15
4.466
74
2.977
54
4.132
34
4.370
14
4.471
73
3.053
53
4.170
33
4.377
13
4.477
72
3.127
52
4.208
32
4.384
12
4.483
71
3.212
51
4.234
31
4.390
11
4.484
70
3.300
50
4.236
30
4.396
10
4.484
69
3.390
49
4.273
29
4.401
9
4.483
68
3.484
48
4.286
28
4.406
8
4.480
67
3.580
47
4.294
27
4.410
7
4.476
66
3.643
46
4.302
26
4.416
6
4.432
65
3.696
45
4.307
25
4.423
5
4.397
64
3.740
44
4.310
24
4.430
4
4.312
63
3.775
43
4.309
23
4.438
3
4.223
62
3.800
42
4.305
22
4.446
2
4.008
61
3.843
41
4.311
21
4.450
1
3.779
60
3.886
40
4.318
20
4.454
0
3.335
59
3.929
39
4.327
19
4.456
58
3.971
38
4.337
18
4.458
Digitized by VjOOQ IC
TABLE XXI.
413
Value of £1 per Annum during the joint Continuftnce of Two Lives.
(Carlisle 5 per Cent)
Older Age Seventy-Eight Years.
AfB.
Valae.
Age.
Value.
Age.
Value.
Age.
Value.
78
2.617
58
3.821
38
4.171
18
4.281
n
2.691
57
3.860
37
4.178
17
4.284
76
2.760
56
3.900
36
4.186
16
4.288
75
2.827
55
3.941
35
4.194
15
4.292
74
2.889
54
3.983
34
4.202
14
4.296
73
2.948
53
4.026
33
4.210
13
4.300
72
3.030
52
4.054
32
4.215
12
4.303
71
3.116
51
4.079
31
4.220
11
4.306
70
3.20S
50
4.099
30
4.224
10
4.308
69
3.305
49
4.114
29
4.227
9
4.310
68
3.407
48
4.126
28
4.229
8
4.312
67
3.472
47
4.135
27
4.235
7
4.279
66
3.528
46
4.141
26
4.242
6
4.243
65
3.576
45
4.144
25
4.250
6
4.214
64
3.614
44
4.143
•24
4.258
4
4.132
63
3.644
43
4.138
23
4.267
3
4.043
62
3.684
42
4.H3
22
4.272
2
3.8.39
61
3.7-22
41
4.149
21
4.276
1
3.624
60
3.757
40
4.155
20
4.278
0
3.204
59
3.790
39
4.163
19
4.280
Older Age Seventy-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
19
Value.
79
2.460
59
3.614
39
3.969
4.079
78
2.530
58
3.651
38
3.976
18
4.082
n
2.596
57
3.690
37
3.983
17
4.085
76
2.657
56
3.731
36
3.992
16
4.087
75
2.714
55
3.775
35
4.001
15
4.090
74
2.767
54
3.821
34
4.011
14
4.092
73
2.845
53
3.851
33
4.016
13
4.096
72
2.928
52
3.876
32
4.020
12
4.100
71
3.017
51
3.898
31
4.023
11
4.104
70
3.111
50
3.916
30
4.025
10
4.109
69
3.210
49
3.930
29
4.026
9
4.114
68
3.276
48
3.941
28
4.032
8
4.101
67
3.334
47
3.948
27
4.038
7
4.084
66
3.385
46
3.951
26
4.046
6
4.055
65
3.423
45
3.951
25
4.054
5
4.031
64
3.464
44
3.947
24
4.063
4
3.951
63
3.502
43
3.951
23
4.068
3
3.861
62
3.537
42
3.955
22
4.072
2
3.670
61
3.567
41
3.960
21
4.075
1
3.469
60
3.592
40
3.964
20
4.078
0
3.074
Digitized by VjOOQ iC
4U
TABLK XXI.
Value of £1 per Annwn during (he joint GpatiaiHuice of Two Llr^*
(CtrliilQ 3 per Cent)
Older Age Eighty Yean.
L
AgeL
Value.
Age.
Valw.
Age.
Value.
Ar.
Valor.
80
2.324
59
3.465
38
3.797
17
3.899
79
2.394
5S
3.502
37
3*806
16
3.900
78
2.459
57
3.542
36
3.815
15
3.901
V
2.519
56
3.585
35
3.826
14
3.905
76
2.574
55
3.030
34
3.831
13
3.909
75
2.623
54
3.060
33
3.836
12
3.914
74
2.695
53
3.687
32
3.839
11
3.919
73
2.770
52
3.710
3)
3.842
10
3.925
72
2.849
51
3.730
30
3.843
9
3.900
71
2.933
50
3.746
29
3.848
8
3.898
70
3.020
49
3.758
28
3.854
7
8.892
69
3.085
48
3.767
27
3.860
6
3.867
68
3.145
47
3.772
26
3.867
5
3.845
67
3.201
46
3.774
25
3.874
4
3.767
66
3.251
45
3.772
24
3.879
3
9.680
65
3.297
44
3.776
23
3.883
2
3.502
64
3.335
43
3.779
22
3.887
I
3.314
63
3.368
42
3.781
21
3.890
0
2.943
62
3.394
41
3.783
20
3.893
61
3.415
40
3.784
19
3.896
60
3.430
39
3,790
18
3.898
Older Age Eighty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Vrioe.
81
0.163
60
8.274
39
3.595
18
3.692
80
2.232
59
3.307
38
3.603
17
3.693
79
2.298
58
3.342
37
3.611
16
3.693
78
2.359
57
3.379
36
3.621
15
3.696
77
2.414
56
3.418
35
3.626
14
8.700
76
2.467
55
3.447
34
3.631
13
3.704
75
2.5?2
54
3.473
33
3.635^
12
3.709
74
2.599
53
3.497
32
3.638
11
3.714
73
2.667
52
3.419
31
3.641
10
3.705
72
2.736
51
3.539
30
3.646
9
3.697
71
2.807
50
3.553
29
3.650
8
3.703
70
2.871
49
8.564
28
8.655
7
3.708
69
2.933
48
3.572
27
3.661
6
3.680
68
2.994
47
3.576
26
3.666
5
3.655
^7
3.053
46
3.577
25
8-671
4
3.583
66
3.111
45
3.581
24
3.675
3
3 498
65
3.151
44
3.!)84
23
3.679
2
3.333
64
3.184
43
3.585
22
3.683
1
3.159
63
3.210
42
3.585
21
3.687
62
3.230
41
3.584
20
3.689
61
3.242
40
3.489
19
3.691
Digitized by LjOOQ iC
TABL9 XXI.
414
Value of £1 per Annum during the joint Continuance of Two Ii¥e8.
(Carlisle 5 per Cent.)
Older Age Eighty-Two Years.
Age.
Velue.
Age.
Velae.
Age.
Veloe.
Age.
Velae.
83
2.027
61
3.105
40
3.414
19
3.507
81
2.096
60
3.134
39
3.420
18
3.507
80
2.161
59
3.164
38
3.428
17
3.507
79
2.22-J
5S
3.194
37
3.436
16
3.510
78
2.279
57
3.224
36
3.441
15
3.513
77
2.333
56
3.251
35
3.446
14
3.516
76
2.391
55
3.27d
34
3.451
13
3.520
75
2.449
h4
3.303
33
3.455
12
3.524
74
2.506
53
3.328
32
3.459
11
3.524
73
2.561
52
3.352
31
3.463
10
3,524
7«
2.616
51
3.368
30
3.467
9
3.522
71
2.677
5U
3.381
29
3.470
8
3.520
70
2.740
49
3.391
28
3.474
7
3.516
69
2.805
48
3.398
27
3.477
6
3.494
68
2.871
47
3.402
26
3.481
fi
3.464
67
2.938
46
3.406
25
3.486
4
3.398
66
2.980
46
3.409
24
3.491
3
3.317
65
3.015
44
3.409
23
3.496
2
3.164
64
3.043
43
3.408
22
• 3.501
63
3.063
42
3.405
21
3.504
62
3.076
41
3.409
20
3.506
Older Age Eighty-Three Yeara,
Age.
Vtlue.
Age.
VUue.
A«c.
Value.
Age.
Value.
83
1.882
62
2.931
41
3.228
20
3.315
82
1.947
61
2.956
40
3,233
19
3.315
81
2.011
60
2.980
39
3.239
18
'3.315
80
2.073
59
3.003
38
3.245
17
3.317
79
2.134
58
3.024
37
3.250
16
3 320
78
2.194
57
3.050
36
3.255
15
3.322
77
2.247
56
3.076
35
3.260
14
3.325
76
2.298
55
3.103
34
H.265
13
3.3-28
75
2.345
54
3.131
33
3.270
12
3.330
74
2.389
53
3.159
32
3.273
11
3.332
73
2.430
52
3.177
31
3.276
10
3.333
72
2.488
51
3.192
30
3.279
9
3.334
71
2.550
50
3.204
29
3.281
8
3.335
70
2.615
49
3.212
23
3.282
7
3.338
69
2.684
48
3.218
27
3.286
6
3.308
68
2.757
47
3.223
26
3.291
5
3.274
67
2.801
46
3.226
25
3.296
4
3.214
66
2.838
45
3.2-27
24
3.302
3
3,135
65
2.867
44
3.225
23
3.308
64
2.890
43
3.221
22
3.311
63
2.905
42
3.224
21
3 313
Digitized by LjOOQ IC
416 TABLE XXI.
Valae of £1 per Annttm during the joint Continuance of Tvo liret.
(Carlisltt 5 per Cent.)
Older Age Eighty-Four Yeart.
Age.
Vtaue.
x^t,
Vala«.
Age.
Valae.
•Age.
YaIocl
84
1.741
62
2.781
40
3.054
18
3.130
83
1.802
61
2.801
39
3.058
17
3.132
82
1.863
60
2.818
38
3.083
16
3.133
81
1.924
59
2.632
37
3.063
15
3.135
80
1.9ci5
58
2.856
36
3.073
14
3.137
79
2.045
57
2.883
35
3.079
13
3.139
78
2.095
56
2.910
34
3.085
12
3.142
77
2.142
55
2.940
33
3.0^8
11
3.145
76
2.185
54
2.971
32
3.091
10
3.148
75
2.224
53
2.990
31
3.093
9
3.151
74
2.260
52
3.006
30
3.094
8
3.178
73
2.315
51
3.019
29
3.094
7
3.160
7Z
2.374
50
3.029
28
3.098
6
3.123
7\
2.437
49
3.036
27
3.102
5
3.083
70
2.504
48
3.042
26
3.107
4
3.030
69
2.575
47
3.046
25
3.113
68
2.619
46
3.047
24
3.119
67
2.658
45
3.046
23
3.122
66
2.690
44
3.042
22
3.125
65
2.715
43
3.044
21
3.126
64
2.735
42
3.047
20
3.128
63
2.759
41
3.050
19
3.128
Oldei
Age Eighty-Five Years.
Age.
Vmlue.
Age.
Value.
Age.
Value.
Age.
Value.
85
1.583
63
2.599
41
2.861
19
2.934
84
1.645
62
2.615
40
2.863
18
2.935
83
1.705
61
2,628
39
2.867
17
2.936
82
1.769
60
2.637
38
2.872
16
2.937
81
1.832
59
2.660
37
2.877
15
•-^.937
80
1.895
58
2.685
36
2.883
14
2.939
79
1.945
57
2.712
35
2.890
13
2.942
78
1.990
56
2.741
M
2.893
12
2.945
77
2.031
55
2.773
33
2.896
11
2.949
76
2.068
54
2.791
32
2.898
10
2.953
7b
2.100
53
2.808
31
2.899
9
3.011
74
2.ir)0
52
2.822
30
2.900
8
3.020
73
2.203
51
2.833
29
2.903
7
2.981
72
2.259
50
2.842
28
2.907
6
2.937
71
2.318
49
2.849
27
2.911
5
2.893
70
2.380
48
2.854
26
2.916
69
2.423
47
2.856
25
2.921
68
2.463
46
2.856
24
2.924
67
2.498
45
2.854
23
2.927
66
2.528
44
2.856
22
2.929
65
2.555
43
2.858
21
2.931
64
2,579
42
2.860
20
2.932
Digitized by LjOOQ IC
TABLE XXI.
417
Value of £1 per Annum daring the joint Continuance of Two Lives.
(Carlisle 5 per Cent)
Older Age Eighty- Six Yeara.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
86
1.444
64
2.439
42
2.694
20
2.760
85
1.500
63
2.456
41
2.693
19
2.761
84
1.558
62
2.467
40
2.696
IS
2.762
83
1.618
61
2.474
39
2.701
17
2.762
82
1.681
60
2.495
38
2.706
16
2.762
81
1.747
59
2.517
37
2.711
15
2.764
80
1.796
58
2.541
36
2.718
14
2.767
79
1.842
57
2.567
35
2.721
13
2.770
78
1.884
56
2.594
34
2.724
12
2.773
77
1.922
55
2.613
33
2.726
11
2.777
76
1.956
54
2.629
32
2.728
10
2.822
75
2.001
53
2.644
31
2.729
9
2.871
74
2.048
52
2.657
30
2.732
8
2.863
73
2.096
51
2.668
29
2.735
7
2.803
72
2.145
50
2.676
28
2.739
6
2.751
71
2.195
49
2.683
27
2.742
70
2.238
48
2.687
26
2.746
69
2.279
47
2.689
25
2.749
68
2.319
46
2.689
24
2.752
67
2.357
45
2.691
23
2.754
66
2.393
44
2.693
22
2.757
65
2.419
43
2.693
21
2.759
\
Older Age Eighty-Seven Years.
«
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
87
1.331
65
2.304
43
2.556
21
2.619
B6
1.378
64
2.321
42
2.554
20
2.620
85
1.430
63
2.334
41 '
2.557
19
2.621
84
1.489
62
2.341
40
2.560
18
2.621
B3
1.555
61
2.360
39
2.565
17
2.621
82
1.626
60
2.380
38
2.570
16
2.623
81
1.675
69
2.400
37
2.576
15
2.625
80
1.721
58
2.421
36
2.579
14
2.627
79
1.763
57
2.442
35
2.583
13
2.630
78
1.802
56
2.460
34
2.585
12
2.633
n
1.838
55
2.477
33
2.588
11
2.633
76
1.879
54
2.493
32
2.590
10
2.633
75
1.919
63
2.508
31
2.593
9
2.631
74
1.959
52
2.523
30
2.595
8
2.628
73
1.998
51
2.533
29
2.597
7
2.625
72
2.037
50
2.541
28
2.600
71
2.079
49
2.547
27
2.602
70
2.1-21
48
2.551
26
2.605
69
2.165
47
2.553
25
2.608
68
2.208
46
2.556
24
2.611
67
2.253
45
2.557
23
2.614
66
2.281
44
2.557.
22
2.617
Digiti;
3d Sv Google
418 TABLE XXI. "
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 5 per Cent.)
Older Age Eighty-Eight Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
88
1.273
65
2.234
42
2.474
19
2.535
87
1.311
64
2.249
41
2.477
18
2.535
86
1.355
63
2.258
40
2.480
17
2.536
85
1.407
62
2.276
39
2.484
16
2.538
84
1.467
61
2.293
38
2.488
15
2.540
83
1.535
60
2.310
37
2.491
14
2.542
82
1.583
59
2.326
36
2.495
13
2.544
81
1.629
58
2.341
35
2.498
12
2.545
80
1.674
57
2.359
34
2.502
11
2.546
79
1.717
56
2.376
33
2.505 •
10
2.547
78
1.759
55
2.395
32
2.507
9
2.548
n
1.797
54
2.413
31
2.509
8
2.548
76
1.833
53
2.432
30
2.511
75
1.867
52
2.444
29
2.512
74
1.899
51
2.454
28
2.513
73
1.928
50
2.462
27
2.516
72
1.969
49
2.467
26
2.519
71
2.013
48
2.471
25
2.523
70
2.059
47
2.474
24
2.527
69
2.108
46
2.476
23
2.531
68
2.159
45
2.476
22
2.533
67
2.189
44
2.475
21
2.534
66
2.214
43
2.472
20
2.535
Older Age Eighty-Nine Years.
Age.
Valueu
Age.
Value.
Age.
Value.
Age.
Value.
89
1.199
66
2.129
43
2.378
20
2.436
88
1.226
65
2.146
42
2.379
19
2.436
87
1.263
64
2.159
41
2.382
18
2.437
86
1.310
63
2.176
40
2.384
17
2.438
85
1.366
62
2.192
39
2.387
16
2.440
84
1.433
61
2.206
38
2.390
\b
2.441
83
1.479
60
2.218
37
2.394
14
2.442
82
1.524
59
2.229
36
2.397
13
2.444
81
1.569
58
2.246
35
2.402
12
2.446
80
1.613
57
2.265
34
2.406
11
2.448
79
1.657
56
2.284
33
2.408
10
2.450
1^
1.694
55
2.305
32
2.410
9
2.452
77
1.728
54
2.327
31
2.411
76
1.760
53
2.340
30
2.412
75
1.789
52
2.352
29
2.412
74
1.815
51
2.361
28
2.415
73
1.856
50
2.368
27
2.41S
72
1.899
49
2.373
26
2.421
71
1.945
48
2.377
25
2.425
70
1.995
47
2.379
24
2.430
69
2.047
46
2.380
23
2.432
68
2.079
45
2,379
22
2.434
67
2.106
44
2.376
21
2.435
Digitized by LjOOQ IC
TABLE XXI.
419
Value of £1 per Annum during the joint Continuance of Two lives^
(Carlisle 5 per Cent)
Older Age Ninety Yeara.
A^.
Valoa.
Age.
Valoe.
Age.
Vdue.
Age.
Value.
90
1.045
67
1.967
44
2.228
21
2.282
89
1.063
66
1.990
43
2.230
20
2.283
88
1.096
65
2.009
42
2.231
19
2.284
87
1.143
64
2.027
41
2.232
18 '
2.285
86
1.204
63
2.042
40
2.233
17
2.286
85
1.279
62
2.054
39
2.236
16
2.286
84
1.326
61
2.063
38
2.239
15
2.287
83
1.373
60
2.070
37
2.243
14
2.289
82
1.420
59
2.087
36
2.248
13
2.291
81
1.468
58
2.105
35
2.253
12
2.293
80
1.515
57
2.124
34
2.255
11
2.296
79
1.552
56
2.145
33
2.257
10
2.299
78
1.586
55
2.168
32
2.259
77
1.617
54
2.182
31
2.260
76
U645
53
2.194
30
2.260
75
1.669
52
2.205
29
2.263
74
1.707
51
2.213
28
2.265
73
1.747
50
2.220
27
2.269
72
1.789
49
2.225
26
2.272
71
1.833
48
2.228
25
2.276
70
1.880
47
2.230
24
2.278
69
1.912
46
2.229
23
2.280
68
1.941
45
2.227
22
2.281
Older Age Ninety-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
91
1.007
68
1.916
45
2.211
22
2.263
90
1.018
67
1.947
44
2.212
21
2.265
89
1.043
66
1.976
43
2.213
20
2.266
88
1.083
65
1.997
42
2.213
19
2.267
87
1.136
64
2.013
41
2.212
18
2.268
86
1.203
63
2.026
40
2.215
17
2.268
85
1.248
62
2.036
39
2.218
16
2.268
84
1.296
61
2.041
38
2.222
15
2.270
83
1.345
60
2.038
37
2.227
14
2.271
82
1.397
59
2.075
36
2.232
13
2.274
81
1.450
58
2.094
35
2.235
12
2.276
80
1.490
57
2.114
34
2.237
11
2.279
79
1.528
56
2.135
33
2.239
78
1.562
55
2.150
32
2.241
77
1.593
54
2.163
31
2.242
76
1.621
53
2.175
30
2.244
75
1.658
52
2.186
29
2.247
74
1.696
51
2.195
28
2.249
73
1.735
50
2.202
27
2.252
72
1.775
49
2.206
26
2.255
71
1.816
48
2.209
25
2.257
70
1.851
47
2.211
24
2.259
69
1.884
46
2.210
23
2.261
SgiSedly Google
420
TABLE XXL
Valae of £1 per Annum during the joint Continuance of Two LiTet.
(Carlisle & per Cent.)
Older
Age Ninety-Two Years.
Aije,
Value.
Age.
Value.
Ag«.
52
Valae.
A«e.
VahiB.
92
1.073.
72
1.836
2.273
32
2.329
91
1.079
71
1.874
51
3.282
31
2.331
90
1.093
70
1.913
50
2.289
30
2.333
89
1.117
69
1.952
49
2.294
29
2.335
88
1.150
68
1.992
48
2.297
28
2.337
87
1.192
67
2.033
47
2.298
27
2.S39
86
1.234
66
2.058
46
2.300
26
2.342
85
1.281
65
2.079
45
2.301
25
2.344
84
1.333
64
2.094
44
2.301
24
2.347
83
1 395
63
2.105
43
2.299
23
2.350
82
1.460
62
2.111
42
2.297
22
2.353
81
1.505
61
2.128
41
2.299
21
2.355
80
1.547
60
2.145
40
2.302
20
2.356
79
1.586
59
2.163
39
2.306
19
2.356
78
1.623
58
2.181
38
2.311
18
2.356
77
1.656
;57
2.199
37
2.316
17
2.356
76
1.693
56
2.2)5
36
2,319
16
2.357
75
1.730
55
2.230
35
2.322
15
2.359
74
1.766
54
2.245
34
2.325
14
2.361
73
1.801
53
2.239
33
2.327
13
12
2.363
2.366
Older Age Ninety-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
93
1.173
73
1.873
53
2.366
33
2.432
92
1.175
72
1.914
52
2.377
32
2.434
91
1.181
71
1.957
51
2.387
31
2.436
90
1.190
70
2.003
50
2.394
30
2.437
89
1.203
69
2.052
49
2.398
29
2.438
88
1.219
68
2.103
48
2.401
28
2.438
87
1.254
67
2.133
47
2.404
27
2.441
86
1.297
66
2.158
46
2.405
26
2.444
85
1.349
65
2.177
45
2.404
25
2.447
84
1.410
64
2.191
44
2.402
24
2.451
83
1.479
63
2.199
43
2.399
23
2.456
82
1.527
62
2.216
42
2.401
22
2.458
81
U574
61
2.232
41
2.403
21
2.459
80
1.619
60
2.248
40
2.406
20
2.460
79
1.663
59
2.262
39
2 410
19
2.460
78
1.706
58
2.276
38
2.415
18
2.460
77
1.744
57
2.293
37
2.418
17
2.461
76
1.780
56
2.310
36
2.422
16
2.463
75
1.813
55
2.328
35
2.425
15
2.464
74
1.844
54
2.347
34
2.429
14
13
2.466
2.468
Digitized by VjOOQ IC
TABLE XXI.
Value of £1 per ADnum during the joint Continuance of Two lives.
(Carlisle 5 per Cent.)
421
Older
Age Ninety-Four Years.
Age.
Value.
Age.
74
Value.
Age.
Value.
Age.
Value.
94
1-245
1.880
54
2.408
34
2.482
93
1.246
73
1.923
53
2.421
33
2.484
92
1.243
72
1.969
52
2.432
32
2.486
91
1.287
71
2.018
51
2.441
31
2.487
90
1.227
70
2.071
50
2.447
30
2.487
89
1.214
69
2.126
49
2.451
29
2.487
88
1.242
68
2.161
48
2.454
28
2.490
87
1.281
67
2.187
47
2.456
27
2.493
86
1.332
66
2.210
46
2.456
26
2.497
85
1.394
65
2.229
45
2.454
25
2.501
84
1.468
64
2.240
44
2.451
24
2.506
83
1.518
63
2.257
43
2.452
23
2.508
82
1.567
62
2.272
42
2.454
22
2.510
81
1.616
61
2.285
41
2.456
21
2.511
80
1.665
60
2.297
40
2.458
20
2.511
79
1.713
59
2.306
39
2.461
19
2.511
78
1.753
58
2.324
38
2.464
18
2.512
77
1.789
57
2.343
37
2.468
17
2.513
76
1.823
56
2.363
36
2.472
16
2.515
75
1.853
55
2.385
35
2.477
15
14
2.516
2.517
Older Age Ninety-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
95
1.323
75
1.893
65
2.430
35
2.510
94
1.327
74
1.935
54
2.445
34
2.513
93
1.314
73
1.980
53
2.457
33
2.514
92
1.282
72
2.028
52
2.467
32
2.516
91
1.234
71
2.078
51
2.474
31
2.516
90
1.167
70
2.130
50
2.479
30
2.516
89
1.188
69
2.165
49
2.483
29
2.519
88
1.226
68
2.197
48
2.486
28
2.522
87
1.281
67
2.224
47
2.486
27
2.525
86
1.353
66
2.247
46
2.485
26
2.529
85
1.443
65
2.266
45
2.482
25
2.533
84
1.498
64
2.284
44
2.483
24
2.535
83
1.554
63
2.298
43
2.484
23
2.537
82
1.609
62
2.309
42
2.485
22
2.538
81
1.665
61
2.317
41
2.486
21
2.539
80
1.720
60
2.322
40
2.487
20
2.540
79
1.763
59
2.339
39
2.490
19
2.541
78
1.802
58
2.359
38
2.494
18
2.542
77
1.836
57
2.381
37
2.499
17
2.542
76
1.867
56
2.404
36
2.504
16
15
2.543
2.543
Digitized by
^oogle
422
TABLE XXI.
Value of £1 per Annum during the joint Gontinaanee of Two Lives.
(Carlisle 5 per Cent.)
Older Age Ninety-
Six Yeara
A«e.
Value.
Age.
Value.
A«t.
56
Velaa.
A«e.
Veliw.
96
1.364
n
1.866
2.388
36
2.473
95
1.383
75
1 906
55
2.402
35
2.476
94
1.372
74
1.947
54
2.415
34
2.478
93
1.331
73
1.988
53
2.426
33
2.479
92
1.261
72
2.031
52
2.435
32
2.480
91
1.161
71
2.075
51
2.442
31
2.481
90
1.173
70
2.111
50
2.447
30
2.483
89
1.203
69
2.145
49
2.451
29
2.486
88
1.250
68
2.178
48
2.453
28
2.488
87
1.315
67
2.208
47
2.453
27
2.491
86
1.397
66
2.237
46
2.451
26
2.494
85
1.450
65
2.256
45
2.452
25
2.500
84
1.505
64
2.271
44
2.452
24
2.500
83
1.563
63
2.282
43
2.453
23
2.500
82
1.622
62
2.288
42
2.452
22
2.502
81
1.683
61
2.290
41
2.452
21
2.504
80
1.728
60
2.306
40
2.455
20
2.505
79
1.769
59
2.324
39
2.458
19
2.506
78
1.805
58
2.343
38
2.462
18
2.506
n
1.838
57
2.365
37
2.467
17
16
2.506
2.505
Older Age Ninety-Seven Years.
A<«.
Value.
Ag«.
Value.
Age.
Value.
Age.
Value.
97
1.339
n
1.791
57
2.266
37
2.354
96
1.383
76
1.826
56
2.279
36
2.357
95
1.389
75
1.860
55
2.291
35
2.359
94
1.357
74
1.894
54
2.303
34
2.361
93
1.288
73
1.927
53
2.313
33
2.362
92
1.181
72
1.959
52
2.323
32
2.363
91
1.186
71
K993
51
2.329
31
2.365
90
1.202
70
2.028
50
2.334
30
2.366
89
1.231
69
2.063
49
2.337
29
2.368
88
1.271
68
2.098
48
2.338
28
2.370
87
1.324
67
2.134
47
2.338
27
2.371
86
1.369
66
2.154
46
2.339
26
2.373
85
1.420
65
2.170
45
2.339
25
2.375
84
1.477
64
2.180
44
2.338
24
2.377
83
1.539
63
2.186
43
2.337
23
2.380
82
1.607
62
2.187
42
2.335
22
2.382
81
1.652
61
2.201
41
2.337
21
2.383
80
1.693
60
2-216
40
2.340
20
2.384
79
1.729
59
2.231
39
2.344
19
2.384
78
1.762
58
2.248
38
2.348
18
17
2.384
2.383
Digitized by VjOOQ IC
TABLE XXI.
423
Value of £1 per Annum during the joint Continuance of Two Idves.
(Carlisle 5 per Cent.)
Older Age Ninety-Eight Years.
Ag».
Value.
Age.
Value.
Age.
Value.
Age.
Value.
98
1.323
78
1.708
58
2.125
38
2.212
97
1.396
77
1.738
hi
2.137
37
2.214
96
1.422
76
1.766
56
2.149
36
2.217
95
1.400
75
1.792
55
2.161
35
2.219
94
1.331
74
1.816
54
2.173
34
2.220
93
1.215
73
1.837
53
2.185
33
2.222
92
1.214
72
i:869
52
2.192
32
2.223
91
1.220
71
1.902
51
2.197
31
2.224
90
1.233
70
1.938
50
2.201
30
2.225
89
1.253
69
1.976
49
2.203
29
2.226
88
1.280
68
2.015
48
2.203
28
2.226
87
1.315
67
2.036
47
2.204
27
2.228
86
1.356
66
2.051
46
2.204
26
2.230
85
1.405
65
2.061
45
2.203
25
2.233
84
1.461
64
2.067
44
2.201
24
2.236
83
1.524
63
2.067
43
2.198
23
2.239
82
1.566
62
2.078
42
2.199
22
2.240
81
1.605
61
2.090
41
2.201
21
2.241
80
1.642
60
2.101
40
2.204
20
2.241
79
1.676
59
2.113
39
2.208
;i9
18
2.241
2.240
Older Age Ninety -Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
99
1.251
79
1.561
59
1.910
39
1.990
98
1.239
78
1.586
58
1.920
38
1.992
97
1.227
71
1.609
57
1.931
37
1.994
96
1.215
76
1.630
b^
1.942
36
1.996
95
1.203
75
1.648
55
1,955
35
1.998
94
1.191
74
1.663
54
1.968
34
2.000
93
1.186
73
1.691
53
1.975
33
2.001
92
1.184
72
1.720
52
1.980
32
2.002
91
1.184
71
1.753
51
1.983
31
2.002
90
1.187
70
1.787
50
1.985
30
2.002
89
1.192
69
1.824
49
1.985
29
2.001
88
1.217
68
1.843
48
1.986
28
2.003
87
1.250
67
1.857
47
1.986
27
2.005
86
1.291
66
1.866
46
1.985
26
2.007
85
1.340
65
1.871
45
1.984
25
2.010
84
1.398
64
1.872
44
1.981
24
2.013
83
1.434
63
1.880
43
1.982
23
2.014
82
1.468
62
1.888
42
1.983
22
2.015
81
1.501
61
1.896
41
1.985
21
2.015
80
1.532
60
1.903
40
1.987
20
19
2.015
2.014
Digitized by VjOOQ IC
4S4 TABUB XXI.
Value of £1 per Annum during the joint Continuance of Two liree.
(Carlisle 5 per Cent.)
Older Age One Hundred Years.
Ag«.
Valae.
Ag«.
Value.
Age.
Value.
Age.
Value.
100
0.962
79
1.293
58
1.538
37
1.589
99
0.977
78
1.310
57
1.548
36
1.591
98
0.992
77
1.325
56
1.558
35
1.593
97
1.008
76
1.337
55
1.569
34
1.594
96
1.023
75
1.346
54
1.574
33
1.594
95
1.038
74
1.366
53
1.578
32
1.595
94
1.034
73
1.387
52
1.581
31
1.594
93
1.023
72
1.410
51
1.583
30
1.594
92
1.005
71
1.435
50
1.583
29
1.595
91
0.981
70
1.462
49
1.584
28
1.596
90
0.950
69
1.476
48
1.584
27
1.598
89
0.965
68
1.487
47
1.584
26
1.600
88
0.991
67
1.495
46
1.583
25
1.602
87
1.027
66
1.500
45
1.581
24
1.603
86
1.075
65
1.502
44
1.581
23
1.603
85
1.133
64
1.508
43
1.582
22
1.603
84
1.164
63
1.513
42
1.582
21
1.603
83
1.194
62
1.517
41
1.583
20
1.603
82
1.222
61
1.520
40
1.584
81
1.248
60
1.523
39
1.585
80
1.273
59
1.530
38
1.587
Older Age One Hundred and One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
101
0.670
80
0.972
59
1.137
38
1.170
100
0.702
79
0.984
58
1.142
37
1.171
99
0.733
78
0.995
57
1.149
36
1.173
98
0.765
77
1,003
56
1.156
35
1.174
97
0.796
76
1.010
b^
1.160
34
1.174
96
0.828
75
1.023
54
1.162
33
1.174
95
0.829
74
1.036
53
1.164
32
1.174
94
0.820
73
1.050
52
1.166
31
1.174
93
0.801
72
1.065
51
1.166
30
1.175
92
0.772
71
1.081
50
1.167
29
1.176
91
0.733
70
1.091
49
1.167
28
1.177
90
0.740
69
1.099
48
U167
27
1.178
89
0.756
68
1.106
47
1.167
26
1.179
88
0.780
67
1.111
46
1.166
25
1.180
87
0.813
66
1.115
45
1.166
24
1.180
86
0.855
65
1.119
44
1.166
23
1.180
85
0.877
64
1.122
43
1.167
22
1.180
84
' 0.898
63
1.125
42
1.167
21
1.180
83
0.919
62
1.126
41
1.167
82
0.938
61
1.127
40
1.168
81
0.957
60
1.131
39
1.169
Digitized by VjOOQ IC
TABLB XXI.
4125
Value of £1 per Annum duxing the joint Continuance of Two lives.
(Carlisle 5 per Cent)
Older Age One Hundred and Two Years.
Af*
Valu.
Age.
Valae.
Age.
Value.
Age.
Value.
102
.379
81
.632
60
.723
39
.741
101
.414
80
.639
59
.726
38
.742
100
•449
79
.646
58
.729
37
.743
99
.485
78
.650
57
.733
36
.743
98
.520
77
.654
56
.735
35
.744
97
.555
76
.661
55
.736
34
.744
96
.563
75
.667
54
.737
33
.743
95
.563
74
.674
53
.738
32
.743
94
.554
73
.681
52
.738
31
.743
93
.535
72
.688
51
.739
30
.744
92
.508
71
.694
50
.739
29
.744
91
.510
70
.699
49
.739
28
.744
90
.517
69
.703
48
.739
27
.745
89
.527
68
.707
47
.739
26
.745
88
.541
67
.711
46
.739
25
.746
87
.559
66
.714
45
.739
24
.746
86
.571
65
.716
44
.739
23
.746
85
.583
64
.717
43
.739
22
.746
84
.696
63
.718
42
.739
83
.609
62
.718
41
.740
82
.623
61
.720
40
.740
Older Age One Hundred and Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
103
.106
82
.273
61
.307
40
.314
102
.135
81
.276
60
.308
39
.314
101
.163
80
.279
59
.309
38
.314
100
.192
79
.281
58
.310
37
.314
99
.220
78
.283
57
.311
36
.314
98
.249
77
.285
56
.311
35
.314
97
.259
76
.287
55
.312
34
.314
96
.262
75
.289
54
.312
33
.314
95
.259
74
.291
53
.312
32
.314
94
.250
73
.293
52
.312
31
.314
93
.235
72
.295
51
.313
30
.315
92
.235
71
.297
50
.313
29
.315
91
.237
70
.299
49
.313
28
.315
90
.240
69
.301
48
.313
27
.315
89
.243
68
.303
47
.313
26
.315
88
.248
67
.304
46
.313
25
.315
87
.252
66
.305
45
.313
24
.315
86
.2.'>§
65
.305
44
.313
23
.315
85
.260
64
.305
43
.313
84
.265
63
.305
42
.313
83
.270
62
.306
41
.313
Digitized by VjOOQIC
TABLE XXI.
Value of £1 per Annum during the Joint Contiuuance of Two Lives.
(Carliile 6 per Cent.)
Older Age 0 Years.
Older Age One Year.
Age.
Value.
Age.
Value.
0
6.783
1
0
9.043
7.471
Older Age Two Years.
Older Age Three Years.
Age.
Value.
Age.
Value.
2
1
0
10.340
9.543
8.063
3
2
1
0
11.535
10.712
9.972
8.561
Older Age Four Years.
Older Age Five Years.
Age.
Value.
Age.
Value.
4
3
2
1
Q
12.211
11.766
11.028
10.328
8.963
5
4
3
2
1
0
12.721
12.352
11.958
11.287
10.612
9.270
Older Age Six Years.
Older Age Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
6
5
4
3
12.977
12.783
12.466
12.112
2
1
0
11.489
10.824
9.314
7
6
5
4
13.100
12.990
12.830
12.553
3
2
1
0
12.228
11.635
10.834
9.347
Digitized by VjOOQ IC
TABLE XXI.
427
Value of £1 per Annam during the joint Continuance of Two lives.
(Carlisle 6 per Cent)
Older Age Eight Yean.
Older Age Nine Years.
A««.
Value.
Age.
Value.
Age.
Valae.
Age.
Value.
8
7
6
5
4
13.L34
13.083
12.995
12.861
12.614
3
2
1
0
12.306
11.618
10.837
9.369
9
8
7
6
5
13.107
13.098
13.062
12.991
12.876
4
3
2
1
0
12.649
12.271
11.598
10.833
9.380
Older Age
Ten Years.
Older Age Eleven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
10
9
8
7
6
5
13.036
13.061
13.061
13.036
12.978
12.875
4
3
2
1
0
12.603
12.235
11.574
10.821
9.379
n
10
9
8
7
6
12.943
12.987
13.015
13.023
13.006
12.957
5
4
3
2
1
0
12.824
12.557
12.197
11.547
10.803
9.343
Older Age Twelve Years.
Older Age Thirteen Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
12
11
10
9
8
7
6
12.853
12.885
12.913
12.937
12.957
12.973
12.908
5
4
3
2
1
0
12.775
12.512
12.159
11.516
10.763
9.308
13
12
11
10
9
8
7
12.761
12.799
12.837
12.873
12.909
12.943
12.927
6
5
4
3
2
1
0
12.860
12.727
12.468
12.120
11.475
10.723
9.274
Digitized
DyVjUUvIv
428
TABLK XXI.
Valae of £1 per Annum during the joint Continuance of Two LiTee.
(Carlisle 6 per Cent)
Older Age Fourteen Years.
Older Age Fifteen Years.
Ag..
Value.
Age.
Value.
Age.
Value.
Age.
Value.
14
13
12
11
10
9
8
7
12.668
12.710
12.752
12.795
12.838
12.882
12.901
12.881
6
5
4
3
2
1
0
12^12
12.680
12.424
12.080
11.434
10.683
9.240
15
14
IJ
12
11
10
9
8
12.578
12.62a
12.664
12.708
12.754
12.801
12.844
12*858
7
6
5
4
3
2
0
12.835
12.766
12.634
12.386
12.040
11.393
10.644
9.207
Older Age Sixteen Years.
Older Age Seventeen Years.
Age.
Value.
Age.
Value.
Age.
Valiia
Age.
Value.
16
12.499
7
12.789
17
12.428
8
12.729
15
12^41
6.
12.720
16
12.469
7
12.743
14
12.583
5
12.598
15
12.511
6
12.684
13
12.626
4
12.347
14
12.552
5
12.560
12
12.670
3
11.998
IS
12*594
4
12.305
11
12.715
2
11.352
12
12.635
3
11.954
10
12.766
1
10.606
11
12.665
f
11.310
9
12.804
0
9.180
10
12.690
10.576
8
12.814
9
12.712
0
9.152
Older Age Eighteen
Years.
Older Age Nineteen Years.
Age.
Value.
Ag«.
Value.
Age.
Value.
Age.
9
Value.
18
12.358
8
12.722
19
12*284
12.670
\7
12.399
7
12.705
18
12.325
8
12.680
16
12.439
6
12.644
17
12.365
7
12.663
15
12.479
5
12.518
16
12.402
6
12.601
14
12.517
4
12.260
15
12.437
5
12.472
13
12.554
3
11.910
14
15.470
4
12.214
12
12.590
2
11.275
13
12.509
3
11.869
11
12.625
1
10.541
12
12.548
2
11.236
10
12.658
0
9.121
11
12.588
1
10.504
9
12.691
10
12.629
0
9.088
Digitized by VjOOQ IC
TABLE XXI.
429
Value of £1 per AnBum during the joint Continuance of Two lives.
(Carliflle 6 per Cent.)
Older Age Twenty
Yeaw.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
20
19
18
17
16
15
12.206
12.248
12.287
12.322
12.355
12.385
14
13
12
11
10
9
12.424
12.465
12.507
12.550
12.594
12.624
8
7
6
5
4
3
12.635
12.616
12.554
12.424
12.167
11.825
2
1
0
11.194
10.465
9.053
-
Older Age Twenty-One Years.
Age.
Valoeu
Age.
Value.
Age.
Value.
Age.
Value.
21
20
19
18
17
16
12.123
12.166
12.206
12.242
12.275
12.304
15
14
13
12
11
10
12.343
12.382
12.422
12.463
12.505
12.542
9
B
7
6
5
4
12.574
12.586
12.566
12.503
12.370
12.117
3
2
1
0
11.777
11.149
10.422
9.015
Older Age Twenty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
22
21
20
19
18
17
12.031
12.077
12.119
12.157
12.191
12.222
16
15
14
13
12
11
12.260
12.298
12.337
12.375
12.413
12.440
10
9
8
7
6
5
12.464
12.483
12.500
12.512
12.443
12.314
4
3
2
1
0
12.065
11.726
11.100
10.372
8.975
Older Age Twenty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
23
22
21
20
19
18
17
11.933
11.981
12.026
12.066
12.104
12.137
. 12.175
16
15
14
13
12 .
11
10
12.212
12.248
12.283
12.317
12.350
12.383
12.414
9
8
7
6
5
4
3
12.445
12.475
12.445
12.382
12.257
12.009
11.671
2
1
0
11.041
10.322
8.934
Digitized by VjOOQ IC
430
TABLE XXI.
ValiM of £\ per Annum during the joint Continuance tfCTiro Lifot.
(Carlisle 6 per Cent.)
Older Age Twenty-Four Yearsa
Age.
Valaa.
Ag*.
ValM.
Alts.
Valae.
A<«.
YaIim.
24
11.829
17
12.121
10
12.366
3
11.604
23
11.879
16
12.155
9
12.405
2
10.982
22
11.926
15
12.187
8
12.404
1
10.270
21
11.969
14
12.217
7
12.379
0
8.891
20
12*010
13
12.253
6
12.320
19
12.047
12
12.290
5
12.197
18
12.085
11
12.328
4
11.950
Older Age Twenty-Five Years.
Age.
Value.
Age.
Value.
A<^
Value.
Age.
ValM.
25
11.718
18
12.026
11
12.269
4
11.881
24
11.769
17
12.058
10
12.311
3
11.539
23
11.818
16
12.088
9
12.334
2
10.923
22
11.865
IS
12.115
8
12.334
1
10.218
21
11.909
14
12.152
7
12.313
0
8.847
20
11.952
13
12.189
6
12.267
19
11.990
12
12.229
5
12.135
Older Age Twenty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
26
25
24
23
22
21
20
11.605
11.657
11.707
11.757
11.805
11.853
11.893
19
18
17
16
15
14
13
11.929
11.962
11.991
12.017
12.053
12.089
12.127
12
11
10
9
8
7
6
12.166
12.205
12.244
12.263
12.265
12.247
12.193
5
4
3
2
1
0
12.068
11.812
11.474
10.865
10.165
8.798
Older Age Twenty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
27
26
25
24
23
22
21
11.485
11.537
11.589
11.641
11.694
11.746
11.788
20
19
18
17
16
15
14
11.826
11.860
11.891
11.919
11.954
11.989
12.025
13
12
11
10
9
8
7
12.060
12.096
12.121
12.141
12.459
12.172
12.182
6
5
4
3
2
1
0
12.130
12.001
11.744
11.409
10.806
10.112
8.750
Digitized by LjOOQ iC
TABLE XXI.
431
Value of £1 per Annom during^ the joint Continuance of Two Lifei.
(Carlisle 6 per Cent.)
Older Age Twenty-Eight Years.
Age.
Value.
Age.
Value.
Age.
Veloe.
Age.
Value.
28
11.365
20
11.758
12
12.017
4
11.677
27
11.418
19
11.792
11
12.047
3
11.346
26
11.471
18
11.822
10
12.075
2
10.754
25
11.525
17
11.857
9
12.103
I
10.058
24
11.581
16
11.890
8
12.130
0
8.701
23
11.637
15
11.923
7
12.124
22
11.681
14
11.956
6
12.066
21
11.721
13
11.987
5
11.934
Older Age Twenty-Nine Years.
Older Age Thirty Years.
Older Age Thirty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Ag«.
Valo0.
29
11.259
21
11.660
13
11.917
5
11.866
28
11.312
20
11.696
12
11.951
4
11.611
27
11.366
19
11.730
11
11.9S6
3
11.293
26
11.420
18
11.764
10
12.021
2
10.698
25
11.476
17
11.797
9
12.057
1
10.002
24
11.532
16
11.828
8
12.076
0
8.651
23
11.578
15
11.857
7
12.063
22
11.620
14
11.884
6
11.999
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
30
11.173
22
11.566
14
11.826
6
11.931
29
11.226
21
11.607
13
11.861
5
11.797
28
11.278
20
11.646
12
11.897
4
11.556
27
11.330
19
11.681
11
11.934
3
11.237
26
11.382
18
11.713
10
11.973
2
10.640
25
11.433
17
11.742
9
12.002
1
9.945
24
11.479
16
11.769
8
12.017
0
8.602
23
11.524
15
11.793
7
11.999
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
31
11.086
23
11.471
15
11.740
7
11.931
30
11.139
22
11.516
14
11.773
6
11.861
29
11.190
21
11.559
13
11.807
5
11.736
28
11.239
20
11.695
12
11.843
4
11.497
27
11.287
19
11.628
11
11.879
3
11.176
26
11.333
18
11.657
10
11.914
2
10.579
25
11.380
17
11.684
9
11.942
1
9.886
24
11.426
16
11.707
8
11.953
0
8.558
Digitized by VjOOQ iC
432
TABLE XXI.
Valua of £1 per Annum during the joint Gontinuance of Two Lives.
(Carlisle 6 per Gent.)
Older Age Thirty-Two Years.
Age.
Value.
A^e.
Value.
Age.
Valae.
Age.
Value. .
32
10.995
23
11.418
14
11.718
5
11.671
31
11.048
22
11.466
13
11.750
4
11.433
30
11.097
21
11.504
12
11.783
3
11.111
29
11.143
20
11.538
11
11.805
2
10.515
28
11.187
19
11.570
10
11.824
1
9.829
27
11.227
18
11.597
9
11.839
0
8.512
26
11.274
17
11.622
8
11.851
25
11.322
16
11.654
7
11.860
24
11.370
15
11.686
6
11.793
Older Age Thirty-Three Yeare.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
33
10.894
24
' 11.313
15
11.624
6
11.721
32
10.947
23
11.365
14
11.653
5
11.601
31
10.995
22
11.405
13
11.681
4
11.364
30
11.040
21
11.442
12
11.709
3
11.042
29
11.080
20
11.475
11
11.736
2
10.447
28
11.116
19
11.505
10
11.762
1
9.769
27
11.164
18
11.532
9
11.788
0
8.462
26
11.212
17
11.563
8
11.813
25
11.262
16
11.594
7
11.784
Older Age Thirty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
34
10.783
25
11.204
16
11.523
7
11.706
33
10.837
24
11.255
15
11.549
6
11.646
32
10.886
23
11.296
14
11.573
5
11.527
31
10.931
22
11.335
13
11.603
4
11.290
30
10.971
21
11.371
12
11.634
3
10.963
29
11.007
20
11.404
11
11.664
2
10.377
28
11.055
19
11.435
10
11.699
1
9.707
27
11.103
18
11.466
9
11.733
0
8.408
26
11.153
17
11.495
8
11.730
Digitized by LjOOQ IC
TABLE XXI.
433
Value of £1 per Annum during the joint Conlinnanca of Two lanM*
(Carlisle 6 per Cent)
Older Age Thirty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Valoe.
35
10.666
26
11.092
17
11.418
8
11.646
34
10.722
25
11.139
16
11.441
7
11.625
33
10.774
24
11.181
15
11.462
6
11.566
32
10.822
23
11.221
14
11.402
5
11.448
31
10.865
22
11.260
13
11.524
4
11.203
30
10.904
21
11.297
12
11.558
3
10.883
29
10.951
20
11.332
11
11.593
2
10.304
28
10.998
19
11.363
10
11.629
1
9.G41
27
11.045
18
11.392
9
11.644
0
8.352
Older Age Thirty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Ag..
Valn^.
36
10.541
26
11.018
16
11.3:)2
6
11.483
35
10.599
25
11.060
15
11.381
5
11.355
34
10.654
24
11.102
14
11.412
4
11.116
33
10.705
23
11.143
13
11.444
3
10.fe02
32
10.753
22
11.183
12
11.477
2
10.230
31
10.797
21
11.223
11
11.511
I
9.572
30
10.844
20
11.255
10
11.537
0
8.286
29
10.890
19
11.284
9
11.!i55
28
10.934
18
11.310
8
11.560
27
10.977
17
11.332
7
11.541
Older Age Thirty-Seven Years.
Age.
Value.
Age.
Value.
Ako.
Value.
Age.
Value.
37
10.413
27
10.891
17
11.244
7
11.455
36
10.473
26
10.933
16
11.273
6
11.390
35
10.530
25
10.976
15
11.302
5
11. 26 J
34
10.584
24
11.019
14
11.331
4
11.(j23
33
10.636
23
11.063
13
11.361
3
io.7i:o
32
10.686
22
11.107
12
11.391
2
10.1.53
31
10.732
21
11.141
11
11.410
1
9.496
30
10.776
20
11.171
10
11.427
0
8.220
29
10.817
19
11.199
9
11.439
•i8
I0.fc55
18
11.223
8
11.449
434
TABLE XXI.
V«1q9 of £1 per Annum during the joint Continuance of Two lives.
(CarUele 6 per Cent.)
Older Age Thirty-Eight Years.
Afe.
Value.
Age.
Valne.
Age.
Value.
Age.
Value.
38
10.281
28
10.763
18
11.133
8
11.384
37
10.342
27
10.805
17
11.161
7
11.364
36
10.401
26
10.849
16
11.188
6
11.296
35
10.458
25
10.893
15
11.215
5
11.170
34
10.514
24
10,939
14
11.242
4
10.940
33
10.569
23
10.986
13
11.268
3
10.636
32
10.615
22
11.022
12
11.293
2
10.073
31
10.658
21
11.054
11
11.317
1
9.419
30
10.697
20
11.083
10
11.340
0
8.154
29
10.732
19
11.110
9
11.362
Older Age Thirty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
39
10.145
29
10.639
19
11.018
9
11.284
38
10.206
28
10.681
18
11.046
8
11.298
37
10.267
27
10.724
17
11.072
7-
11.271
36
10.327
26
10.768
' 16
11.097
6
11.201
35
10.336
25
10.814
15
11.120
5
11.078
34
10.445
24
10.860
14
11.142
4
10.851
33
10.492
23
10.897
13
11.169
3
10.556
32
10.535
22
10.931
12
11.197
2
9.991
31
10.574
21
10.962
11
11.225
1
9.341
30
10.609
20
10.991
10
11.254
0
8.089
Older Age Forty Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
40
10.014
29
• 10.567
18
10.956
7
11.176
39
10.075
28
10.609
17
10.979
6
11.106
38
10.137
27
10.650
16
11.000
5
10.985
37
10.198
25
10.692
15
11.019
4
10.773
36
10.259
25
10.733
14
11.046
3
10.472
35
10.320
24
10.770
13
11.074
2
9.908
34
10.369
23
10.805
12
11.104
1
9.263
33
10.414
22
10.839
11
11.1.35
0
8.023
32
10.456
21
10.872
10
11.167
31
10.493
20
10.903
9
11.203
30
10.526
19
10.931
8
11.208
TABLE XXL
435
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 6 per Cent;
Older Age Forty-One Years.
A«e.
Value.
Air*.
Vtloe.
Ag..
Va]a«.
Age.
Value.
41
9.896
30
10.461
19
10.847
8
11.114
40
9.958
29
10.500
18
10.870
7
11.080
39
10.019
28
10.539
17
10.890
6
11.011
38
10.079
27
10.576
16
10.908
5
10.910
37
10.139
26
10*612
15
10.934
4
10.689
36
10.198
25
10.649
14
10.961
3
10.384
35
10.249
24
10.686
13
10.989
2
9.823
34
10.296
23
10.722
12
11.017
1
9.184
33
10.341
22
10.758
U
11.047
0
7.971
32
10.382
21
10.793
10
11.090
31
10.420
20
10.821
9
11.116
Older Age Forty-Two Years.
AgUL
Value.
Age.
Value.
Age.
Value.
Age.
Value.
42
9.785
31
10.355
20
10.738
9
10.971
41
9.847
30
10.393
19
10.762
8
10.978
40
9.907
29
10.428
18
10.784
7
10.982
39
9.966
28
10.461
17
10.803
6
10.936
38
10.023
27
10.491
16
10.828
5
10.826
37
10.078
26
10.528
15
10.854
4
10.599
36
10.130
25
10.565
14
10.879
3
10.293
35
10.180
24
10.603
13
10.905
2
9.736
34
10.227
23
10.642
12
10.931
1
9.121
33
10.272
22
10.681
11
10.947
0
7.912
32
10.315
21
10.711
10
10.961
Older Age Forty-Three Years.
Age.
Value.
Age;
Value.
Age.
Value.
Age.
Value.
43
9.677
32
10.247
21
10.628
10
10.877
42
9.740
31
10.283
20
10.655
9
10.897
41
9,799
30
10.316
19
10.678
8
10.916
40
9.855
29
10.345
18
10.699
7
10-904
39
9.908
28
10.371
17
10.723
6
10.850
38
9.957
27
10.408
16
10,747
5
10.733
37
10.009
26
10.446
15
10.770
4
10.504
36
10.061
25
10.485
14
10.798
3
10.198
35
10.111
24
10.526
13
10.815
2
9.665
34
10,159
23
10.568
12
10.836
1
9.049
33
10«207
22
10.600
11
10.857
0
7.847
L
igitiz*^ ^
VjjUUVli^
4.16
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 6 per Cent.)
Older Age Forty-Four Years.
Age.
ValttP.
Age.
VMiie.
Age.
Value.
Age.
Valne.
44
9.563
32
10.168
20
10.565
8
10.831
43
9.627
31
10.200
19
10.589
7
10.813
42
9.686
30
10.229
18
10.613
6
10.753
41
9.740
29
10.254
17
10.635
5
10.632
40
9.788
28
10.290
16
10.056
4
10.402
39
9.831
27
10.328
15
10,676
3
10.117
38
9.884
26
10.367
14
10.694
2
9.584
37
9.936
25
10.407
13
10.718
1
8.968
36
9.983
24
10.449
12
10.742
0
7.776
35
10.040
23
10.4dl
11
10.767
34
10.091
22
10.512
10
10.793
33
10.131
21
10.540
9
10.820
Older Age Forty-Five Years.
Age.
Value.
Age
Value.
Age.
Value.
Age.
Value.
45
9.444
33
10.048
21
10.446
9
10.724
44
9.511
32
10.083
20
10.473
8
10.733
43
9.571
31
10.114
19
10.497
7
10.710
42
9.623
30
10.142
IS
10.518
6
10.645
41
9.668
29
10.178
17
10.538
5
10.523
40
9.705
28
10. 2M
16
10.555
4
10.308
39
9.757
27
10. 2-0
15
10.570
3
10.024
38
9.810
26
10.286
14
10.5U4
2
9.492
37
9.863
25
10.323
13
10.618
1
8.879
3»i
9.915
24
10.356
12
10.645
0
7.698
33
9.968
23
10.3i7
11
10.672
34
10.010
22
10.417
10
10.701
Older Age Forty-Six Years.
Age.
Value.
Age.
Value.
9.920
Age.
22
Value.
Age.
10
Value.
46
9.314
34
10.317
10.591
45
9.386
33
9.9->7
21
10.348
9
10.615
44
9.449
32
9.y92
20
10,372
8
10.622
43
9.50i
31
10.024
19
10.394
7
10.595
42
9.545
30
10.059
18
10.413
6
10.527
41
9.579
29
10.093
17
10.429
5
10.412
40
9.631
28
10.126
16
10.443
4
10.201
39
9.683
27
10.158
15
10.405
3
9.918
38
9.734
26
10.189
14
10.489
2
9.3>9
37
9.785
25
10.221
13
10.513
1
8.781
36
9.fc36
24
10.253
12
10.539
0
7.618
35
9.879
23
10.285
11
10.566
(
r-^/-^r\ 1 /~>
uigi
tABLE XXI.
437
Value of jCl per Annum during^ the joint Continuance of Two Lwcs.
(Carlisle 6 per Cent.)
Older Age Forty-Seven Years.
Ase.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
47
9.172
35
9.782
23
10.177
11
10.438
46
9.250
34
9.82i
22
10.212
10
10.450
45
9.317
33
9.860
21
10.237
9
10.458
44
9.372
32
9.896
20
10.2r)0
8
10.464
43
9.417
31
9.930
19
10.280
7
10. 407
42
9.450
30
9.961
18
10.297
6
10.398
41
9.502
29
9.991
17
10.312
5
10.289
40
9.552
28
10.019
16
10.333
4
10.082
39
9.601
27
10.044
15
10.355
3
9.801
38
9.649
26
10.076
14
10.378
2
9.276
37
9.696
25
10.109
13
10.401
1
8.G75
36
9.740
24
10.142
12
10.424
0
7.530
Older Age Forty-Eight Years.
A-e.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
48
9.013
35
9.673
22
10.089
9
10.342
47
9.097
34
9.714
21
10.113
8 .
10.359
46
9.170
33
9.754
20
10.135
7
10.321
45
9.230
32
9.787
19
10.154
6
10.2:)8
44
9.278
31
9.817
18
10.170
5
10.155
43
9.314
30
9.844
17
10.191
4
9.950
42
9.366
29
9.868
16
10.211
3
9.671
41
9.415
28
9.8S9
15
10.231
2
9.147
40
9.461
27
9.921
14
10.251
1
8.560
39
9.504
26
9.954
13
10.270
0
7.433
38
9.5-15
25
9.988
12
10.289
37
9.589
24
10.024
11
10.307
36
9.631
23
10.062
10
10.325
Older Age Forty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
49
8.826
36
9.506
23
9.920
10
10.185
48
8.917
35
9.549
22
9.946
9
10.209
47
8.996
34
9.592
21
9.969
8
10.198
46
9.063
33
9.625
20
9.990
7
10.165
45
9.118
32
9.655
19
10.009
6
10.108
44
9.161
31
9.681
18
10.029
5
10.008
43
9.214
30
9.704
17
10.048
4
9.806
42
9.261
29
9.724
IG
10.066
3
9.520
41
9.304
28
9.755
15
10.082
2
9.010
40
9.343
27
9.787
14
10.098
1
8.437
39
9.376
26
9.821
13
10.118
0
7.3.i9
38
9.419
25
9.856
12
10.140
37
9.462
24
9.893
11
10.162
Digitized by LjOOQ IC
438 TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 6 per Cent.)
Older Age Fifty Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
50
8.617
37
9.326
24
9.735
11
10.002
49
8.715
36
9.370
23
9.762
10
10.028
48
8.802
35
9.414
22
9.787
9
10.036
47
8.878
34
9.448
21
9.810
8
10.028
46
8.942
33
9.479
20
9.833
7
10.000
45
8.994
32
9.507
19
9.853
6
9.947
44
9.049
31
9.532
18
9,870
5
9.850
43
9.096
30
9.554
17
9.886
4
9.638
42
9.137
29
9.584
16
9.901
3
9.361
41
9.170
28
9.614
1ft
9.913
2
8.865
40
9.197
27
9.645
14
9.933
1
8.305
39
9.239
26
9.676
13
9.955
0
7.216
38
9.282
25
9.708
12
9.978
Older Age Fifty-One Years.
Age.
Value.
Age.
Value.
Age,
Value.
Age.
Value.
51
8.384
38
9.136
25
9.534
12
9.800
50
8.490
37
9.177
24
9.561
11
9.823
49
8.585
36
9.219
23
9.587
10
9.842
48
8.670
35
9.254
22
9.614
9
9.855
47
8.744
34
9.286
21
9.640
8
9.851
46
8.808
33
9.316
20
9.660
7
9.826
45
8.866
32
9.344
19
9.678
6
9.775
44
8.916
31
9.370
18
9.693
5
9.658
43
8.957
30
9.399
17
9.706
4
9.464
42
8.989
29
9.427
16
9.717
3
9.194
41
9.012
28
9.454
15
9.736
2
8.7H
40
9.053
27
9.481
14
9.756
1
8.164
39
9.094
26
9.507
13
9.777
0
7.086
Older Age Fifty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
52
8.147
39
8.945
26
9.325
13
9.594
51
8.260
38
8.983
25
9.a53
12
9.614
50
8.363
37
9.020
24
9.381
11
9.625
49
8.456
36
9.055
23
9.409
10
9.633
48
8.540
35
9.088
22
9.439
9
9.639
47
8.614
34
9.120
21
9.460
8
9.642
46
8.677
33
9.151
20
9.479
7
9.642
45
8.730
32
9.180
19
9.495
6
9.575
44
8.772
31
9.207
18
9.509
5
9.464
43
8.805
30
9.233
17
9.520
4
9.283
42
8.827
29
9.256
16
9.538
3
9.022
41
8.867
28
9.279
15
9.556
2
8.549
40
8.907
27
9.299
14
9.575
1
0
8.001
6.952
Digitized by VjVJiJ
gle
TABLE XXI.
4S»
Value of £1 per Annum durinp; the joint Continuance of Two Livei.
(Carlisle 6 per Cent)
Older Age Fifty-Three
Years.
Ag».
Valae.
Age.
Valufl.
Age.
Value.
Age.
20
Valae.
Aipi.
Value.
L 1 •
53
r.905
42
8.678
31
9.031
9.290
9
9.457
52
8.024
41
8.716
30
U.052
19
9.305
8
9.470
51
8.134
40
8.751
29
9.071
18
0.318
7
9.426
50
8.236
39
8.784
28
9.087
17
9.335
6
9.373
49
8.327
38
8.815
27
9,113
16
9.351
5
9.270
4d
8.410
37
8.849
26
9.140
15
9.368
4
9.095
47
8.478
36
8.883
25
9.169
14
9.384
3
8.840
46
8.535
35
8.916
24
9.199
13
9.400
2
8.359
45
8.581
34
8.949
23
9.231
12
9.415
1
7.836
44
8,615
33
8.982
22
9.253
11
9.429
0
6.815
43
8.639
32
9.008
21
9.273
10
9.443
Older Age Fifty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
10
Value.
54
7,656
43
8.485
32
8.824
21
9.077
9.251
53
7.778
42
8.521
31
8.844
20
9.094
9
9.271
52
7.893
41
8.553
30
8.861
19
9.109
8
9.240
51
7,999
40
8.581
29
8.876
18
9,125
7
9.212
50
8.098
39
8.605
28
8.901
17
9.140
6
9.170
49
8.189
38
8.638
27
8.927
16
9.154
5
9.076
48
8.262
37
8.672
26
8.955
15
9.168
4
8.900
47
8.325
36
8.706
25
8.985
14
9.180
3
8.626
46
8.376
35
8.740
24
9.016
13
9.197
2
8.170
45
8.416
34
8.775
23
9.038
12
9.214
1
7.669
44
8.445
33
8.801
22
9.059
11
9.232
0
6.674
Older Age Fifty-Five Years,
Age.
Value.
Age.
43
Value.
Age.
Value.
Age.
19
Value.
Age.
7
Value.
55
7.397
8.319
31
8.650
8.907
9.000
54
7.521
42
8.348
30
8.666
18
8.921
6
8.965
53
7.638
41
8.371
29
8.689
17
8.933
5
8.880
52
7.749
40
8.389
28
8.714
16
8.944
4
8.671
51
7.854
39
8.421
27
8.738
15
8.953
3
8.416
50
7.952
38
8.454
26
8.764
14
8.969
2
7.983
49
8.031
37
8.488
25
8.790
13
8.987
1
7.501
48
8.100
36
8.523
24
8.812
12
9.006
0
6.630
47
8.158
35
8.559
23
8.833
11
9.026
46
8.206
34
8.585
22
8.853
10
9.047
45
8.243
33
8.609
21
8.873
9
9.033
44
8.284
32
8.631
20
8.891
8
9.015
Digitized by
"Google
440
TABLK XXI.
Value of £1 per Annam during the joint Continuance of Two Lives.
(Carlisle 6 per Gent.) .
Older .
Age Fifty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
20
Value.
Age
8
Value.
66
7.130
44
8.111
32
8.430
8.681
8.796
55
7.251
43
8.140
31
8.449
19
8.694
7
8.789
54
7.369
42
8.161
30
8.471
18
8.706
6
8.758
53
7.483
41
8.175
29
8.493
17
8.716
5
8.694
52
7.593
40
8.206
28
8.515
16
8.724
4
8.450
51
7.699
39
8.237
27
8.537
15
8.739
3
8.211
50
7.784
38
8.269
26
8.558
14
8.755
2
7.798
49
7.860
37
8.301
25
8.580
13
8.772
I
7.331
48
7.927
36
8.334
24
8.601
12
8.790
0
6.365
47
7.984
35
8.361
23
8.622
11
8.809
46
8.031
34
8.385
22
8.644
10
8.812
45
8.075
33
8.408
21
8.665
9
8.803
Older Age Fifty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value,
Age.
Value.
57
6.853
45
7.894
33
8.200
21
8.444
9
8.582
56
6.972
44
7.923
32
8.223
20
8.459
8
8.583
55
7.090
43
7.944
31
8.244
19
8.471
7
8.581
54
7.208
42
7.956
30
8.264
18
8.482
6
8.538
53
7.324
41
7.985
29
8.282
17
8.490
5
8.488
52
7.440
40
8.014
28
8.300
16
8.5U4
4
8.235
51
7.531
39
8.043
27
8.316
15
8.518
3
8.012
50
7.614
38
8.072
26
8.337
14
8.533
2
7.615
49
7.687
37
8.101
25
8.359
13
8.549
1
7.150
48
7.752
36
8.127
24
8.381
12
8.565
0
6.205
47
7.S08
35
8.153
23
8.404
11
8.573
46
7.g55
34
8.177
22
8.428
10
8.579
Older Age Fifty-Eight
Years.
Age.
Value.
Age.
46
Value.
Age.
Value.
Age.
22
Value.
Age.
Value.
58
6.577
7.671
34
7.968
8.206
10
8.353
57
6.694
45
7.703
33
7.994
21
8.221
9
8.363
56
6.812
44
7.726
32
8.014
20
8.235
8
8.373
55
6.932
43
7.739
31
8.032
19
8.246
7
8.379
54
7.055
42
7.767
30
8.047
18
8.255
6
8.323
53
7.179
41
7.794
29
8.061
17
8.268
5
8.290
52
7.275
40
7.819
28
8.073
16
8,281
4
8.027
51
7.363
39
7.843
27
8.093
15
8.294
3
7.817
50
7.443
38
7.866
26
8.115
14
8.306
2
7.437
49
7.514
37
7.892
25
8.138
13
8.319
I
6.972
48r
7.578
36
7.917
24
8.163
12
8.331
0
6.050
47
7.629
35
7.943
23
8.189
11
8.342
TABLE XXI.
441
Value of £1 pet Annum during; the joint Continuance of Two Lives.
(Carlisle 6 per Cent.)
Older Age Fifty-Nine Years.
Age.
Value.
Age.
Value.
Age.
35
Value.
Axe.
Value.
.K^.
Value.
59
6.322
47
7.450
7.744
23
7.977
11
■ 8.125
5S
6.436
46
7.487
34
7.772
22
7.992
10
8.139
57
6.553
45
7.514
33
7.791
21
8.007
9
8.155
56
6.674
44
7.532
32
7.809
20
8.019
8
8.189
55
6.798
43
7.560
31
7.8-24
19
8.030
7
8.177
54
6.926
42
7.585
30
7.836
18
8.042
6
8.111
53
7.025
41
7.607
29
• 7.847
17
8.054
5
8.090
52
7.117
40
7.626
28
7.866
16
8.064
4
7.826
51
7.201
39
7.642
27
7.887
15
8.075
3
7.646
50
7.278
38
7.666
26
7.910
14
8.084
2
7.259
49
7.348
37
7.692
25
7.934
13
8.097
1
6.798
48
7.404
36
7.718
24
7.959
12
8.110
0
5.900
Older
Age Sixty Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
21
Value.
Age.
8
Value.
60
6.097
47
7.282
34
7.585
7.808
8.001
59
6.208
46
7.3)5
33
7.603
20
7.822
7
7.974
58
6.322
45
7.339
32
7.619
19
7.834
6
7.902
57
6.440
44
7.368
31
7.633
18
7.844
5
7.890
56
6.561
43
7.392
30
7.645
17
7.853
4
7.661
55
6.685
42
7.411
29
7.663
16
7.861
3
7.470
54
6.785
41
7.426
28
7.682
15
7.867
2
7.081
53
6.879
40
7.436
27
7.702
14
7.880
1
6.627
52
6.968
39
7.459
26
7.723
13
7.893
0
5.755
51
7.050
38
7.484
25
7.744
12
7.908
50
7.127
37
7.510
24
7.761
11
7.925
49
7.188
36
7.537
23
7.778
10
7.942
48
7.239
35
7.565
22
7.793
9
7.984
Older
Age
Sixty-One Years.
Age.
Value.
Age.
Value.
Age.
35
Value.
Age.
Value.
Age.
Value.
61
5.919
48
7.096
7.402
22
7.622
9
7.805
60
6.026
47
7.137
34
7.421
21
7.639
8
7.808
59
6.135
46
7.1/0
33
7.439
20
7,651
7
7.771
58
6.244
45
7.201
32
7.4r)5
19
7.661
6
7.698
57
6.355
44
7.226
31
7.470
18
7.670
5
7.699
56
6.466
43
7.244
30
7.487
17
7.677
4
7.489
55
6.565
42
7.257
29
7.504
16
7.682
3
7.290
54
6.660
41
7.263
28
7.521
15
7.694
2
6.903
53
6.751
40
7.285
27
7.538
14
7.706
1
6.459
52
6.839
39
7.308
26
7.555
13
7.719
0
5.640
51
6.923
38
7.331
25
7.572
12
7.734
50
6.989
37
7.356
24
7.589
11
7.749
49
7.047
36
7.382
23
7.606
10
7.777
J
Digitized by VjiJVJ
gte
442
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Li?e8.
(Carlisle 6 per Cent.)
Older Age Sixty-Two Years.
Age.
Valac
Age.
ViUie.
Age.
Value.
Age.
Value.
62
5.748
42
7.096
22
7.457
2
6.724
61
5.852
41
7.116
21
7.470
1
6.320
60
5.953
40
7.137
20
7.480
0
5.517
59
6.053
39
7.158
19
7.489
58
6.151
38
7.180
18
7.497
&7
6.246
37
7.202
17
7.502
56
6.343
36
7.222
16
7.513
55
6.439
35
7.241
15
7.524
54
6.534
34
7.260
14
7.535
53
6.628
33
7.278
13
7.647
52
6.721
32
7.296
12
7.560
61
6.793
31
7.312
11
7.566
50
6.856
30
7.327
10
7,569
49
6.912
29
7.341
9
7.571
48
6.961
28
7.355
8
7.570
47
7.001
27
7.367
7
7.568
46
7.035
26
7.384
6
7.528
45
7.061
25
7.401
5
7.502
44
7.080
24
7.419
4
7.308
43
7.092
23
7.438
3
7.106
Older Age Sixty-Three Yean.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
ValiM.
63
5 576
43
6.928
23
7.269
3
6.918
62
5.677
42
6.947
22
7.282
2
6.564
61
5.772
41
6.966
21
7.294
1
6.172
60
5.861
40
6.984
20
7.304
0
5.387
59
5.945
39
7.001
19
7.312
58
6.024
38
7.018
18
7.318
57
6.119
37
7.037
17
7.328
56
6.215
36
7.057
16
7.338
55
6.313
35
7.076
15
7.347
54
6.413
34
7.097
14
7.357
53
6.515
33
7.117
13
7.367
52
6.591
32
7.132
12
7.376
51
6.660
31
7.M6
11
7.384
50
6.722
30
7.158
10
7.393
49
6.777
29
7.168
9
7,400
48
6.824
28
7.177
8
7.408
47
6.861
27
7.193
7
7.386
46
6.890
»6
7.210
6
7.347
45
6.911
25
7.228
5
7.298
44
6.924
24
7.248
4
7,121
Digitized by LjOOQ iC
TABLE XXL
443
Value of £1 per Annum during the joint Continuance of Two Lirei.
(Carlisle 6 per Cent.)
Older Age Sixty-Four Years.
Ag.,
Valo*.
Age.
Value.
Ai5e.
Valoe.
Age.
Value.
64
5,390
44
6.749
24
7.069
4
6.925
63
5.490
48
6,768
23
7.083
3
6.734
62
5.581
42
6,784
22
7.095
2
6.394
61
5.664
41
6,799
21
7.106
1
6.014
60
5.739
40
6.811
20
7.115
0
5.250
59
5.805
39
6.822
19
7.123
58
5.898
38
6.840
18
7,132
57
5.993
37
6.859
17
7.140
56
6.092
36
6.880
16
7.148
55
6,194
35
6.901
15
7.155
54
6.299
34
6.924
14
7.162
53
6.378
33
6.939
13
7.172
52
6.450
32
6.952
12
7.183
51
6.516
31
6,963
11
7.194
50
6.575
30
6.972
10
7.206
49
6.627
29
6.979
9
7.219
48
6.668
28
6.994
8
7.209
47
6,701
27
7.011
7
7.192
46
6.725
26
7.029
6
7.154
45
6.741
25
7.048
5
7.088
Older Age Sixty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value,
Age.
Value.
65
5,197
45
6,562
25
6.859
5
6.871
64
5,298
44
6.581
24
6.872
4
6.716
63
5.388
43
6.596
23
6.8S5
3
6.541
62
5,467
42
6.608
22
6.897
2
6.215
61
5.536
41
6.617
21
6.908
1
5.847
60
5.594
40
6.622
20
6. 918
0
5.106
59
5.683
39
6.639
19
6.927
58
5.776
38
6.657
18
6.934
57
5.872
37
6.677
17
6,940
56
5.971
36
6.698
16
6.946
55
6.073
35
6.721
15
6.950
54
6.153
34
6.736
14
6.960
53
6.227
33
6,750
13
6.971
52
6.296
32
6.762
12
6.983
51
6.359
31
6.772
11
6,996
50
6.417
30
6.781
10
7.010
49
6.462
29
6.795
9
7.001
48
6.499
28
6.810
8
7.002
47
6.528
27
6.826
7
6.988
46
6.549
26
6.842
6
6.949
Digitized by VjOOQ IC
444
TABLE \XU
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlitle 6 per Cent.)
Older Age Sixty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
66
4.991
46
6.362
26
6.633
6
6.733
65
5.096
45
6.382
25
6.6J1
5
6.633
64
5.190
44
6.398
24
6.664
4
6.502
63
5.271
43
6.409
23
6.677
3
6.340
62
5.341
42
6.415
22
6.689
2
6.026
61
5.398
41
6.416
21
6.702
1
5.670
60
5.483
40
6.431
20
6.711
0
4.938
59
5.570
39
6.448
19
6.718
58
5.657
38
6.466
18
6.724
57
5.746
37
6.486
17
6.728
56
5.836
36
6.507
16
6.731
55
5.914
35
6.522
15
6.740
54
5.988
34
6.536
14
6.749
53
6.059
33
6.549
13
6.759
52
6.126
32
6.561
12
6.771
51
6.190
31
6.572
11
6.783
50
6.239
30
6.585
10
6.768
49
6.281
29
6.598
9
6.778
43
6.315
28
6.612
8
6.785
47
6.342
27
6.625
7
6.773
Older Age Sixty-Seven Years.
Age.
Value.
Aue.
Value.
Age.
Value.
Age.
Value.
67
4.770
47
6.149
27
6.403
7
6.546
66
4.880
46
6.171
26
6.415
6
6.467
65
4.977
45
6.188
25
6.428
5
B..397
64
5.063
44
6.198
24
6.442
4
6.284
63
5.137
43
6.203
23
6.456
3
6.131
62
5.198
42
6.202
22
6.471
2
5.827
61
5.279
41
6.216
21
6.4S0
1
5.453
60
5.358
40
6.230
20
6.488
0
4.771
59
5.435
39
6.246
19
6.494
58
5.511
38
6.262
IS
6.498
57
5.585
37
6.280
17
6.501
56
5.660
36
6.'J95
16
6.509
55
5.734
35
6.309
15
6.517
54
5. 808
34
6.323
14
6.526
53
5.8S0
33
6.337
13
6.536
52
5.952
32
6.351
12
6.546
51
6.005
31
6.363
11
6,530
50
6.051
30
6.374
10
6.551
49
6.091
29
6.385
9
6.551
48
6<123
28
6.394
8
6.5.i0
Digitized by LjOOQ IC
TABLE XXL
445
Value of £1 per Annum iluring the joint Continuance of Two LUes.
(Carlisle 6 p«r Cent.)
Older Age Sixty-Eight Years.
As*.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
68
4.537
48
5.922
28
6.158
8
6.326
67
4.650
47
5.946
27
6.170
7
6.260
66
4.751
46
5.964
26
6.153
6
6.208
65
4.842
43
5.976
25
6.197
5
6.161
64
4.921
44
5.981
24
6.213
. 4
6.060
63
4.990
43
5.980
23
6.229
3
5.913
62
5.067
42
5.993
*22
6.239
2
5.576
61
5.139
41
6.006
21
6.247
1
5.241
60
5.207
40
6.018
20
6.253
0
4.604
59
5.270
39
6.031
19
6.258
59
5.328
38
6.043
18
6.262
57
5.400
37
6.057
17
6.269
56
5.474
36
6.071
16
6.276
55
5.549
35
6.086
15
6.283
54
5.626
34
6.101
14
6.291
53
5.704
33
6.116
13
6.298
52
5.760
32
6.127
12
6.304
51
5.810
31
G.137
11
6.310
50
5.8.>4
30
6.145
10
6.316
49
5.891
29
6.152
9
6.321
Older Age Sixty-Nine Years.
Age.
Value.
Age.
49
Vnlue.
Age.
Value.
Age.
Val6e.
69
4.289
5.676
29
5.905
9
6.079
68
. 4.402
48
5.703
28
5.916
8
6.032
67
4.506
47
5.723
27
5.929
7
5.987
66
4.602
46
5.737
26
5.942
6
5.957
65
4.689
45
5.745
25
5.957
'
5.927
64
4.767
44
5.746
24
5.973
4
5.832
63
4.842
43
5.767
23
5.983
3
5.640
62
4.909
42
5.768
22
5.992
2
5.336
61
4.969
41
5.777
21
5.999
1
5.036
60
5.023
40
5.785
20
6.005
0
4.438
59
5.069
39
5.793
19
6.010
58
5.138
38
5.806
IS
6.016
b7
5.211
37
5.822
17
6.022
56
5.286
36
5.835
16
6.027
55
5.364
35
5.851
15
6.032
54
5.445
34
5.868
14
6.037
53
5.503
33
5.878
13
6.044
52
5.555
32
5.887
12
6.052
51
5.601
31
5.895
11
6.0r)0
50
5.641
30
5.901
10
6.069
Digitized
By'^uuyk
446
TABLE XXI.
Vttlufl of £1 per Anaunn during the joint Gontiauaaee of Tiro lif ■■•
(Cadisle 6 ptr Cent)
Older Age Setenty
Yean.
Age.
Valae.
Ag..:
Valae.
Age.
VaIoc.
Age.
ValiM.
70
4.028
50
5.415
30
5.648
10
5.811
69
4.139
49
5.445
29
5.658
9
5.794
68
4.245
48
5.468
28
5.669
8
5.754
67
4.346
47
5.486
27
5.681
7
5.727
66
4.442
46
5.497
26
5.693
6
5.714
65
4.534
45
5.502
25
5.706
5
5.693
64
4.608
44
5.513
24
5.715
4
5.559
63
4.674
43
5.522
23
5.724
3
5.382
62
4.730
42
5.529
22
5.732
2
5.108
61
4.778
41
5.533
21
5.739
I
4.836
60
4.816
40
5.536
20
5.746
0
4.271
59
4.882
39
5.548
19
5.752
58
4.950
38
5.561
18
5.757
57
5.022
37
5.575
17
5.761
56
5.096
36
5.591
16
5.764
55
5.174
35
5.609
15
5.767
54
5.232
34
5.620
14
5.774
53
5.284
33
5.629
13
5.782
52
5.333
32
5.637
12
5.791
51
5.376
31
5.643
11
5.800
Older Age Seventy-One Years.
L
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
71
3.748
51
5.135
31
5.378
U
5.524
70
3.856
50
5.168
30
5.387
10
5.551
69
3.964
49
5.195
29
5.396
9
5.524
68
4.071
48
5.216
28
5.406
8
5.494
67
4.178
47
5.232
27
5.415
7
5.481
66
4.285
46
5.242 •
26
5.425
6
5.479
65
4.362
45
5.254
25
5.434
5
5.438
64
4.429
44
5.262
24
5.443
4
5.301
63
4.486
43
5.268
23
5.452
3
5.140
62
4.532
42
5.270
22
5.460
2
4.892
61
4.569
41
5.269
21
5.469
1
4.643
60
4.630
40
5.279
20
5.475
0
4.087
59
4.692
39
5.290
19
5.479
58
4.756
38
5.303
18
5.482
57
4.821
37
5.318
17
5.485
56
4.888
36
5.384
16
5.486
55
4.943
35
5.345
15
5.492
54
4.995
34
5.354
14
5.499
53
5.045
33
5.363
13
5.506
52
5.091
32
5.371
12
5.515
f
^ T
UiylLl^iii!
ftyCoOglc
TABLE XXL
447
Value of £1 per Anniim during the joint Continuance of Two Lives.
(Carlisle 6 per Cent.)
Older Age Seventy-Two Years.
Age.
Value.
Ag«.
Valhe.
Age.
Valoe.
Age.
Valm.
72
3«485
52
4.867
32
5.119
12
5.252
71
3.589
51
4.903
31
5.127
11
5.254
70
3.696
50
4.933
30
5.135
10
5.255
69
3.807
49
4.958
29
5.142
9
5.254
68
3.922
48
4.978
28
5.149
8
5.252
67
4.041
47
4.993
27
5.155
7
5.248
66
4.121
46
5.006
26
5.164
6
5.252
65
4.191
45
5.015
25
5.173
5
5.195
64
4.250
44 -
5.020
24
5.182
4
5.058
63
4.299
43
5.020
23
5.192
3
4.913
62
4.337
42
5.017
22
5.202
2
4.687
61
4.394
41
5.025
21
5.208
1
4.455
60
4.450
40
5.035
20
5.213
0
3.912
59
4.505
39
5.046
19
5.217
58
4,559
38
5.058
18
5.219
57
4.612
37
5.071
17
5.221
56
4.665
36
5.081
16
5.226
55
4.716
35
5.091
15
5.232
54
4.767
34
5.101
14
5.238
53
4.818
33
5.110
13
5.245
Older Age Seventy-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
73
3.254
63
4.622
33
4.883
13
5.004
72
3.353
52
4.660
32
4.890
12
5.008
71
3.458
51
4.693
31
4.897
11
5.012
70
3.569
50
4.721
30
4.902
10
5.016
69
3.686
49
4.745
29
4.907
9
5.019
68
3.810
48
4.763
28
4.910
8
5.022
67
3.892
47
4.778
27
4.918
7
5.050
66
3.965
46
4.788
26
4,927
6
5.032
65
4.028
45
4.793
25
4.937
5
4.965
64
4.081
44
4.794
24
4.947
4
4.831
63
4.125
43
4.790
23
4.959
3
4.702
62
4.178
42
4.797
22
4.965
2
4.513
61
4.228
41
4.805
21
4.971
1
4.274
60
4.275
40
4.813
20
4.975
0
3.746
59
4.318
39
4.822
19
4.978
58
4.35S
38
4.832
18
4.980
57
4.408
37
4.842
17
4.985
56
4.460
36
4.851
16
4.989
55
4.513
35
4.862
15
4.994
54
4.567
34
4.872
14
4.999
tI
"DTgiTTzed"
448
TABLE XXI.
Value or£l per Atinum during the joint Continuance of Two Livei*
(Carlisle 6 per Cent.)
Older
Age Seventy-Four Years.
Ajje.
Value.
A,,e.
Value.
A^e.
Value.
Aje.
Value.
74
3.058
54
4.402
34
4.671
14
4.784
73
3.152
53
4.442
33
4.678
13
4.789
72
3.253
52
4.477
32
4.684
12
4.794
71
3.360
51
4.507
31
4.689
11
4.800
70
3.474
50
. 4.53 i
30
4.692
10
4.806
69
3.594
49
4.555
29
4.695
9
4.813
68
3.677
48
4.571
28
4.703
8
4.847
67
3.753
47
4.533
27
4.711
7
4.855
66
3.820
46
4.590
26
4.721
6
4.820
66
3. 880
45
4.592
25
4.732
5
4.747
64
3.931
44
4.589
24
4.743
4
4.620
63
3.983
43
4.595
23
4.750
3
4.539
62
4.029
42
4.602
22
4.755
2
4.342
61
4.070
41
4.608
21
4.760
1
^.098
60
4.105
40
4.613
20
4.763
0
3.589
59
4.136
39
4.619
19
4.766
58
4.184
38
4.628
18
4.770
57
4.235
37
4.637
17
4.774
56
4.2S8
30
4.64S
16
4.777
55
4.344
35
4,659
15
4.781
Older Age Seventy-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age,
Value.
75
2.916
55
4.217
35
4.498
15
4.604
74
3.004
54
4,257
34
4.505
14
4.609
73
3.097
53
4.294
53
4.512
13
4.614
72
3.194
52
4.326
32
4.517
12
4.C21
71
3.296
51
4.355
31
4.521
11
4.G28
70
3.403
50
4.380
30
4.524
10
4.6.36
69
3.486
49
4.399
29
4.531
9
4.644
68
3.r)64
48
4.413
28
4.53':)
8
4.671
67
3.638
47
4.422
27
4.547
7
4.663
66
3.706
46
4.427
26
4.556
6
4.015
65
3.770
45
4.427
25
4.f65
5
4.541
64
3.822
41
4.433
24
4.572
4
4.458
63
3.807
43
4.438
23
4.578
3
4,376
62
3.905
42
4.442
22
4.ne3
2
4.172
61
3.935
41
4.444
21
4.588
1
3.fJ2U
60
3.959
40
4.446
20
4.592
0
3*441
59
4.005
39
4.454
19
4.5%
58
4.054
3rt
4.463
18
4.599
57
4.106
37
4.473
17
4.601
56
4.160
36
4.485
16
4.603
Digitized by VjUUVLC
TABLE XXI.
449
Value of £1 per Aanum during the joint Coutinuaace of Two Livea.
(Carlisle 6 per Cent.)
Older Age Seventy-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
76
2.779
56
4.032
36
4.326
16
4.430
7&
2.861
55
4.071
35
4.333
15
4.434
74
2.944
54
4.108
34
4.340
14
4.439
73
3.029
53
4.142
33
4.346
13
4.444
72
3. 116
52
4.174
32
4.351
12
4.450
71
3.205
51
4.203
31
4.356
11
4.457
70
3.287
50
4.224
30
4.362
10
4.468
69
3.369
49
4.241
29
4.369
9
4.474
68
3.4:)0
48
4.254
28
4.375
8
4.493
67
3.529
47
4.262
27
4.382
7
4.473
66
3.608
46
4.266
26
4.389
6
4.418
65
3.663
45
4.273
25
4.395
5
4.377
64
3.710
44
4.277
24
4.402
4
4.295
63
3.749
43
4.280
23
4.408
3
4.211
62
3.779
42
4.280
22
4.414
2
4.006
61 •
3.800
41
4.279
21
4.420
1
3.766
60
3.843
40
4.286
20
4.424
0
3.320
69
3.888
39
4.294
19
4.427
6S
3.934
3S
4.303
18
4.429
57
3.982
37
4.314
17
4.430
Older
Age Seventy-Seven Years.
«
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
77
2.661
57
3.856
37
4.167
17
4.270
76
2.736
53
3.894
36
4.174
16
4.274
75
2.810
53
3.931
35
4.181
15
4.278
74
2.883
54
3.967
34
4.188
14
4.2S2
73
2.954
53
4.003
33
4.195
13
4.287
72
3.025
52
4.038
32
4.201
12
4.293
71
3.103
61
4.062
31
4.207
11
4.294
70
3.18S
50
4.082
30
4.212
10
4.294
69
3.274
49
4.098
29
4.217
9
4.292
68
3.362
48
4.109
28
4.221
8
• 4.290
67
3.452
A7
4.117
27
4.223*
7
4.286
66
3.511
45
4.125
26
4.231
6
4.244
65
3.561
43
4.129
23
4.237
5
4.210
64
3.602
44
4.131
24
4.244
4
4.130
63
3.634
43
4.131
23
4.251
3
4.045
62
3.657
42
4.127
22
4.239
2
3.841
61
3.697
41
4.133
21
4.263
1
3.622
60
3.737
4U
4.139
20
4.266
0
3.199
59
3.777
39
4.147
19
4.268
58
3.817
38
4.157
18
4.270
450
TABLE XSa.
Value of £1 per Annmn daring the joint Continuaiiee of Two Lives.
<CerliBle6perCent)
Older
Age Seventy-Eight Years.
All.
Valoe.
Age.
Valae.
Age.
Value.
Age.
VjUtte.
78
2.540
58
3.678
38
4.003
18
4.106
77
2.610
57
3.714
37
4.010
17
4.109
76
2.678
56
3.752
36
4.017
16
4.113
76
2.740
55
3.790
35
4.025
15
4.116
74
2.799
54
3.830
34
4.032
14
4.120
73
2.855
53
3.870
33
4.040
13
4.124
72
2.932
52
3.896
32
4.045
12
4.127
71
3.015
51
3.919
31
4.049
11
4.129
70
3.102
50
3.937
30
4.053
10
4.131
69
3.193
49
3.952
29
4.055
9
4.133
68
3.290
48
3.962
28
4.057
8
4.135
67
3.351
47
3.971
27
4.063
7
4.103
66
3.404
46
3.976
26
4.069
J&
4.069
65
3.449
45
3.978
25
4.076
5
4.041
64
3.485
44
3.977
24
4.084
4
3.963
63
3.512
43
3.972
23
4.093
3
3.878
62
3.550
42
3.977
22
4.097
2
3.683
61
3.585
41
3.982
21
4.101
1
3.478
60
3.618
40
3.988
20
4.104
0
3.078
59
3.649
39
3.995
19
4.105
Older Age Seventy-Nine Years.
Age.
79
78
77
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
61
60
Value.
2.390
2.457
2.520
2.578
2.633
2.683
2.757
2.836
2.920
3.010
3.104
3.166
3.231
3.269
3.310
3.343
3.379
3.411
3.439
3.463
Age.
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
Value.
3.483
3.518
3.554
3.593
3.635
3.678
3.706
3.730
3.750
3.766
3.779
3.789
3.796
3.799
3.799
3.795
3.799
3.803
3.807
3.811
Age.
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
Value.
3.815
3.821
3.828
3.836
3.845
3.854
3.859
3.863
3.865
3.867
3.868
3.873
3.880
3.887
3.894
3.903
3.908
3.911
3.914
3.917
Age.
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Valae.
3.918
3.921
3.923
3.926
3.928
3.930
3.934
3.937
3.942
3.946
3.951
3.939
3.922
3.894
3.870
3.795
3.708
3.526
3.333
2.957
Digitized by VjUUVIC
TABLE XXL
451
Value of £1 per Annam during the joint Continiiance of Two Lire*.
(Gariisle 6 per Cent.)
Older Age Eighty
Yean.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
80
2.260
59
3.343
38
3.654
17
3.750
79
2.327
58
3.378
37
3.662
16
3.751
78
2.389
57
3.416
36
3.671
15
3.752
77
2.447
56
3.456
35
3.681
14
3.755
76
2.499
65
3.499
34
3.686
13
3.759
75
2.546
54
3.527
33
3.690
12
3.764
74
2.614
53
3.552
32
3.693
11
3.769
73
2.686
52
3.574
31
3.696
10
3.775
72
2.762
51
3.592
30
3.697
9
3.751
71
2.842
50
3.607
29
3.702
8
3.749
70
2.925
49
3.619
28
■3.707
7
3.743
69
2.987
48
3.627
27
3,713
6
3.719
68
3.044
47
3.632
26
3.720
5
3.697
67
3.096
46
3.633
25
3.727
4
3.622
66
3.143
45
3.631
24
3.731
3
3.538
65
3.186
44
3.634
23
3.735
2
3.368
64
3.222
43
3.637
t 22
3.739
I
3.189
63
3.252
42
3.639
21
3.742
0
2.836
62
3,277
41
3.641
20
3.744
61
3.296
40
3.642
19
3.746
60
3.310
39
3.648
18
3.748
Older Age Eighty-One Years.
Age.
81
80
79
78
77
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
Value.
2.105
2.172
2.235
2.293
2.317
2.397
2.460
2.532
2.589
2.655
2.723
2.784
2.843
2.900
2.956
3.010
3.048
3.079
3.104
3.122
Age.
61
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
Value.
3.133
3.163
3.195
3.228
3.263
3.300
3.327
3.352
3.874
3.395
3.413
3.426
3.436
3.443
3.447
3.448
3.432
3.454
3.455
3.455
Age.
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
Value.
3.454
3.459
3.465
3.472
3.480
3.489
3.494
3.499
3.592
3.506
508
512
517
521
526
531
535
539
543
3.547
Age.
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
Value.
3.551
3.553
3.555
3.556
3.556
3.556
3.559
3.563
3.567
3.572
3.577
3.568
3.560
3.566
3.565
3.543
3.517
3.448
3.367
3.211
3.045
}i^z|gb2VjUU^lC
452
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Tiro Lives.
(Carlisle 6 per Cent.)
Older Age Eighty-Two Years.
Age.
Valoe.
Age.
Value.
Age.
Value.
Age.
Value.
82
1.977
62
2.976
42
3.285
22
3.376
81
2.043
61
3.003
41
3.289
21
3.378
80
2.106
60
3.031
40
3.294
20
3.380
79
2.164
59
3.059
39
3.300
19
3.381
78
2.219
58
3.087
33
3.307
18
3.381
n
2.270
^7
3.116
37
3.315
17
3.381
76
2.326
56
3.142
36
3.320
16
3.383
75
2.381
55
3.167
35
3.325
15
3.386
74
2.435
54
3.191
34
3.329
14
3.390
73
2.488
53
3.214
33
3.333
13
3.394
72
2.540
52
3.237
32
3.337
12
3.398
71
2.598
51
3.252
31
3.341
11
3.398
70
2.658
50
3.264
30
3.344
10
3.398
69
2.7'iO
49
3.274
29
3.347
9
3.396
68
2.783
48
3.280
28
3.350
8
3.394
67
2.847
47
3.283
27
3.353
7
3.390
66
2.887
46
3.287
26
3.357
6
3.367
65
•2.920
45
3.289
25
3.361
5
3.338
64
2.946
44
3.290
24
3.366
4
3.275
63
2.964
43
3.23S
23
3.371
3
2
3.197
3.053
Older Age Eighty-Three Years.
Age.
Value.
-Age.
Value.
Age.
Value.
Age.
Value.
83
1.838
63
2.814
43
3.112
23
3.194
82
1.901
62
2.839
42
3.115
22
3.197
81
1.962
61
2.862
41
3.118
21
3.199
80
2.022
60
2.884
40
3.123
20
3.200
79
2.080
59
2.906
39
3.128
19
3.2U0
78
2.137
58
2.926
38
3.134
18
3.200
n
2.18S
57
2.950
37
3.139
17
3.202
76
2.236
5G
2.976
36
3.143
16
3.204
75
2. 2-^1
55
3.001
35
3.148
15
3.207
74
2.323
54
3.028
34
3.153
14
3.210
73
2.362
53
3.055
33
3.158
13
3.213
72
2.418
52
3.072
32
3.161
12
3.215
71
2.477
51
3.086
31
3.164
n
3.216
70
2.539
50
3.097
30
3.166
10
3.217
69
2.605
49
3.105
29
3.168
9
3.218
6S
2. 675
48
3.110
28
3.169
8
3.219
67
2.717
47
3.115
27
3.173
7
3.221
66
2.752
46
3.117
26
3.177
6
3.191
65
2.779
45
3.118
25
3.182
5
3.158
64
2.800
44
3.116
24
3.188
4
3
3.101
3.027
Digitized by ^^UUV IC
TABLE XXI.
458
Vulua of £1 per Annum during the joint Continuance of Two Liym.
(Carlisle 6 per Ct^nt.)
Older Age Eighty-Four Years.
A(je.
Value,
Aga
Value.
Age.
Value.
A..
Value.
84
1.702
64
2.652
44
2.942
24
3.015
83
1.761
63
2.675
43
2.944
23
3.018
82
1.820
62
2.696
42
2.947
22
3.020
8]
1.878
61
2.714
41
2.9,50
21
3.022
80
1.936
60
2.730
40
2.953
20
3.023
79
1.994
59
2.744
39
2.957
19
3.023
78
2.042
58
2.767
38
2.961
18
3.025
77
2.086
57
2.792
37
2.966
17
3.026
76
2.127
56
2.818
36
2.971
16
3,028
75
2.165
55
2.846
35
2.976
15
3.029
74
2.199
54
2.876
34
2.982
14
3.031
73
2.232
53
2.894
33
2.985
13
3.033
72
2.308
52
2.909
32
2.988
12
3,036
71
2.369
51
2.921
31
2.9S9
11
3.039
70
2.434
50
2.931
30
2.991
10
3,042
69
2.502
49
2.937
29
2.991
9
3.045
63
2.544
48
2.943
28
2.995
8
3.069
67
2.580
47
2.946
27
2.999
7
3.051
66
2.610
46
2.9-17
26
3.004
6
3.014
65
2.634
45
2.946
25
3.009
5
4
2.979
2.928
Older Age Eighty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age,
Value.
85
1.549
65
2.480
45
2.763
25
2.826
84
1.609
64
2.503
44
2.765
24
2.829
83
1.669
63
2.522
43
2.767
23
2.831
82
1.729
62
2.537
42
2.768
22
2.833
81
1.789
61
2.549
41
2.770
21
2.835
80
1.850
60
2.r>58
40
2.771
20
2.836
79
1.898
59
2.530
39
2.775
19
2.837
78
1.941
58
2.603
38
2.779
18
2.839
77
1.980
57
2.629
37
2.784
17
2.840
76
2.015
56
2.656
36
2.790
16
2.840
75
2.046
55
2.686
35
2.797
15
2.841
74
2.094
54
2.704
34
2.800
14
2.843
73
2.145
53
2.720
33
2.803
13
2.846
72
2.199
52
2.733
32
2.804
12
2.849
71
2.263
51
2.744
31
2.806
11
2.853
70
2.315
50
2.752
30
2.806
10
2.857
69
2.356
49
2.759
29
2.809
9
2.911
68
2.394
48
2.763
28
2.813
8
2.919
67
2.427
47
2.765
27
2.817
7
2.882
66
2.455
46
2.765
26
2.821
6
5
2.838
2.799
Digitized by N^UUV
le
454
TABLE XXI.
Value of £1 per Annum during tlie joint Gontinuanoe of Two Lives.
(Carlisle 6 per Cent)
Older Age Eighty-Six Years.
Age.
Valae.
Age.
Value.
Age.
Value.
Age.
Value.
86
1.414
64
2.369
42
2.609
20
2.672
85
1.468
63
2.384
41
2.608
19
2.673
84
1.524
62
2.39.5
40
2.611
IS
2.674
83
1.583
61
2.401
39
2.615
17
2.674
82
1.643
60
2.421
38
2.620
16
2.674
81
1.706
59
2.442
37
2.626
15
2.676
80
1.754
58
2.465
36
2.632
14
2.678
79
1.797
57
2.489
35
2.635
13
2.681
78
1.838
56
2.515
34
2.638
12
2.634
77
1.874
55
2.533
33
2.640
11
2.688
76
1.907
54
2.548
32
2.642
10
2.731
75
1.951
53
2.562
31
2.643
9
2.778
74
1.996
52
2.575
30
2.646
8
2.769
73
2.042
51
2.585
29
2.649
7
2.712
72
2.089
50
2.593
28
2.652
6
2.662
71
2.138
49
2.599
27
2.655
70
2.179
48
2.603
26
2.659
69
2.213
47
2.605
25
2.662
68
2.256
46
2.605
24
2.664
67
2.291
45
2.607
23
2.667 .
66
2.325
44
2.603
22
2.669
65
2.349
43
2.609
21
2.671
Older Age Eighty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
87
1.304
65
2.239
43
2.477
21
2.537
86
1.349
64
2.255
42
2.475
20
2.538
85
1.400
63
2.267
41
2.478
19
2.538
84
1.458
62
2.273
40
2.481
18
2.538
83
1.521
61
2.291
39
2.485
17
2.538
82
1.590
60
2.310
38
2.490
16
2.540
81
1.637
59
2.329
37
2.496
15
2.542
80
1.681
58
2.349
36
2.499
14
2.544
79
1.722
57
2.370
35
2,502
13
2.547
78
1.760
56
2.387
34
2.505
12
2.550
n
1.794
55
2.403
33
2.507
11
2.550
76
1.833
54
2.419
32
2.509
10
2.550
75
1.872
53
2.433
31
2.512
9
2.548
74
1.910
52
2.447
30
2.514
8
2.546
73
1.9-18
51
2.457
29
2.516
7
2.543
72
1.985
50
2.464
28
2.519
71
2.025
49
2.470
27
2.521
70
2.066
48
2.473
26
2.524
69
2.107
47
2.475
25
2.526
68
2.149
46
2,477
24
2.529
67
2.191
45
2.478
23
2.532
66
.2.217
44
2.478
22
2.535
Digitized by VjOOQ IC
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Lives*
(Carlisle 6 per Cent.)
Older Age Eighty-Eight Years.
4d5
Age.
88
87
86
85
84
83
82
81
80
79
78
77
76
75
74
73
72
71
70
69
68
67
66
Value.
1.249
1.284
1.326
1.377
1.436
1.502
1.548
1.593
1.636
1.678
1.718
1.755
1.790
1.822
1.853
1.881
1.920
1.962
2.006
2.052
2.100
2.129
2.153
A«e.
65
64
63
62
61
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
Value.
2.171
2.185
2.194
2.211
2.227
2.243
2.258
2.273
2.290
2.307
2.324
2.342
2.360
2.371
2.381
2.388
2.393
2.896
2.399
2.401
2.401
2.400
2.397
Age.
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
Value.
2.400
2.401
2.404
2.408
2.412
2.415
2.418
2.422
2.425
2.428
2.430
2.432
2.434
2.435
2.436^
2.439'
2.442
2.445
2.449
2.453
2.455
2.456
2.457
Age.
19
18
17
16
15
14
13
12
11
10
9
8
Value.
2.457
2.457
2.458
2.460
2.462
2.464
2.466
2.467
2.468
2.469
2.469
2.469
Older Age Eighty-Nine Years.
Age.
ValuA
Age.
Value.
Age.
43
Value.
Age.
Value.
89
1.176
66
2.070
2.306
20
2.362
88
1.202
65
2 087
42
2.307
19
2.362
87
1.238
64
2.099
41
2.310
18
2.363
86
1.283
63
2.115
40
2.312
17
2.364
85
1.338
62
2.130
39
2.315
16
2.366
84
1.403
61
2.143
38
2.318
15
2.367
83
1.447
60
2.155
37
2.321
14
2.368
82
1.491
. 59
2.165
36
2.325
13
2.370
81
1.534
58
2.182
35
2.329
12
2.371
80
1.577
57
2.199
34
2.333
11
2.373
79
1.619
56
2.218
33
2.335
10
2.375
78
1.655
55
2.238
32
2.337
9
2.377
77
1.688
54
2.259
31
2.338
76
1.718
53
2.272
30
2.339
75
1.746
52
2.282
29
2.339
74
1.772
51
2.291
28
2.342
73
1.811
50
2.298
27
2.345
72
1.852
49
2.302
26
2.348
•
71
1.896
48
2.306
25
2.352
70
1.943
47
2.308
24
2.356
69
1.993
46
2.808
23
2.858
68
2.023
45
2.307
22
2.360
67
2.049
44
2. 804
21
2.361
Digitized by VjiOOQlC
466
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two liYet.
(Carlisle 6 per Cent)
Older Age Ninety Years,
Age,
Value.
Age.
Valae.
Age.
Value.
Age.
Value.
.90
1.025
67
1.914
44
2.161
21
2.212
89
1.043
66
1.936
43
2.162
20
2.213
88
1.075
65
1.954
42
2.163
19
2.214
87
1.120
64
1.971
41
2.164
IS
2.215
86
1.180
63
1.984
40
2.165
17
2.216
85
1.253
62
1.996
39
2.168
16
2.216
84
1.299
61
2.004
38
2.171
15
2.217
83
1.344
60
2.010
37
2.175
14
2.219
82
1.390
59
2.026
36
2.179
13
2.221
81
1.435
58
2.043
35
2.184
12
2.223
80
1.481
57
2.062
34
2.186
11
2.225
79
1.517 .
56
2.083
33
2.183
10
2.228
78
1.550
55
2.105
32
2.190
77
1.580
54
2.118
31
2.191
76
1.607
53
2.130
30
2.191
75
1.631
52
2.139
29
2.193
74
1.667
51
2.147
28
2.196
73
1.705
50
2.153
27
2.199
72
1.745
49
2.158
26
2.202
71
1.787
48
2.161
25
2.206
70
1.831
47
2.162
24
2.208
69
1.862
46
2.162
23
2.210
68
1.889
45
2.160
22
2.211
Older Age Ninety-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
91
0.987
68
1.863
45
2.144
22
2.194
90
0.998
67
1.892
44
2.145
21
2.195
89
1.022
66
1.920
43
2.146
20
2.196
88
1.061
65
1.940
42
2.146
19
2.197
87
1.112
64
1.956
41
2.145
18
2.198
86
1.178
63
1.968
40
2.147
17
2.198
85
1.222
62
1,977
39
2.151
16
2.198
84
1.268
61
1.982
38
2.154
15
2.199
83
1.316
60
1.998
37
2,159
14
2.201
82
1.365
59
2.015
36
2.164
13
2.203
81
1.417
58
2.033
35
2.167
12
2.205
80
1.4S6
57
2.052
34
2.169
11
2.208
79
1.493
56
2.072
33
2.171
78
1.526
55
2.086
32
2.172
77
1.557
54
2.099
31
2.173
76
1.585
53
2.110
30
2.175
75
1.620
52
2.120
29
2.178
74
1.656
51
2.128
28
2.180
73
1.693
50
2.134
27
2.183
72
1.730
49
2.139
26
2.186
71
1.768
48
2.142
25
2,188
70
1.801
47
2.143
24
2.190
69
1.833
46
2.143 '
23
2.192
Digitized by VjOOQ IC
TABLE XXI.
457
V&lue of £1 per Annum during the joint Continuance of Two Litci.
(Carlisle 6 per Cent.)
Older
Age Ninety-Two Years.
Age
Value.
Age.
Value.
Agft.
52
Value.
Age.
32
Value.
92
1.051
72
1.788
2.204
2.258
91
1.057
71
1.324
51
3.212
31
2.260
90
1.071
70
1.860
50
2.219
30
2.262
89
1.094
69
1.898
49
2.224
29
2.264
88
1.127
68
1.937
A^
2.227
28
2.266
87
1.168
67
1.976
47
2,228
27
2.268
8G
1.208
66
2.000
46
2.230
26
2.270
85
1.255
65
2.019
45
2.231
25
2.273
84
1.306
64
2.034
44
2.230
24
2.275
83
1.364
63
2.044
43
2.229
23
2.278
82
1.427
62
2.050
42
2.227
22
2.281
81
1.471
61
2.066
41
2.229
21
2.282
80
1.513
60
2.083
40
2.232
20
2.283
79
1.552
59
2.100
39
2.236
19
2.284
78
1.589
58
2.U7
38
2.240
18
2.284
17
1.623
57
2.135
37
2.245
17
2.283
76
1.659
56
2.150
36
2.248
16
2.284
n
1.693
bb
2.165
35
2.251
15
2.286
74
1.726
54
2.178
34
2.253
14
2.288
73
1.758
53
2.192
33
2.256
13
12
2.290
2.293
Older Age Ninety-Three Years
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
93
1.148
73
1 .824
53
2.296
33
2.358
92
1.150
72
1.862
52
2.307
32
2.360
91
1,156
71
1.904
51
2.316
31
2.362
90
1.165
70
1.948
50
2.322
30
2.363
89
1.178
69
1.995
49
2.327
29
2.364
88
1.194
68
2.045
48
2.329
28
2.365
87
1.228
67
2.074
47
2.331
27
2.368
86
1.270
66
2.097
46
2.332
26
2.370
85
1.320
65
2.115
45
2.332
25
2.374
84
1.378
64
2.128
44
2.330
24
2.377
83
1.445
63-
2.136
43
2.327
23
2.381
82
1.493
62
2.152
42
2.329
22
2.383
81
1.540
61
2.168
41
2-331
21
2.384
80
1.586
60
2.182
40
2.334
20
2.385
79
.1.631
59
2.197
39
2 338
19
2.385
78
1.676
58
2.210
38
2.342
18
2.385
77
1.712
57
2.226
37
2.345
17
2.386
76
1.745
56
2.243
36
2.348
16
2.388
75
1.775
55
2.260
35
2.352
15
2.389
74
1.801
54
2.278
34
2.355
14
13
2.391
2.393
Digitized by VjOOQ IC
458
TABLB XZI.
Value of £\ per Aonum during^ the joint Gontinaence of Two IiT«.
(Carlisle 6 per Cent)
Older
Age Ninety-Four Yeara.
A««.
Value.
Are
74
Value.
Age.
Value.
Age.
Valae.
94
1.218
1.832
54
2.339
34
!{.409
93
1.218
73
1.872
53
2.352
33
2.411
92
1.216
72
1.915
52
2.362
32
2.413
91
1.210
71
1.963
51
2.370
31
2.413
90
1.202
70
2.014
50
2.376
30
2.413
89
1.190
69
2.069
49
2.379
29
2.413
88
1.217
68
2.101
48
2.382
28
• 2.416
87
1.266
67
2.128
47
2.384
27
2.419
86
1.305
66
2.150
46
2.384
86
2.422
85
1.365
65
2.166
45
2.382
25
2.426
84
1.436
64
2.178
44
2.379
24
2.431
83
1.486
63
2.194
43
2.380
23
2.433
82
1.537
62
2.209
42
2.382
22
2.435
81
1.588
61
2.221
41
2.384
21
2.436
80
1.640
60
2.232
40
2.386
20
2.437
79
1.692
59
2.241
39
2.389
19
2.437
78
1.7^^9
58
2.258
38
2.392
18
2.438
77
1.762
57
2.276
^7
2.396
17
2.439
76
1.790
56
2.296
36
2.400
16
2.440
7b
1.813
55
2.317
35
2.404
15
14
2.441
2.442
Older Age Ninety-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
95
1.295
75
1.846
55
2.362
35
2.439
94
1.299
74
1.887
54
2.376
34
2.442
93
1.285
73
1.930
53
2.388
33
2.443
92
1.255
72
1.976
52
2.397
32
2.445
91
1.207
71
2.024
51
2.405
31
2.445
90
1.143
70
2.075
50
2.410
30
2.445
89
1.163
69
2.109
49
2.414
29
2.447
88
1.200
68
2.139
48
2.416
28
2.450
87
1.254
67
2.165 •
47
2.417
27
2.453
86
1.325
66
2.187
46
2.415
26
2.457
85
1.413
65
2.205
45
2.412
25
2.461
84
1.467
64
2.222
44
2.413
24
2.463
83
1.520
63
2.236
43
2.414
23
2.465
82
1.574
62
2.247
42
2.415
22
2.466
81
1.627
61
2.254
41
2.416
21
2.467
80
1.680
60
2.259
40
2.417
20
2A6%
79
1.721
59
2.276
39
2.420
19
2.469
78
1.759
58
2.294
38
2.424
18
2.470
77
1.792
57
2.315
37
2.428
17
2.470
76
1.821
56
2.338
36
2.433
16
15
2.471
2.471
Digitized by LjOOQ IC
TABLE XXI.
459
Value of £1 per Annum dnring the joint Continuance of Two Livee.
(Carlisle 6 per Cent.)
Older Age Ninety-
Six Years.
Age.
Value.
Age.
Valne.
Age.
56
Value.
Age.
Value.
96
1.336
76
1.822
2.326
36
2.407
95
1.354
75
1 861
55
2.340
35
2.410
94
1.343
74
1.900
54
2.352
34
2.412
93
1.303
73
1.941
53
2.362
33
2.413
92
1.236
72
1.982
52
2.370
32
2.414
91
1.138
71
2.025
51
2.377
31
2.415
90
1.218
70
2.060
50
2.382
30
2.417
89
1.281
69
2.093
49
2.386
29
2.420
88
1.327
68
2.124
48
2.387
28
2.422
87
1.356
67
2.163
47
2.388
27
2.425
86
1.368
66
2.180
46
2.386
26
2.428
85
1.420
65
2.199
45
2.387 .
25
2.430
84
1.473
64
2.212
44
2.387
24
2.432
83
1.529
63
2.223
43
2.387
23
2.433
82
1.586
62
2.229
42
2.387
22
2.435
81
1.645
61
2.231
41
2.386
21
2.436
80
1.688
60
2.247
40
2.389
20
2.437
79
1.728
59
2.264
39
2.392
19
2.438
78
1.763
58
2.283
38
2.396
18
2.438
77
1.795
57
2.304
37
2.401
17
16
2.439
2.438
Older Age Ninety-Seven Years.
Age.
Value.
AgP.
Value.
Age.
Value.
Age.
Value.
97
1.312
77
1,751
57
2.211
37
2.295
96
1.355
76
1.785
56
2.224
36
2.298
95
1.360
75
1.818
55
2.236
35
2.300
94
1.330
74
1.851
54
2.247
34
2.302
93
1.262
73
1.883
53
2.257
33
2.303
92
1.158
72
1.914
52
2.266
32
2.304
91
1.162
71
1.947
51
2.272
31
2.306
90
1.178
70
1.981
50
2.277
SO
2.307
89
1.206
69
2.015
49
2.279
29
2.309
88
1.246
68
2.049
48
2.281
28
2.311
87^
1.297
67
2.083
47
2.280
27
2.312
86'
1.341
66
2,103
46
2.281
26
2.314
85
1.391
65
2.118
45
2.281
25
2.316
84
1.446
64
2.128
44
2.280
24
2.318
83
1.507
63
2.133
43
2.279
23
2.321
82
l.i>73
62
2.134
42
2.277
22
2.323
81
1.616
61
2.147
41
2.279
21
2.324
80
1.656
60
2-162
40
2.262
20
2.325
79
1.692
59
2.177
39
2.285
19
2.325
78
1.723
58
2.194
38
2.290
18
17
2.325
2.324
gle
Digitized by VjVJVJ
460
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two LiTes.
(Carlisle 6 per Cent.)
Older Age Ninety-Eight Yean.
Agf.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
98
1.299
78
1.673
53
2.078
38
2.163
97
1.370
17
1.702
57
2.090
37
. 2.165
96
1.395
76
1.730
56
2.101
36
2.167
95
1.374
75
1.755
55
2.113
35
2.169
94
1.306
74
1.778
54
2.124
34
2.171
93
1.192
73
1.799
53
2.136
33
. 2.172
92
1.191
72
1.830
52
2.143
32
2.173
91
1.197
71
1.862
51
2.148
31
2.174
90
1.210
70
1.897
50
2.151
30
2.175
89
1.230
69
1.933
49
2.153
29
2.176
88
1.256
68
1.971
48
2.153
28
2.176
87
1.290
67
1.991
47
2.154
27
2.178
86
1.330
66
2.006
46
2.154
26
2.180
85
1.378
65
2.016
45
2.153
25
2.182
84
1.433
64
2.021
44
2.152
24
2.185
83
1.494
63
2.021
43
2.149
23
2.188
82
1.535
62
2.032
42
2.150
22
2.189
81
1.573
61
2.043
41
2.152
21
2.190
80
1.609
60
2.054
40
2.155
20
2.190
79
1.642
59
2.066
39
2.159
19
18
2.190
2.189
Older Age Ninety-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
99
1.231
79
1.533
59
1.873
39
1.950
98
1.219
78
1.558
58
1.883
38
1.952
97
1.207
77
1.580
57
1.893
37
1.954
96
1.195
76
1.600
56
1.904
36
1.956
95
1.183
75
1.617
55
1.916
35
1.958
94
1.171
74
1.632
54
1.929
34
1.960
93
1.166
73
1.659
53
1.936
33
1.961
92
1.164
72
1.688
52
1.941
32
1.962
91
1.164
71
1.719
51
1.944
31
1.962
90
1.167
70
1.753
50
1.946
30
1.962
89
1.172
69
1.789
49
1.946
29
1.962
88
1.196
68
1.807
48
1.947
28
1.964
87
1.229
67
1.821
47
1.947
27
1.965
86
1.269
66
1.830
46
1.946
26
1.968
85
1.318
65
1.835
45
1.945
25
1-970
84
1.374
64
1.836
44
1.942
24
1.973
83
1.409
63
1.844
43
1.943
23
1.974
82
1.443
62
1.852
42
1.944
22
1.975
81
1.475
61
1.859
41
1.945
21
1.975
80
1.505
60
1.866
40
1.947
20
19
1.975
1.974
Digitized by ^^UUV IC
* TABLE XXI.
Value of £1 per Annum duriug; the joint Continuance of Two Lives.
(Carlisle 6 per Cent.)
Older Age One Hundred Years.
461
Age.
Value.
Age.
Value.
Age.
Value.
Age.
37
Value.
100
0.948
79
1.271
58
1.512
1.562
99
0.963
78
1.288
&7
1.521
36
1.564
98
0.978
77
1.301
56
1.531
35
1.565
97
0.992
76
1.313
55
1.542
34
1.567
96
1.007
75
1.321
54
1.547
33
1.567
95
1.022
74
1.340
53
1.551
32
1.568
94
1.018
73
1.362
52
1.554
31
1.567
93
1.007
72
1.3S5
51
1.556
30
1.567
92
0.989
71
1.410
50
1.556
29
1.668
91
0.965
70
1.437
49
1.557
28
1.569
90
0.935
69
1.451
48
1.557
27
1.571
89
0.950
68
1.462
47
1.557
26
1.573
88
0.975
67
1.470
46
1.556
25
1.575
87
l.OU
66
1.475
45
1.554
24
1.576
86
1.058
65
1.477
44
1.554
23
1.576
85
1.116
64
1.483
43
1.555
22
1.576
84
1.147
fi3
1.487
42
1.555
21
1.576
83
1.176
62
1.491
4L
1.556
20
1.576
82
1.203
61
1.495
40
1.557
81
1.228
60
1.497
39
1.553
80
1.252
59
1.504
38
1.560
.
Older Age One Hundred and One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
101
0.662
80
0.957
59
1.121
38
1.153
100
0.693
79
0.969
58
1.126
37
1.154
99
0.724
78
0.980
57
1.133
36
1.156
98
0.755
77
0.988
56
1.140
35
1.157
97
0.786
76
0.995
55
1.143
34
1.157
96
0.817
76
1.008
54
1.14G
33
1.157
95
0.818
74
1.021
53
1.148
32
1.157
94
0.809
73
1.035
52
1.149
31
1.157
93
0.791
72
1.050
51
1.149
30
1.158
92
0.762
71
1.066
50
1.150
29
1.159
91
0.723
70
1.076
49
1.150
23
1.160
90
0.730
69
1.084
48
1.150
27
1.161
89
0.746
68
1.090
47
1.150
26
1.162
88
0.770
67
1.095
46
1.149
25
1.163
87
0.803
66
1.099
45
1.149
24
1.163
86
0.844
65
1.103
44
1.149
23
1.163
85
0.866
64
1.106
43
1.150
22
l.lt>3
84
0.886
63
1.109
42
l.liiO
21
1.163
83
0.906
62
1.110
41
1.150
82
0.925
61
I. Ill
40
1.151
81
0.943
60
1.115
39
. 1.152
Digitized by VjiOOQlC
468
TABLK XXI.
Value of £1 per Annum during the joint Continuance of Two lives.
(Carlisle 6 per Cent)
Older Age One Hundred and Two Years.
Age.
ValM.
Age.
Value.
Age.
Value.
Age.
Value.
102
.375
81
.625
60
.715
39
.732
101
.410
80
.632
59
.718
38
.733
100
•445
79
.639
58
.721
37
.734
99
.479
78
.643
57
.724
36
.735
98
t514
11
.647
56
.726
2b
.735
97
.549
76
.653
55
.727
34
.735
96
.557
75
.660
54
.729
33
.735
95
• 557
74
.667
53
.729
32
.735
94
.547
73
.673
52
.730
31
.735
93
.529
72
.680
51
.731
30
.736
92
.502
71
.665
50
-.731
29
.736
91
.504
70
.690
49
.731
28
.737
90
.510
69
.695
48
.731
27
.737
89
.520
68
.699
47
.731
26
.737
88
.534
67
.703
46
.731
25
•738
87
.552
66
.706
45
.731
24
.738
86
.564
65
.708
44
.731
23
.738
85
.576
64
.709
43
.731
22
.738
84
.589
68
.710
42
.731
83
.602
62
.710
41
.731
82
.616
61
.712
40
.732
Older Age One Hundred and Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
103
.105
82
.270
61
.304
40
.311
102
.133
81
.273
60
.305
39
.311
101
.162
80
.276
59
.306
38
.311
100
.190
79
.278
58
.307
37
.311
99
.219
78
.280
57
.308
36
.311
98
.247
77
.282
56
.308
35
.311
97
.257
76
.284
55
.309
34
.311
96
.260
1^
.286
54
.309
33
.311
95
.257
74
.288
53
.309
32
.311
94
.248
73
.290
52
.309
31
.311
;93
.233
72
.292
51
.310
30
.312
92
.233
71
.294
50
.310
29
.312
91
.235
70
.296
49
•310
28
.312
•90
.237
69
.298
48
.310
27
.312
89
.241
68
.300
47
.310
26
.313
88
.245
67
.301
46
.310
25
.312
87
.249
66
.302
45
.310
24
.312
86
.253
65
.302
44
.310
23
.312
85
.257
64
.302
43
.310
84
•262
63
.302
42
.310
83
.267
62
.303
41
•310
Digitized by VjOOQ IC
TABLE XXI.
463
Value of £1 per Annum daring the joint Continuance of Two Latoi.
(Carlisle 3} per Cent.)
Older Age 0 Yean.
Older Age One Year.
Afe.
YalUB.
Age.
Vain*.
0
9.629
1
0
12.921
10.346
Older Age Two Years.
Older Age Three Years.
Age.
Valoe.
Age.
Value.
2
1
0
14.821
13.428
11.063
3
2
1
0
16.544
15.180
13.935
11.779
Older Age Four Yeani.
Older Age Five Yeara.
Ag«.
Valae.
Ag«.
Valae.
4
3
2
1
0
17.500
16.746
15.539
14.442
12.496
5
3
2
1
0
18.199
17.602
16.948
15.898
14.949
13.213
Older Age Six Years.
Older Age Seven Years.
Age.
Voliw.
Age.
Vahie.
Age.
Value.
Age.
Value.
6
5
4
3
18.525
18.217
17.704
17.150
2
1
0
16.257
15.456
13.224
7
6
5
4
18.654
18.492
18.235
17.806
3
2
1
0
17.352
16.616
15.426
13.235
Digitized by VjOOQ iC
464
TABLB XXI.
Value of £1 per Annimi during the joint Contiauonce of Two Lives.
(Carlisle 3^ per Cent.)
Older Age Eight Years.
Older Age Nine Years.
Age.
Valae.
A«e.
Value.
Age.
Valoe.
Age.
Value.
8
7
6
6
4
18.651
18.590
18.460
18.255
17.909
3
2
1
0
17.555
16.555
15.395
13.247
9
8
7
6
5
18.560
18.569
18.526
18.427
18.273
4
3
2
1
0
18.011
17.473
16.494
15.365
13.258
Older Age Ten Years.
Older Age Eleven Years.
A«e.
Value.
Ajie.
Value.
Age.
Value.
Age.
Value.
10
9
8
7
6
5
18.407
18.468
18.486
18.461
18.394
18,291
4
3
2
1
0
17.917
17.391
16.434
15.334
13.269
11
10
9
8
7
6
18.223
18.313
18.377
18.404
18.397
18.361
5
4
3
2
1
0
18.192
17.823
17.310
16.373
15.304
13.196
Older Age Twelve Years.
Older Age Thirteen Years.
Age.
Value.
Age.
Value.
Age.
Valu«».
Age.
Value.
12
11
10
9
8
7
6
18.044
18.102
18.160
18.217
18.275
18.333
18.263
5
4
3
2
1
0
18.093
17.730
17.228
16.312
15.220
13.123
13
12
11
10
9
8
7
17.864
16.939
17.014
18.089
18.164
18.239
18.237
6
5
4
3
2
1
0
18.165
17.995
17.636
17.146
16.223
15.136
13.050
Digitized by LjOOQ iC
TABLB XXI.
Value of £1 per Annum during the joint ContinuauM ^f Two Lives.
(Carlule 3^ per Cent.)
Older Age Fourteen Years.
Older Age Fifteen Years.
Afe.:
Value.
Age.
Value.
Age.
Value.
Age.
Value.
14
13
12
11
10
9
8
7
17.682
17.766
17.850
17.934
13.018
18.102
18.145
18.141
6
5
4
3
^ 2
1
0
18.066
17.896
17.542
17.054
16.134
15.051
12.977
15
14
13
12
11
10
9
8
17.505
17.591
17.677
17.763
17.849
17.935
17.011
18.052
7
6
5
4
3
2
1
0
18.044
17.9fi8
17.797
17.449
16.962
16.046
14.967
12.904
Older Age Sixteen Yean.
Older Age Seventeen Yearsi
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
16
17.344
7
17.948
17
17.195
8
17.801
15
17.428
6
17.870
16
17.276
7
17.852
14
17.512
5
17.703
15
17.357
6
17.773
IS
17.595
4
17.356
14
17.437
5
17.608
12
. 17.679
3
16.870
13
17.518
4
17.262
11
17.763
2
15.957
12
17.599
3
16.778
10
17.845
I
14.883
11
17.650
2
15.868
f
16.919
0
12.834
la
17.700
1
14.800
•
17.9j8
9
17.751
0
12.765
Older Age Eighteen
Years.
Older Age Nineteen
Years.
A»fc
Valoe.
Age.
v.i.,...
Age.
Value.
Age.
Value.
18
17.045
8
17.771
19
16.890
17.646
17
17.123
7
17.761
18
16.965
17.666
16
17.201
6
17.676
17
17.040
17.660
15
17-278
5
17.514
16
17.115
17.580
14
17.3J6
4
17,169
15
17.190
17.419
13
17.434
3
16.686
14
17.265
17.076
12
17.501
2
15.775
13
17.3«
16.582
11
17.569
1
14.717
12
17.417
15.682
10
17.636
0
12.695
11
17.403
14.6.''6
9
17.704
10
17.569
12.C26
DigfSzlby^OOgle
48]6
TABLE XXt
Value of £1 per Annum during tlie joint Continuance of Two Lives*
(CarUde 3^ per Cent.)
Older Age Twenty Yean.
Af*.
Value.
Age.
Value.
Age.
Valoe.
Age.
Value.
20
19
18
17
16
15
16.729
16. £02
16.875
16.949
17.022
17.095
14
13
12
11
10
9
17.173
17.251
17.329
17.407
17.485
17.534
8
7
6
5
4
3
17.559
17..'i48
17.483
17.325
16.964
16.479
2
1
0
15.568
14.552
12.556
Older Age Twenty-One Years.
Age.
Valiit.
Age.
Value.
Age.
Value.
Age.
Va!ue.
21
20
19
18-
17
16
16.5Q1
16.635
16./09
16.782
16.856
16.930
15
14
13
12
11
10
17.006
17.081
17.157
17.272
17.318
17.3G9
9
8
7
6
5
4
17.423
17.452
17.447
17.386
17.205
16.852
3
2
1
0
16.375
15.495
14.469
12.169
Older Age Twenty-Two Years.
Age.
Vitlut.
Afte.
Value.
Age.
Value.
A<e.
Value.
22
21
20
19
18
17
16.382
16.459
16.533
16.612
16.683
16.765
16
15
14
13
12
11
16.837
16.909
16.982
17.054
17.126
17.170
10
9
8
7
6
5
17.214
17.258
17.302
17.346
17.260
17.086
4
3
2
1
0
16.741
16.27*
]5.40i
14.362
12.382
Older Age Twenty-Three Years.
Age.
Value.
Age.
Valne.
Af.
Value.
Age.
Value.
23
22
21
20
19
18
17
16.195
16.275
16.355
16.435
16.515
16.595
16.664
16
15
14
13
12
11
10
16.733
16.802
16.871
16.940
17.000
17.060
17.120
9
8
7
6
5
4
3
17.180
17.240
17.214
17.131
16.966
16.629
16.168
2
1
0
15.2S3
14.256
12.295
Digitized by LjOOQ IC
TABLB XXI,
467
YsliM of £1 per Aiiniim during the joint Continaa&ce of Tiro Lives. «
(Carlisle ^ per Cent.)
Older Age Twenty-Four Years,
Age.
.Vmlne.
Age.
Value.
A9^.
Value.
A^e.
Valoe. •
24
23
22
21
20
19
18
16.000
16.084
16.168
16.251
16.335
16.419
16.485
17
16
15
14
13
12
11
16.551
16.617
16.683
16.749
16.817
16.885
16.953
10
9
8
7
6
5
4
17.021
17.089
17.104
17.0fc3
17.008
16.847
16.517
3
2
1
0
16.038
15.163
14.149
12.208
Older Age Twenty-Five Years.
At*.
Valoe.
Age.
Value.
Age.
Value.
Ajje.
Value.
25
24
23
22
21
20
19
15.798
15.886
15.973
16.061
16.148
16.236
16.300
18
17
16
15
14
13
12
16.364
16.428
16.492
16.556
16.626
16.696
16.765
11
10
»
8
7
6
5
16.&35
16.905
16.953
16.V69
16.951
16.882
16.727
4
3
2
1
0
16.381
15.907
15.044
14.043
12.121
Older Age Twenty-Six Years.
Ajse.
Vulne.
Age.
Value.
Age.
Value.
Age.
Value.
26
25
24
23
22
21
20
15.592
15.683
15.775
15.866
15.958
16.0^19
16.113
19
18
17
16
15
14
13
16.177
16.242
16.306
16.370
16.437
16.504
16.571
12
11
10
9
8
7
6
16.638
16.705
16.771
16.816
16.833
16.820
16,756
5
4
3
2
1
0
16.591
16.246
15.777
14.924
13.936
12.022
Oldei
Age Twenty-Seven Years.
Age.
Value.
Age.
Value.
A^-.
Value.
Age.
Valup.
27
•26
25
24
23
22
21
15.378
15.473
15.567
15.662
15.756
15.831
15.918
20
19
18
17
16
15
14
15.984
16.051
16.117
16.184
16.248
16.311
16.375
13
12
11
10
9
8
7
16.4.38
16.502
16.539
16.576
16.614
16.651
I6.0i^8
6
5
4
3
2
1
0
ir,.ri-2i
16.454
16.110
15.646
14.S05
13.823
11.924
2h 2
Digitized by
Google
4«8
TABLK XXL
4 Value of £1 par Ananni during the jolul ContimuuiM of Two livea.
(CetUsle 3i per Cent.)
Older Age Tweoty-Etght Yean.
Ate.
Value.
Af.
Value.
Aje.
Value.
Age.
ValM.
€8
15.167
20
15.859
12
16.352
4
15.975
27
15.264
19
15.929
11
16.405
3
15.516
26
15.360
18
15.999
10
16.457
2
14.683
23
15.457
17
16.059
9
16.510
1
13.709
24
15.553
16
16.119
8
16.562
0
11.825
23
15.650
15
16.180
7
16.555
2d
15.720
14
16.240
6
16.486
21
15.790
13
16.300
5
16.318
Older Age Twenty-Nine Ycare.
Age.
Vahie.
Age.
Value.
Age.
VaUe.
Age.
Value.
29
14.974
21
15.675
13
16.167
5
16.181
28
15.070
20
15.748
12
16.2-'7
4
15.839
•^7
15.167
19
15.821
11
16.287
3
15.390
26
15.263
18
15.878
10
16.347
8
14.565
25
15.360
17
15.935
9
16.407
1
13.596
24
15.456
16
15.993
8
16.430
0
11 ,727
23
15.529
16
16.050
7
16.422
22
15.602
14
16.107
6
16.350
Older Age Thirty Years.
Age.
Value.
Age.
Value.
Age.
Value.
A^.
Value.
30
14.808
22
15.501
14
15.991
6
16.215
29
11.901
21
15.578
13
16.053
5
16.045
28
14.993
20
15.655
12.
16.114
4
i:>.706
27
15.086
10
15.710
11
16.176
3
15.'2C3
26
15.178
18
15.765
10
16.237
2
14.445
25
15.271
17
15.820
9
16.273
I
13.482
24
15.348
16
15.875
B
16.298
0
11.628
23
15.425
15
15.930
t
16.290
Older Age Thirty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
31
14.641
23
15.324
15
15.818
7
16.1.57
30
15.730
22
15.404
14
15.877
6
16.080
29
15.819
21
15.484
13
15.935
5
15.903
28
15.907
20
15.539
12
15.994
4
15.573
27
15.996
19
15.594
11
16.053
3
15.137
26
15.065
18
15.649
10
16.097
i
14.325
25
15.165
17
15.704
9
16.139
1
13.369
24
15.245
16
15.759
8
16.167
0
11.526
Digitized by CjOOQ IC
TABLX XXL
469
TalM ff 41 par Alin<» during the joint Continuaiic* of Two Litoi.
(C«rU«ia3|porCont)
Older Age Thirty«Two Yean.
A|^
Value.
A|«.
V«lw.
At*.
V«lw.
Af*.
Value.
33
14.467
83
15.222
15.757
5
15.761
81
14.552
22
15.305
15.818
4
15.441
do
14.637
21
15.362
15.868
3
15.010
29
14.721
20
15.419
15.699
8
14.2U5
28
14.806
19
15.476
15.930
1
13.243
27
14.891
18
15.533
15.968
0
11.484
2«i
14.974
17
15.590
15.993
25
15.057
16
15.646
16.084
24
15.139
15
15.701
15.930
Older Age Thirty-Three Yean.
Agn.
Value.
Age.
Value.
Age.
Value.
A«e.
Value.
33
14.281
24
15.030
15
15.571
6
15.779
32
14.363
23
15.115
14
15.623
5
15.620
31
14.445
22
15.175
13
15.675
4
15.308
30
14.528
21
15.235
12
15.721
3
14.884
29
14.610
20
15.295
11
15.766
2
14.063
28
14.692
19
15.355
•lo
15.818
1
13.118
27
14.777
18
15.415
9
15.857
0
11.328
26
14.861
17
15.467
8
15.903
25
14.946
16
15.519
7
15.866
Older Age Thirty-Four Yean.
Age.
Value.
AiC..
Value.
Age.
Value.
Age.
Value.
34
14.083
25
14.831
16
15.375
7
15.708
33
14.165
24
14.915
15
15.424
6
15.629
38
14.248
23
14.978
14
15.473
5
15.478
31
14.330
22
15.041
13
15.526
4
16.175
30
14.413
21
15.103
12
15.579
3
14.728
29
14.495
20
15.166
11
15.631
2
13.921
28
14.579
19
15.229
10
]5.68^(
1
12.992
27
14.663
18
15.278
9
15.737
0
11.220
26
14.747
17
15.327
8
15.739
Digitized by LjOOQ IC
470
TABLK XXI;
Value of CI per Annum during the joint Continuance of Tin> lifesb
(Carlisle d| per Cent.)
Older Age Thirty-Five Years*
Age.
Valu.
Age.
Value.
Age.
Value.
Age.
Value.
33
13.876
26
14.627
17
15.176
8
15.574
34
13.962
25
14.707
16
15.222
7
15.549
33
14.048
24
14.773
15
15.269
6
15.478
32
14.135
23
14.839
J4
15.323
6
15.^36
31
14.221
22
14.904
13
15.377
4
15.008
30
14.307
21
14.970
12
15.431
3
14.571
29
14 387
20
15.036
11
15.485
2
13.780
28
14.467
19
15.083
10
15.539
1
12.867
27
14.547
18
15.129
9
15.567
0
11.118
Older Age Thirty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
36
13.661
26
14.493
16
15.067
6
15.32^
35
13.752
25
14.562
15
15.118
5
15. 162
34
13.842
24
14.630
14
15.169
4
U.t42
33
13.933
23
14.699
13
15.220
3
14.415
3i
14.023
22
14.767
12
15.271
2
13.638
31
14.114
21
14.836*
11
15.322
1
12.741
30
14.190
20
14.882
10
15.366
0
10.9J3
29
14.266
19
14.928
9
15.398
28
14.341
18
14.975
8
15.410
27
14.417
17
15.021
7
15.391
Older Age Thirty-Seven Years.
Aip».
Value.
Age.
Value.
Age,
Valu«.
Age.
Value.
37
13.443
27
14.272
17
14.867
7
15. 23 J
36
13.537
26
14.343
16
14.915
6
15.152
35
13.632
25
14.414
15
14.962
5
14.968
34
13.726
24
14.485
14
15.0)0
4
14.675
33
13.821
23
14.556
13
15.057
3
14.258
32
13.915
22
14.627
12
15.105
2
13.496
31
13.986
21
14.675
11
15.131
1
12.594
30
14.058
20
14.723
10
15.156
0
10.869
29
]4.1'29
19
14.771
9
15.182
28
14.201
18
14.819
8
15.207
Digitized by
Googk
TABLS XXL
471
Value of £1 per Annum during the joint Continuance of Two livea,
(Carlisle 3^ |ier Cent.)
Older Age Thirty-Eight Years.
Affe.
Valve.
Ago.
V.laa.
Afe.
Value.
Age.
Valoe.
38
13.220
28
14.051
18
14.664
8
15.081
37
13.318
27
14.123
17
14.708
7
15.056
36
13.416
26
14.196
16
14.752
6
14.975
35
13.513
25
14.268
15
14.797
5
14.815
34
13.611
24
14.341
14
14.841
4
14.509
33
13.709
23
14.413
1
13
14.885
3
14.102
32
13.777
22
14.463
12
I4.9V4
2
13.338
31
13.846
21
14.513
11
14.963
1
12.447
30
13.914
20
14.564
10
15.003
0
10.744
'29
13.983
19
14.614
9
15.042
Older Age Thirty-Nine Years.
Ajir.
Valoe.
Agr.
Vftlae.
Age.:
Valne.
Agr.
Value.
39
12.994
29
13.836
19
14.456
9
14.889
38
13.094
28
13.907
18
14.497
8
14.905
37
13.194
27
13.979
17
14.538
7
14.879
36
13.295
26
14.050
16
14.579
6
14.799
35
13.395
25
14.122
15
14.620
5
14.641
31
13.495
24
14.193
14
14.661
4
14.342
33
13.563
23
14.246
13
14.707
3
13.935
32
13.631
22
14.298
12
14.71^2
2
13.180
31
13.700
21
14.351
11
14.798
1
12.301
30
13.768
20
14.403
10
14.843
0
10.620
Older Age Forty Years.
Age:
Value.
Age.
Value.
Age.
Value.
Age.
Value.
40
12.774
29
13.703
18
14.326
7
14.703
39
12.875
28
13.770
17
14.365
6
14.622
38
12.977
27
13.838
16
14.403
5
14.467
37
tS.OiS
26
13.905
15
14.442
4
14.171
36
13.180
25
13.972
14
14.489
3
13.768
35
13.281
24
14.027
13
14.536
2
13.021
31
13.352
23
14.083
12
14.582
1
12.154
33
13.423
22
14.13d
11
14.629
0
10.495
32
13.494
21
14.194
10
14.676
31
13.565
20
14.249
9
14.714
30
13.636
19
14.288
8
14.729
Digitized by VjOOQ IC
472
TABU XXX.
Value of £1 per Anoum daring the joint ContinoAOoe of Two Lfoee.
(Carlisle 3( per Cent.)
Older Age Forty-One Yean.
Ag«.
Valoe.
Age.
Valne.
Afo.
ValttB.
Aie.
Valw.
41
12.571
30
13.508
19
14.194
8
14.553
40
12.671
29
I3.a71
18
14. 163
7
14.52i
39
12.771
28
13.634
17
14.201
6
14.446
38
12.871
27
13.697
16
14.239
5
14.291
37
12.971
26
13.760
15
14.273
4
1J.999
36
13.071
25
13.818
14
14.327
S
13.603
35
13.146
24
13.875
• 13
14.371
2
12.863
34
13.221
23
13.933
U
14.415
1
12.007
33
13.295
22
13.990
11
14.459
0
10.369
9%
13.370
21
14.048
10
14.500
31
13.44d
20
14.086
9
14.539
Older Age Forty-Two Yean.
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
Value.
42
12.377
31
13.314
20
13.925
9
14.308
41
12.474
30
13.373
19
13.965
8
14.329
40
12.572
29
13.431
18
14.004
14.349
39
12.669
28
13.490
17
14.044
14.263
38
12.767
27
13.548
16
14.085
14.114
37
18.864
26
13.608
15
14.125
13.828
36
12.942
25
13.667
It
14.166
13.435
35
13.021
24
13.727
13
14.203
12.705
34
13.099
23
lS.7i:6
12
14.2^17
11.865
33
13.178
22
13.846
11
14.267
10.243
ai
13.256
21
13.886
10
14.2«9
Older Age Forty-Three Yean.
Age.
Value.
Age.
Valne.
Value.
Age.
Value.
43
42
41
40
39
38
37
36
35
34
33
12.187
12.281
12.375
12.46S
12.562
12.656
12.737
12.818
12.900
12.981
13.062
32
31
30
'^9
28
27
26
25
24
23
22
13.117
13.172
13.228
13.283
13.338
13.399
13.460
13.520
13.581
13.642
13.684
21
SO
19
18
17
16
15
14
13
12
II
13.725
13.767
13.808
13.850
13.^87
13.924
13.962
13.999
14.036
14.069
14.102
10
9
8
1
6
5
4
3
2
1
0
14.135
14.168
14.201
14.158
14.080
13.938
13.656
13. '268
12.535
11.704
10.117
Digitized by LjOOQ IC
TABLXXXL
41$
Vahw of £\ per Aonoin during the joint Continuance of Two Litob.
(Carlisle 3^ per Cent.)
Older Age Forty-Four Years.
A,..
V»lae.
A««.
Value.
Age.
Valpe.
Age.
Value.
44
11.990
32
12. 96!^
20
13.605
8
13.999
43
12.081
31
13.023
19
13.649
7
13.966
43
12.171
30
13.077
18
13.683
6
13.897
41
12.262
29
13.132
17
13.717
5
13.761
40
12.352
28
13.192
16
13.751
4
13.485
39
12.443
27
13.251
15
13.785
3
13.077
38
12.526
26
13.311
H
13.819
2
12.365
37
12.609
25
13.370
13
13.858
I
11.552
16
12.693
24
13.430
12
13.&97
0
9.991
35
12.776
23
13.474
U
13.936
34
12.859
22
13.518
10
13.979
33
12.914
21
13.561
9
14.014
Older Age Forty-Five Ycare.
Aga
Value.
Age.
Value.
Age.
Value.
>ge.
Value.
45
11.785
33
12.761
21
13.394
9
13.799
44
11.874
32
12.818
20
13.440
8
13.797
43
11.963
31
12.875
19
13.472
7
13.775
42
12.051
30
12.932
18
13.503
6
13.714
41
12.140
29
12.988
17
13.535
5
13.585
40
12.229
28
13.043
16
13.566
4
13.275
39
12.313
27
13.099
15
13.598
3
12.887
38
12.396
26
13.154
14
13.638
2
12.194
37
12.480
25
13.210
13
13.678
1
11.401
36
12.563
24
13.256
12
13.718
0
9.865
35
12.647
23
13.302
11
13.758
34
12.704
22
13.348
10
13.798
Older Age Forty-Six Yean.
Age.
Value.
Age.
▼alae.
AVf.
Value.
Age.
Value
46
11.568
34
12.544
22
13.172
10
13.567
45
11.658
33
12.605
21
13.220
9
13.584
44
11.748
32
12.665
20
13.251
8
13.595
43
11.837
31
12.725
19
13.282
7
13.583
42
11.927
30
12.776
18
13.313
6
13.531
41
12.017
29
12.827
1.7
13.344
5
13.355
40
12.098
28
12.878
16
13.375
4
13.065
39
12.180
27
12.929
15
13.412
3
12.696
38
12.261
26
12.980
14
13.449
2
12.0-24
37
12.313
25
13.028
13
13.487
1
11.249
36
12.424
24
13.076
12
13.524
0
9.702
35
li.484
23
13.124
11
13.561
«
Digitized by VjOOQ iC
474 TABLE XXI.
Vftlue of £1 per Annum during the joint Conliituance of Two Lives.
(Carlisle 3^ p«r Cent.;
Older Age Forty-Seven Years.
Age.
V«lae.
Age.
Value.
Aga.
Valna.
Age.
Value.
47
11.334
35
12.318
23
12.936
11
13.331
46
11.427
34
12.380
22
12.986
10
13.346
43
11.5-21
33
12.443
21
13.018
13.362
41
11.614
32
12.506
20
13.050
13.377
43
U.70S
31
12.552
19
13.082
13.392
42
11.801
30
12.599
18
13.114
13.231
41
11.879
29
12.645
17
13.146
13.125
40
11.957
28
12.692
16
13.180
12.856
39
12.036
27
12.738
15
13.214
12.506
38
12.114
26
12.788
11
13.V48
11.854
37
12.192
25
12.fe37
13
13.282
11.044
36
12.265
24
12.887
12
13.316
9.539
Older Age Forty-Eight Years.
Age.
Value.
Age.
Valae.
Age.
Valoe.
Age.
ValM.
48
11.081
35
12.140
22
12.770
9
13.164
47
11.180
34
12.205
21
12.803
8
13.191
46
11.279
33
12.270
20
12.837
7
13.125
45
11.378
32
12.313
19
12.870
6
13.032
44
11.477
31
12.356
12.904
5
12.896
43
11.576
30
12.398
12.934
4
12.646
42
11.650
211
12.441
12.965
3
12.315
41
11.724
28
12.484
12.995
2
11.618
40
11.798
27
12.534
13.0;:6
1
10.a38
3J
11.872
26
12.585
13.056
0
9.376
38
11.946
25
12.635
13.084
37
12.011
24
12.6i6
13.110
36
12.076
23
12.736
10
13.137
Older Age Forty-Nine Years.
Aye.
Value.
Age.
VHlae.
Age.
Valoe.
Age.
Valie.
49
10.796
36
11.878
23
12.497
10
12.905
48
10.903
35
11.944
22
12.533
12.938
47
11.010
34
12.010
21
12.568
12.910
40
11.116
33
12.052
20
12.604
12.8)8
45
11.223
32
12.093
19
12.639
12.782
44
11.330
31
12.135
18
12.666
12.666
43
11.400
30
12.176
17
12.693
12.436
42
11.470
29
12.218
16
12.721
12.051
41
11.541
2S
12.267
15
12.748
2
11.382
40
11.611
27
12.316
14
12.775
1
10.633
39
11.681
26
12.364
13
12.808
0
9.213
38
11.747
25
12.413
12
12.840
37
11.813
24
12.462
11
12.873
Digitized by VjOOQ IC
TABLE XXI.
Value of XI per Annum during the joiut Cuatiuuance of Two Lives.
(Carlisle 3^ per Cent.)
Older Age Fifty Years.
475
Age.
Value. .
Age.
Value.
Ago.
Value.
Age.
Value.
60
10.486
37
11.601
24
12.208
11
12.612
49
lO.GOi
36
11.666
23
12.245
10
12.645
48
10.718
35
11.732
22
12.283
12.646
47
10.635
34
11.775
21
12.320
12.628
46
10.951
33
11.818
20
12.357
12.591
45
11.067
32
11.862
19
12.382
12.533
44
11.134
31
11.905
18
12.407
12.436
43
J 1.202
30
11.948
17
12.431
1^.154
42
11.269
29
11.993
16
12.436
11.768
41
11.337
28
12.037
15
12.481
11.146
40
11.404
27
12.0b2
14
12.514
10.427
39
11.470
26
12.126
13
12.547
0
9.050
38
11.533
23
12.171
12
12.579
Older Age Fifty-One
Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
51
10.150
38
11.310
25
11.901
12
12.296
50
10.277
37
11.372
24
11.939
11
12.326
49
10.404
36
11.435
23
11.978
10
12.345
48
10.531
35
11.481
22
12.016
9
12.354
47 _
10.653
34
11.526
21
12.055
8
12.347
46
10.7fc5
33
11.572
20
12.079
7
12.324
45
10.852
32
11.617
19
12.103
6
12.283
44
10.920
31
11.663
18
1-2.127
5
12.139
43
10.987
30
11.703
17
12.151
4
11.872
42
11.055
29
11.743
16
12.175
3
11.524
41
11.122
28
11.782
15
12.205
2
10.910
40
11.185
27
11.822
14
12.235
1
10.222
39
11.247
26
11.862
13
12.266
0
8.840
Old
er Age Fifty-Two Years.
Agr.
Value.
A5,e
Value.
Age.
ValiP.
Age.
Value.
52
9.812
39
11.017
26
11.588
13
11.978
51
9.949
38
11.076
2b
11.628
12
12.005
50
10.085
37
11.135
24
11.667
11
12.015
49
10.222
36
11.182
23
11.707
10
12.026
48
10.35S
35
11.230
22
11.747
9
12.036
• 47
10.495
84
11.277
21
11.772
8
12.047
46
10.564
33
11.325
20
11.793
7
12.057
45
10.633
32
11.372
19
11.821
6
11.976
44
10.703
31
11.407
18
11.845
5
11.842
43
10.772
30
11.44i
17
11.870
4
11.589
42
10.841
29
11.478
16
11.897
3
11.261
41
10.900
28
11.513
15
11.924
2
10 674
40
10.959
27
11.548
14
11.951
1
0
9.970
8.6:;0
Digitized by VjiOOQlC
479
TABLE XXI.
Value of £1 per Annum during the joint Continuanee of Two Live»»
(Gwrliele ^ per Cent.)
Older Age Fifty-Three Year*.
Ag..
Value.
Age.
Value.
Age.
Val«e.
Age.
Value.
Aie.
ValiiK.
53
».471
42
10.614
31
11.137
20
11.510
9
11.763
62
9.615
41
10.668
30
11.169
11.536
8
11.784
51
9.760
40
10.723
29
u.aoo
11.562
7
11.742
50
9.904
39
10.777
28
11.232
11.586
6
11.669
49
10.049
38
10.831
27
11.272
11.609
5
11.544
48
10.193
37
10.880
25
U.SI3
11.633
4
11.307
47
10.266
36
10.9-^8
26
11.352
11.656
3
10.997
4G
10.340
35
10.977
24
11.392
11.680
2
10.396
45
10.413
34
11.025
*23
11.432
11.701
1
9.718
44
10.487
33
11.074
22
11.458
11.722
Q
8.419
43
10.560
32
11.106
21
11.484
11.742
Older Age Fifty-Four Yean.
Ar-
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Values
54
0.12/
43
10.323
32
10.828
21
11.194
10
11.453
53
9.277
42
10.373
31
10.859
20
11.221
9
11.479
52
9.426
41
10.423
30
10.889
11.248
8
11.463
51
9.576
40
10.473
29
10.919
11.269
7
11.427
50
9.725
39
10.523
28
10.958
11.289
6
11.3G3
49
9.875
38
10.572
27
10.996
11.310
5
11.247
48
0.955
37
10.621
26
11.035
11.330
4
11.025
47
10.034
36
10.670
•25
11.073
11.351
3
10.697
46
10.114
35
10.719
24
11.112
11.377
2
10.119
45
10.193
34
10.768
23
11.139
11.402
1
9.467
44
10.273
33
10.798
22
11.166
11.428
0
8.209
1
Older Age Fifty-Five Years.
Age.
Value.
Age.
Value.
Aje.
Value.
Age.
Value.
Age.
Value.
55
8.774
43
10.071
31
10.578
19
10.943
11.112
54
8.927
42
10.113
30
10.609
18
10.962
11.056
53
9.080
41
10.164
29
10.644
17
10.980
10.950
52
9.234
40
10.211
28
10.678
16
10.999
10.714
51
9.387
39
10.259
27
10.713
15
11.017
10.397
50
9.510
38
10.308.
26
10.747
14
11.043
9.841
49
9.628
37
10.356
25
10,782
13
11.069
9.215
48
9.715
36
10.405
24
10.811
12
11.095
7.999
47
9.803
3)
10.453
23
10.839
11
11.121
46
9.S90
34
10.484
22
10.868
10
11.147
45
9.978
31
10.515
21
10.896
9
11.157
44
10.025
32
10.547
20
10.923
8
11,142
Digitized by LjOOQ iC
TABLE XXI.
477
Value of £1 per Annum during the joint Continuance of Two Livei.
(Carlisle 3^ per Cent)
Older Age Fifty-Six Yean
.
A|^
Value.
Mb^
V«lu0.
Age.
Value.
Age.
Value.
Age.
Volue.
56
8.416
44
9.766
32
10.263
20
10.613
8
10.821
55
8.571
43
9.811
31
10.296
19
10.631
7
10.797
54
8.726
42
• 9.857
30
10.326
18
10.648
6
10.7^^9
53
8.881
41
9.903
29
10.336
17
10.666
5
10.637
5i
9.036
40
9.949
28
10.387
16
10.683
4
10.403
51
9.191
39
9.994
27
10.417
15
10.707
3
10.G98
50
9.288
38
10.040
26
10.447
14
10.730
2
9.564 '
49
9.384
37
10.085
25
10.477
13
10.754
1
8.963
48
9.481
36
10.131
24
10.507
12
10.777
0
7.777
47
9.577
35
10.164
23
10.536
11
10.801
46
9.674
34
10.197
22
10.566
10
10.830
45
9.720
33
10.230
21
10.596
9
10.836
Older Age Fifty-Seven Years.
Agf,
Value.
Ar.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
57
8.051
45
9.453
33
9.940
21
10.276
9
10.4f.9
56
8.208
44
9.501
32
9.974
20
10.294
8
10.476
55
8.366
43
9.548
31
10.000
19
10.311
7
10.482
54
8.523
42
9.595
30
10.026
18
10.329
6
10.446
53
8.681
41
9.636
29
10.0J2
17
10.347
5
10.324
52
8.838
40
9.678
28
10.078
16
10.368
4
10.U93
51
8.942
39
9.719
27
10.104
15
10.388
3
9.798
50
9.046
38
9.761
26
10.135
14
10.409
2
9.286
49
9.151
37
9.802
25
10.166
13
10.429
1
8.714
48
9.255
36
^.836
24
10.196
IX
10.450
0
7.555
47
9.359
33
9.871
23
10.227
11
10.456
46
9.406
34
9.905
22
10.258
10
10.463
Older Age Fifty-Eight
Years.
A^e.
Value.
Age.
VAhie.
Age.
Value.
Age.
Value.
Age.
Value.
58
7.692
46
9.141
34
9.617
22
9.938
10
10.148
57
7.851
45
9.190
33
9.652
21
9.957
9
10.104
56
8.010
44
9.240
32
9.674
20
9.976
8
10.179
55
8.168
43
9.290
31
9.697
19
9.995
7
10.192
54
8.327
42
9.327
30
9.719
18
10.014
6
10.143
53
8.486
41
9.364
29
9.742
U
10.032
5
10.012
52
8.597
40
9.401
28
9.764
16
10.049
4
9.782
51
8.708
39
9.438
27
9.795
15
10.067
3
9.498
50
8.819
38
9.475
26
9.826
14
10.084
9
9.031
49
8.930
37
9.510
25
9.857
13
10.102
1
8.465
48
9.041
36
9.546
24
9.888
12
10.117
0
7.332
47
9.091
35
9.581
28
9.919
11
10.133
Digitized by LjOOQ IC
478
TABLE XXI.
Valuj of XI per Anuum during Hm joint Continuance of Tiro Livex.
(Carlisle 3^ per Cent.
Older Age Fifty-Nine Years.
^
Agi>.
Value.
7.361
Age.
47
Value.
Age.
35
Va^oe.
Age.
23
Value.
Age.
Value.
59
8.835
9.306
9.616
11
9.fc29
2)8
7.439
46
8.890
34
9.341
22
9.636
10
9.849
57
7.616
45
.8.945
33
9.362
21
9.636
9
9.868
53
7.794
44
9.0U0
32
9.384
20
9.676
8
9.903
55
7.971
43
9.333
31
9.405
19
9.696
7
9.903
54
8.149
42
9.O06
30
9.427
18
9.711
6
9.839
53
8.264
41
9.098
29
9.448
17
9.726
5
9.609
52
8.379
40
9.131
28
9.478
16
9.741
4
9.471
51
8.49a
39
9.164
27
9.507
15
9.756
3
9.241
50
8.610
38
9.199
26
9.537
14
9.771
2
8.776
49
8.725
37
9.23J
25
9.366
13
9.790
I
8.216
48
8.780
3r>
9.270
24
9.596
12
9.810
0
7.110
Older Age Sixty Years.
Age.
Valae.
Age.
Value.
Ase.
Value.
Age.
21
Value.
Age.
8
Value.
60
7.069
47
8.607
34
9.073
9.380
9.027
59
7.221
46
8.668
33
9.096
20
9.401
7
9.613
58
7.373
45
8.730
32
9.118
19
9.414
6
9.536
57
7.525
44
8.760
31
9.141
18
9.427
5
9.386
56
7.677
43
8.789
30
9.163
17
9.439
4
9.214
55
7.829
42
8.819
29
9.189
16
9.452
3
8.954
54
7.948
41
8.848
28
9.215
15
9.465
2
8.521
53
8.066
40
8.878
27
9.242
14
9.485
1
7.967
52
8.183
39
8.913
26
9.268
13
9.503
0
6.888
51
8.303
38
8.947
25
9.294
12
9.524
5J
8.422
37
8.982
24
9.315
11
9.544
49
8.484
36
9.016
23
9.337
10
9.564
48
8.545
35
9.051
22
9.3)8
9
9.601
Older .
\ge Sixty-One Years.
Age
Vulue.
Age.
Value.
Age.
Value.
Ag^.
Value.
Ase
9
Value.
61
6.832
48
8.330
35
8.818
22
9.116
9.334
60
6.973
47
8.419
34
8.841
21
9.138
8
9.352
59
7.114
46
8.489
33
8.865
20
9.150
7
9.324
53
7.254
45
8.518
32
8.888
19
9.162
6
9.23i
57
7.395
44
8.546
31
8.912
18
9.175
5
9.1:!6
56
7.536
43
8.575
30
8.935
17
9.1fc7
4
8.957
55
7.657
42
8.603
29
8.938
16
9 199
3
8.726
54
7.778
41
8.632
28
8.980
15
9.217
2
8.1>66
53
7.899
40
8.664
:i7
9.003
14
9.235
1
7.718
52
6.020
39
8.697
26
9.026
13
9.252
0
6.704
51
8.141
38
8.729
25
9.048
12
9.270
30
8.211
37
8.762
24
9.071
11
9.288
49
8.280
36
8.794
23
9.093
10
9.300
•
Digitized by LjOOQ IC
TABU XXI.
479
Value of £1 per Annum during the joint Coniiouance of Two Lives.
(Carlisle 3^ per Cent.)
Older Age Sixty-Two Years.
Age.
Valoe.
Age.
Value.
Age.
Value,
Age.
Value.
6S
6.606
42
8.395
22
8.878
2
8.011
61
6.734
41
8.424
21
8.891
I
7.497
60
6.862
40
8.45.1
20
8.903
0
6.5i0
59
6.991
39
8.481
19
8.916
58
7.119
38
8.510
18
8.928
57
7.247
37
8.539
17
8.941
56
7.371
36
8.564
16
8.956
55
7.494
35
8.589
15
8.972
54
7.618
34
8.615
14
8.987
53
7,741
33
8.640
13
9.003
52
7.865
32
8.665
12
9.018
51
7.942
31
8.684
11
9.021
50
8.019
30
8.703
10
9.024
49
8.095
29
8.722
9
9.028
48
8.172
23
8.741
8
9.031
47
8.249
27
8.760
7
9.014
46
8.278
26
8.784
6
8.963
45
8.307
25
8.807
5
8.^66
44
8.3 i7
24
8.831
4
8.700
43
8.366
23
8.S54
3
8.469
Older Age Sixty-Three Years.
Age.
Value.
Age.
Value.
Age.
Vfclue.
Age.
Value.
63
6.378
43
8.159
23
8.613
3
8.212
62
6.494
42
8.184
22
8.627
2
7.7C4
61
6.610
41
8.209
21
8.640
1
7.2:7
60
6.726
40
8.233
20
8.654
0
6.337
59
6.842
39
8.258
19
8.667
58
6.958
39
8.283
18
8.681
57
7.084
37
8.3C9
17
8.694
56
7.210
36
8.335
16
8.707
55
7.336
35
8.360
15
8.719
54
7.462
34
8.386
14
8.732
h3
7.5f8
33
8.412
13
8.745
52
7.671
31
8.428
12
8.756
51
7.753
31
8.444
11
8.767
50
7.836
30
8.461
10
8.778
49
7.918
29
8.477
9
8.789
48-
8.001
28
8.493
8
. 8.800
47
8.033
27
8.517
7
8.753
46
8.064
26
8.541
6
8.693
45
8.096
25
8.565
5
8.605
44
8.127
24
8.589
4
8.443
Digitized by VjOOQ IC
M
TABLE XXI.
Valite of £1 ptr Amam during th« joiBi CoatimuMM 9( Two livM.
(CMliiUaip«rC«it.}
Older Age Sixty-Four
Years.
Aft,
Valne. .
Aue.
Valne.
Age.
Yaliw.
Aip.
Value.
61
6.137
44
7.910
24
8.335
4
8.186
63
6.244
43
7.931
23
8.349
3
7.940
62
6.352
42
7.952
22
8.364
a
7.518
61
6.459
41
7.972
21
8.378
1
7.056
60
6.567
40
7.993
20
8.393
0
6.153
59
6.674
30
8.014
19
8.407
56
6.799
38
8.040
18
8.418
57
6.924
37
8.U66
17
8.428
56
7.049
36
8.093
16
8.439
55
7.174
35
8.119
15
8.449
54
7.299
34
8.145
14
8.460
53
7.386
33
8.160
13
8.475
52
7.472
33
8.175
12
8.489
51
7.559
31
8.190
11
8.504
50
7.645
30
8.205
10
8.518
49
7.732
29
8.220
9
8.533
48
7.768
28
8.243
8
8.507
47
7.803
27
8.266
7
8.472
46
7.839
26
8.289
6
8.424
45
7.874
25
8.312
5
8.345
Older Age Sixty-Five Yean.
A|e.
Value.
Afe.
Value.
Ate.
V.liw.
Age.
Value.
65
5.889
45
7.654
25
8.048
5
8.085 *
64
5.992
44
7.672
24
8.064
4
7.895
63
6.095
43
7.689
23
8.079
3
7.667
62
6.197
42
7.707
22
8.095
2
7.271
61
6.300
41
7.724
21
8.110
1
0.836
60
6.403
40
7.742
20
8.12G
0
5.9G9
59
6.523
39
7.767
19
8.135
58
6.643
38
7.793
18
8.144
57
6.763
37
7.818
17
8.152
56
6.883
36
7.844
16
8.161
55
7.003
35
7.869
15
8.170
54
7.092
34
7.885
14
8.185
53
7.182
33
7.901
13
8.200
52
7.271
32
7.916
12
8.215
51
7.361
^l
7.932
11
8.230
50
7.450
30
7.948
10
8.245
49
7.491
29
7.968
9
8.229
48
7.532
28
7.988
8
8.214
47
7.572
27
8.008
7
8.190
46
7.613
26
8.028
6
8.154
Digitized by LjOOQ iC
TABLE XXI.
461
Voloe of £1 per Aniram duv&ng the joint Gootinuaiicd of Two Live«.
(Carlisle 8} per Cent.)
Older Age Sixty-Six Years,
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
Value.
66
5.629
46
7.386
26
7.750
6
7.884
65
5.733
45
7.402
25
7.767
5
, 7.776
64
5.837
44
7.418
24
7.783
4
7.603
63
5.942
43
7.434
23
7.800
3
7.395
62
6.046
42
7.450
22
7.816
2
7.025
61
6.150
41
IM
21
7.833
1
6.615
60
6.259
40
20
7.841
0
5.751
59
6.369
39
7.512
19
7.849
58
6.478
38
7.536
18
7.857
57
6.588
37
7.559
17
7.865
56
6.697
36
7.582
16
7.873
65
6.788
35
7.599
15
7.886
54
6.878
34
7.616
14
7.899
53
6.969
33
7.632
13
7.913
52
7.059
32
7.649
12
7.926
51
7.150
31
7.666
11
7.939
50
7.197
30
7.683
10
7.931
49
7.244
29
7.700
9
7.926
48
7.292
28
7.716
8
7.921
47
7.339
27
7.733
7
7.909
Older Age Sixty-Seven Years.
A^e.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
67
5.354
47
7J08
27
7.439
7
7.628
66
5.462
46
7.119
26
7.456
6
7.561
65
5.570
45
7.135
25
7.474
5
7.467
64
5.679
44
7.152
24
7.491
4
7.312
63
5.787
43
7.168
23
7.509
3
7.122
62
5.895
42
7.184
22
7.526
2
6.778
61
5.992
41
7.204
21
7.534
1
6.350
60
6.089
40
7.224
20
7.542
0
5.533
59
6.185
39
7.243
19
7.551
58
6.282
38
7.263
18
7.559
67
6.379
37
7.283
17
7.567
56
6.471
36
7.301
16
7.578
55
6.564
35
7.319
15
7.589
54
6.656
34
7.336
14
7.601
53
6.749
33
7.354
3
7.612
52
6.841
32
7.372
12 .
7.623
51
6.893
31
7.385
11
7.624
50
6.946
30
7.399
10
7.625-
49
6.998
29
7.412
9
7.626
48
7.051
28
7.426
8
7.627
Digitiz^b^ Google
48g
TABLE XKl.
Value of £1 per Aaniim dtiriog the joint Contiauanee of Two lives.
(Carlisle 3^ per Cent.)
Older Age Sixty-Bight Yean.
•
Age.
Value.
A«..
Vftlae.
A,..
Valua.
Age.
Valne.
68
5.069
48
6.807
28
7.121
8
7.335
67
5.182
47
6.8-24
27
7.139
7
7.298
66
5r294
46
6.842
26
7.156
6
7.237
65
5.407
45
6.6.i9
25
7.174
5
7.158
64
5.519
44
6.877
24
7.191
4
7.020
63
5.632
43
6.894
23
7.209
3
6.850
62
5.717
42
6.910
22
7.218
2
6.488
61
5.802
41
6.926
21
7.227
1
6.085
60
5.887
40
6.942
20
7.835
0
5.314
59
5.972
39
6.958
19
7.244
58
6.057
38
6.974
18
7.253
57
6.150
37
6.994
17
7.262
56
6.244
36
7.011
16
7.271
f)5
6.337
35
7.030
15
7.280
54
6.431
34
7.048
14
7.289
53
6.524
33
7.067
IS
7.298
52
6.581
32
7.078
12
7.305
51
6.637
31
7.089
11
7.313
50
6.694
30
7.099
10
7.820
49
6.750
29
7.110
9
7.828
Older Age Sixty-Nine Years.
Afe.
Value.
A«e.
Value.
A<e.
Value.
An.
Value.
69
4.769
49
6.493
29
6.797
9
7.015
68
4.887
48
6.513
28
6.814
8
7.008
67
5.004
47
6.533
27
6.830
7
6.968
66
5.122
46
6.554
26
6.847
6
6.914
65
5.239
45
6.574
25
6.863
5
6.849
64
6.357
44
6.594
24
6.880
4
6.729
63
5.4.33
43
6.606
23
6.890
3
6.546
62
5.509
42
6.619
22
6.899
2
6.198
61
5.585
41
6.631
21
6.909
1
6.821
60
5.6ol
40
6.641
20
6.918
0
5.096
59
5.737
39
6.656
19
6.928
58
5.829
38
6.675
18
6.935
57
5.921
37
6.694
17
6.942
56
6.013
36
6.711
16
6.949
55
6.105
35
6.730
15
6.956
54
6.197
34
6.748
14
6.963
53
6.256
33
6.758
13
6.973
52
6.315
32
6.768
12
6.984
61
6.375
31
6.777
11
6.994
50
6.434
30
6.787
10
7.005
Digitized by LjOOQ IC
TABLE XXI.
483
Value of £1 per Annum daring the joint Continuance of Two LiYes.
(Carlttle d| per Gent
Oldex Age Seventy Yean.
Ajje.
Value.
Age.
Veloe.
Ag«.
VeliM.
Age.
Value.
70
4.459
50
6.166
30
6.472
10
6.674
69
4.582
49
6.190
29
6.486
9
6.700
68
4.704
48
6.214
28
6.500
8
6.681
67
4.827
47
6.237
27
6.514
7
6.638
66
4.949
46
6.261
26
6.528
6
6.590
65
5.072
45
6.285
25
6.542
6
6.540
64
5.143
44
6.294
24
6.552
4
6.427
63
5.214
43
6.303
23
6.563
3
6.242
62
5.284
42
6.313
22
6.573
2
5.909
61
5.355
41
6.822
21
6.584
1
5.556
60
5.426
40
6.331
20
6*594
0
4.878
59
5.513
39
6.349
19
6.599
58
5.600
38
6.367
18
6.605
57
5.688
37
6.384
17
6.610
56
5.775
36
6.402
16
6.616
55
5.862
35
6.420
15
6.621
54
5.923
34
6.430
14
6.632
53
5.984
33
6.441
13
6.642
52
6.044
32
6.451
12
6.653
51
6.105
31
6.462
11
6.663
Older Age Seventy-One Yeaxv.
Age.
Value.
AiB.
Value.
Ag».
Value.
Age.
Value.
71
4.132
51
5.820
31
6.135
u
6.317
70
4.2<^0
50
5.848
30
6.146
10
6.536
69
4.388
49
5.877
29
6.158
9
6.369
68
4.516
48
5.906
28
6.169
8
6.344
67
4.644
47
5.934
27
6.181
7
6.304 .
66
4.772
46
5.962
26
6.192
6
6.267
65
4.843
45
5.970
25
6.203
5
6.404
64
4.914
44
5.978
24
6.214
4
6.110
63
4.985
43
5.985
23
6.225
3
5.929
62
5.056
42
5.993
22.
, 6.236
2
5.615
61
5.127
41
6.001
fl
6.247
1
5.292
60
5.204
40
6.017
20
6.252
0
4.784
59
5.282
89
6.032
19
6.257
58
5.359
38
6.048
18
6.261
57
5.437
37
6.063
17
6.266
56
5.514
36
6.079
16
6.271
55
5.575
35
6.090
15
6.280
54
5.636
34
6.101
14
6.289
53
5.698
33
6.113
13
6.299
52
5.759
32
6.124
12
6.308
2i 2
Digitized by
Google
484
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Li vex.
(Carlisle 3^ per Cent)
Older Age Seventy-Two Years.
AfB.
ValM.
Al«
ValM.
Age,
Value.
Age.
V«lae.
72
3.828
52
5.494
32
5.816
12
5.980
71
3.958
51
5.526
31
5.825
11
5.980
70
4.089
50
5.558
30
5.834
10
5.979
69
4.219
49
5.591
29
5.842
9
6.979
68
4.350
48
5.623
28
5.851
8
6.978
67
4.480
47
5.655
27
5.860
7
5.978
66
4.554
46
5.662
26
5.872
6
6.005
65
4.627
45
5.670
25
5.883
5
6.082
64
4.701
44
5.677
24
5.895
4
5.814
63
4.774
43
5.685
23
5.906
3
5.630
62
4.848
42
5.692
22
5.918
2
5.329
61
4.915
41
5.705
21
5.923
1
5.076
60
4.981
40
5.718
20
5.928
0
4.552
59
5.048
39
5.731
19
5.932
58
5.114
38
5.744
18
5.937
57
6.181
37
5.757
17
5.942
56
5.244
36
5.769
16
5.950
65
5.306
35
5.781
15
5.957
54
5.369
34
5.792
14
5.965
53
5.431
33
5.804
13
5.^972
Older Age Seventy-Three Years.
Age.
ValQft.
Ag..
Value.
Age.
Value.
Age.
Value.
73
3.562
53
5.196
33
5.526
13
5.676
72
3.691
52
5.232
32
6.533
12
5.681
71
3.821
51
5.267
31
5.540
11
5.685
70
3.950
50
5.303
SO
5.546
10
5.690
. 69
4.080
49
5.338
29
5.553
9
5.694
68
4.209
48
5.374
28
5.560
8
5.699
67
4.286
47
5.382
27
5.-572
7
5.741
66
4.363
46
5.390
26
5.584
6
5.743
65
4.439
46
5.398
25
5.595
5
5.759
64
4.516
44
6.406
24
6.607
4
5.517
63
4.593
43
5.414
23
5.619
3
5.330
62
4.650
42
5.424
22
6.624
2
5.120
61
4.707
41
5.434
21
5.630
1
4.860
60
4.763
40
5.444
20
5.635
0
4.319
59
4.820
39
6.454
19
5.641
58
4.877
38
5.464
18
5.646
57
4.941
37
5.476
17
5.652
56
5.005
36
5.489
16
5.658
M
5.068
35
5.501
15
5.664
54
5.r.12
34
5-.514
14
6.670
Digitized by VjOOQ IC
TABLE XXI.
ib5
Valae of £1 per Ajinum during the joint Continuance of Two Lives.
^ (Carlisle 3^ per Cent.)
Older Age Seventy- Four Years.
Ag..
Value.
Age.
Value.
Age.
Velue.
Age.
Value.
74
3.338
54
4.929
34
5.267
14
5.405
73
3.461
53
4.967
33
5.273
13
5.412
72
3.585
52
5.005
32
5.279
12
5.419
71
3,708
51
5.042
31
5.285 •
11
5.426
70
3.832
50
5.080
30
5.291
10
5.433
69
3.955
49
5.118
29
5.297
9
5.440
68
4.036
48
5.128
28
5.308
8
5.480
67
4.118
47
5.133
27
5.320
7
5.604
66
4.199
46
5.148
26
5.331
6
5.482
65
4.281
45
5.158
25
5.343
5
5.437
64
4.362
44
5. 168
24
5.S54
4
5.220
63
4.412
43
5.175
23
5.360
3
5.127
62
4.462
42
5.182
22
5.366
2
4.912
61
4.512
41
6.190
21
5.371
1
4.644
60
4.562
40
5.197
20
5.377
0
4.087
59
4.612
39
5.204
19
5.383
58
4.675
38
5.217
18
6.387
57
4.739
37
5.229
17
5.392
56
4.802
36
5.242
16
5.396
55
4.866
35
5.254
15
5.401
Older Age Seventy-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
■Value.
75
3.174
55
4.704
35
5.053
15
5,183
74
3.285
54
4.744
34
5.059
14
5.lyo
73
3.397
53
4.784
33
5.066
13
5.198
72
3.508
52
4.823
32
5.072
12
5.205
71
3.620
51
4.863
31
5.079
11
5.213
70
3.731
50
4.903
30
5.085
10
5.220
69
3.818
49
4.916
29
5.09)
9
5.229
68
3.906
48
4.929
28
5.105
8
5.262
67
3.993
47
4.941
27
5.114
7
5.266
66
4.081
46
4.954
26
5.124
6
5.220
65
4.168
45
4.967
• 25
5.134
5
5.114
64
4.214*
44
4.972
24
5.141
4
5.018
63
4.260
43
4.977
23
5.147
3
4.924
62
4.307
42
4.981
22
5.154
2
4.703
61
4.353
41
4.986
21
5.160
1
4.428
60
4.399
40
4.991
20
5.167
0
3.854
59
4.460
39
5.003
19
5.170
58
4.521
38
5.016
18
5.173
57
4.582
37
5.028
17
5.177
56
4.643
36
5.041
16
5.180
Digitized by VjOOQ IC
486
TABLE XXI.
Value of £1 per Anxicrm darin|^ the joint Coutioaaiice of Two Liret.
(Carlisle 3| per Cent) «
Older Age Seventy- Six Years.
Age.
Value.
Age.
Value.
Aue.
Value.
A{?o.
Value.
76
3.016
56
4.481
36
4.842
16
4.968
75
3.113
55
4.522
35
4.849
15
4.974
74
3.210
54
4.563
34
4.857
14
4.981
73
3.308
53
4.605
33
4.864
13
4.987
72
3.405
52
4.646
32
4.872
12
4.994
71
3.502
51
4.687
31
4.879
11
5.000
70
3.596
50
4.708
30
4.887
10
5.011
69
3.691
49
4.720
29
4.895
9
5.018
68
3.785
48
4.736
28
4.902
8
5.043
67
3.88d
47
4.753
27
4.910
7
5.029
66
3.974
46
4.769
26
4.918
6
4.958
65
4.021
45
4.772
25
4.925
5
4.909
64
4.068
44
4.776
24
4.933
4
4.816
63
4.114
43
4.779
23
4.940
3
4.721
62
4.161
42
4.783
22
4.948
2
4.495
61
4.208
41
4.786
21
4.955
1
4.212
60
4.263
40
4.797
20
4.958
0
3.707
59
4.317
39
4.808
19
4.960
58
4.372
38
4.820
18
4.963
57
4.426
37
4.831
17
4.965
Older Age Seventy-Seven Years.
Ag«.
Value.
Ai*.
Value.
Age.
Value.
Age.
Value.
77
2.878
57
4.270
37
4.647
17
4.771
76
2.961
56
4.313
36
4.655
16
4.776
75
3.044
55
4.357
33
4.663
15
4.781
74
3.128
54
4.400
34
4.671
14
4.787
73
3.211
53
4.444
33
4.679
13
4.792
72
3.294
52
4.487
32
4.687
12
4,797
71
3.393
51
4.507
31
4.693
11
4.796
70
3.492 •
50
4.526
30
4.699
10
4.795
69
3.590
49
4.546
29
4.705
9
4.794
68
3.689
48
4.565
28
4.711
8
4.793
67
3. 788
47
4.585
27
4.717
7
4.792
66
3.837
46
4.588
26
4.725
6
4.747
65
3.887
45
4.591
25
4.733
5
4.703
64
3.936
44
4.594
24
4.741
4
4.613
63
3.986
43
4.597
23
4.749
3
4.518
62
4.035
42
4.600
22
4.757
2
4.286
61
4.082
41
4.609
21
4,760
1
4.039
60
4.129
40
4.619
20
4.763
0
3.560
59
4.176
39
4.628
19
4.765
58
4.223
38
4.638
18
4.768
•
,i^nn]c>
6
TABLE XKi.
4S7
Value of £1 per Annttm during tbe joint Continuance of Two Lives.
(Carlisle 3} per Cent)
Older
Age Seventy-Eig
ht Years.
A«e.
Valae.
Agn.
Value.
A<e.
Value.
Age.
Value.
78
2.740
58
4.057
38
4.447
18
4.570
77
2.812
57
4.102
37
4.456
17
4.574
76
2.884
56
4.147
36
4.465
16
4.578
75
2.955
55
4.193
35
4.473
15
4.583
74
3.027
54
4.238
34
4.482
14
4.587
73
3.099
53
4.283
33
4.491
13
'4.591
72
3.199
52
4.306
32
4.495
12
4.594
71
3.298
51
4.328
31
4.499
11
4.597 *
70
3.398
50
4.351
30
4.504
10
4.600
69
3.497
49
4.373
29
4.508
9
4.603
68
3.597
48
4.396
28
4.512
8
4.606
67
3.650
47
4.399
27
4.521
7
4.578
66
3.703
46
4.402
26
4.529
6
4.536
65
3.755
45
4.405
25
4.538
5
4.498
64
3.808
44
4.408
24
4.546
4
4.4U
63
3.861
43
4.411
23
4.555
3
4.315
62
3.900
42
4.418
22
4.558
2
4.098
61
3.939
41
4.425
21
4.561
1
3.865
60
3.979
'40
4.433
20
4.564
0
3.413
59
4.018
39
4.440
19
4.567
Older Age Seventy-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
79
2,571
59
3.829
39
4.223
19
4.345
78
2.638
58
3.874
38
4.232
18
4.348
77
2.704
57
3.920
37
4.241
17
4.361
76
2.771
56
3.965
36
4.251
16
4,354
75
2.837
55
4.011
35
4.260
15
4.357
74
2.904
54
4.056
34
4.269
14
4.360
73
2.999
53
4.080
33
4.272
13
4.365
72
3.095
52
4.105
32
4.276
12
4.370
71
3.190
51
4.129
31
4.279
11
4.374
70
3.286
50
4.154
30
4.283
10
4.379
69
3.381
49
4.178
29
4.286
9
4.384
68
3.437
48
4.182
28
4.294
8
4.390
67
3.494
47
4.186
27
4.302
7
4.364
66
3.550
46
4.191
26
4.311
6
4.326
65
3.607
45
4.195
25
4.319,
5
4.292
64
3.663
44
4.199
24
4.327
4
4.209
63
3.696
43
4.204
23
4.331
3
4.114
62
3.729
42
4.209
22
4.334
2
3.910
61
3.763
41
4.213
21
4.338
1
3.692
60
3.796
•
40
4.218
20
4.341
0
3.266
JUyVjOOg
488
TABLE XXI.
Value ui' X'l per Annum durin}^ the joint Continuance of Two LiYe*.
(Carlisle 3^ per Cent.)
Older Age Eighty
Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
80
2.424
59
3.669
38
4.036
17
4.143
79
2.4:*9
58
3.713
37
4.045
16
4.145
78
2.553
57
3.756
36
4.054
15
4.147
17
1'.618
56
3.800
33
4.063
14
4.152
76
2.682
55
3.843
34
4.067
13
4.157
1^0
2^.747
54
3.869
33
4.071
12
4.163
74
2.832
53
3.895
32
4.074
11
4.168
73
2.918
52
3.921
31
4.078
10
4.173
72
3.003
51
3.947
30
4.082
9
4.172
71
3.089
50
3.973
29
4.089
8
4.173
70
3.174
49
3.979
28
4.096
7
4.151
69
3.235
48
3,9s:>
27
4.103
6
4.115
68
3.296
47
3.992
26
4.110
5
4.087
67
3.356
46
3.998
25
4.117
4
4.066
66
3.417
45
4.004
24
4.121
3
3.913
65
3.478
44
4.007
23
4.125
2
3.723
64
3.. 508
43
4.010
22
4.129
I
3.518
63
3.537
42
4.012
21
4.133
0
3.119
62
3.567
41
4.015
20
4.137
61
3.596
40
4.018
19
4.139
60
3.626
89
4.027
18
4.141
Older Age Eighty -One Years.
A^e.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
81
2. -252
61
3.421
41
3.797
21
3.910
80
2.317
60
3.459
40
3.805
20
3.911
79
2.383
59
3.497
39
3.813
19
3.913
78
2.448
58
3.536
38
3.821
18
3.914
n
2.514
57
3.574
37
3.829
17
3.916
76
2.579
56
3.612
36
3.837
16
3.917
75
2.652
55
3.639
35
3.842
15
3.922
74
2.725
54
3.665
34
3.846
14
3.926
73
2.798
53
3.692
33
3.861
13
3.931
72
2.871
52
3.718
32
3.855
12
3.985
71
2.944
51
3.745
31
3.860
11
3.940
70
3.010
50
3.754
30
3.865
10
3.961
69
3.07fi
49
3,763
29
3.871
9
3.960
C8
3.1^2
48
3.771
28
3.876
8
3.957
67
3.208
47
3.780
27
3.882
7
3.937
66
3.274
46
3.789
26
3.887
6
3.904
6.-)
3.303
45
3.791
25
3.892
5
3.879
64
3.333
44
3.792
24
3.896
4
3.803
63
3.362
43
3.794
23
3.901
3
3.713
62
3.3yj
42
3.795
2-J
3.905
1
3.535
3.345
Digitized by ^^UUV
IF
TABLE XXI.
489
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 3^ per Cent.)
Older Age Eighty-Two Years.
Ag».
Value.
Age.
Value.
Age.
Value.
Age.
Value.
82
2.107
62
3.238
4-2
3.601
22
3.705
81
2.173
61
3.270
41
3.608
21
3.706
80
2.238
60
3.302
40
3.614
20
3.708
70
2.304
59
3.335
39
3.621
19
3.709
78
2.369
58
3.367
38
3.627
18
3.711
77
2.435
57
3.399
37
3.634
17
3.712
76
2.496
56
• 3.427
36
3.639
16
3.716
75
2.55G
55
3.455
35
3.644
15
3.720
74
2.617
54
3.484
34
3.649
14
3.723
73
2.677
53
3.512
33
3.654
13
3.727
72
2.738
52
3.540
32
3.659
12
3.731
71
2.808
51
3.551
31
3.663
11
3.729
70
2.877
50
3.562
30
3. 607
10
3,728
69
2.947
49
3.574
29
3.671
9
3.726
68
3.016
48
3.585
28
3.675
8
3.725
67
3.086
47
3.596
27
3.679
7
3.723
66
3.116
46
3.597
26
3.684
6
3.702
65
3.147
45
3.598
25
3.689
5
3.671
64
3.177
44
3.509
24
3.695
4
3.601
63
3.208
43
3.600
23
3.700
3
2
3.512
3.347
Older Age Eighty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
3.400
Age.
Value.
83
1.953
63
3.053
43
23
3.494
82
2.020
62
3.079
42
3.405
22
3.496
81
2.086
61
3.105
41
3.410
21
3.497
80
2.153
60
3.130
40
3.415
20
3.499
79
2.219
59
3.156
39
3.420
19
3.500
78
2.286
58
3.182
38
3.425
18
3.502
77
2.337
57
3.212
37
3.431
17
3.505
76
2.387
56
3.241
36
3.436
16
3.508
75
2.438
55
3.271
35
3.442
15
3.510
74
2.488
54
3.300
34
3.447
14
3.513
73
2.539
53
3.330
33
3.453
13
3.516
72
2.609
52
3.343
32
3.456
12
3.518
71
2.679
51
3.356
31
3.458
n
3.519
70
2.750
50
3.369
30
3.461
10
3.521
69
2.820
49
3.382
29
3.463
9
3.522
68
2. 890
48
3.395
28
3.466
8
3.524
67
2.923
47
3.396
27
3.472
7
3.530
66
2.955
46
3.397
26
3.477
6
3.500
65
2.988
45
3.398
23
3.483
5
3.463
64
3.020
44
3.399
24
3.488
4
3
3.398
3.311
Digitized by VjOOQ IC
490
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 3} per Cent.)
Older Age Eighty-Four Years.
' Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
84
1.803
64
2.869
44
3.206
24
3.289
83
1.868
63
2.890
43
3.209
23
3.291
82
1.932
62
2.911
42
3.212
22
3.293
81
1.997
61
2.933
41
3.216
21
3.295
80
2.061
60
2.954
40
3.219
20
3.297
79
2.126
59
2.975
39
3.222
19
3.299
78
2.172
58
3.005
38
3.228
18
3.301
n
2.218
57
3.035
37
3.234
17
3.303
76
2.264
56
3.065
36
3.239
16
3.304
75
2.310
55
3.095
35
3.245
IS
3.306
74
2.356
54
3.125
34
3.251
14
3.308
73
2.424
53
3.139
33
3.253
13
3.311
72
2.491
52
3.154
32
3.255
12
3.314
71
2.559
51
3.168
31
3.257
11
3.318
70
2.626
50
3.183
30
3.259
10
3.321
69
2.694
49
3.197
29
3.261
9
3.324
68
2.729
48
3.199
28
3.267
8
3.354
67
2.764
47
3.201
27
3.272
7
3.838
66
2.799
46
3.202
26
3.278
6
3.298
65
2.834
45
3.204
25
3.283
5
4
3.255
3.195
Older Age Eighty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
85
1.638
65
2.676
45
3.003
25
3.075
84
l.?04
64
2.694
44
3.005
24
3.077
83
1.770
63
2.712
43
3.007
23
3.080
82
1.636
62
2.730
42
3.003
22
3.082
81
1.902
61
2.748
41
3.010
21
3.085
80
1.968
60
2.766
40
3.012
20
3.087
79
2.012
09
2.795
39
3.018
19
3. 088
7S
2.056
58
2.824
38
3.024
18
3.089
77
2.099
57
2.853
37
3.030
17
3.091
76
2.143
56
2.882
36
3.036
16
3.092
75
2.187
55
2.911
35
3.042
15
3.093
74
2.247
54
2.926
34
3.044
14
3.097
73
2.306
53
2.942
33
3,046
13
3.100
72
2.366
52
2.957
32
3.049
12
3.104
71
2.425
51
2.973 .
31
3.051
11
3.107
70
2.485
50
2.988
30
3.053
10
3.111
69
2.523
49
2.991
29
3.057
9
3.174
. 68
2.561
48
2.994
28
3.062
8
3.185
67
2.600
47
2.997
27
3.066
7
3.145
66
2.638
46
3.000
•i6
3.071
6
5
3.096
3.04Z
Digit
zed by V_
lUuylC
TABLE XXI.
491
Value of £1 per AnDum dnriiig the joint Continuance of Two Lives.
(Carlisle 3^ per Cent.)
Older Age Eighty-Six Years.
Age.
Valoe.
Age.
Valoe.
Age.
Value.
Ago.
Value.
86
1.492
64
2.538
42
2.829
20
2.903
85
1.556
63
2.556
41
2.830
19
2.904
84
1.620
62
2.574
40
2.835
18
2.904
83
1.683
61
2.592
39
2.841
17
2.905
82
1.747
60
2.618
38
2.846
16
2.906
81
1.811
59
2.643
37
2.852
15
2.909
80
1.856
58
2.669
36
2.857
14
2.912
79
1.900
57
2.694
33
2.860
13
2.915
78
1.945
56
2.720
34
2.862
12
2.918
n
1.989
53
2.736
33
2.865
11
2.921
76
2.034
54
2.752
32
2.867
10
2.971
75
2.085
53
2.769
31
2.870
9
3.024
74
2.136
52
2.785
30
2.874
8
3.015
73
2.187
51
2.801
29
2,877
7
2.953
72
2.238
60
2.806
28
2.881
6
2.894
71
2.289
49
2.811
27
2.884
70
2.332
48
2.816
26
2.888
69
2.374
47
2.821
23
2.891
68
2.417
46
2.826
24
2.894
67
2.459
45
2.827
23
2.896
66
2.502
44
2.828
22
2.899
65
2.520
43
2.828
21
2.902
Older Age Eighty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
87
1.374
65
2.392
43
2.682
21
2.751
86
1.436
64
2.411
42
2.682
20
2.752
85
1.498
63
2.431
41
2.687
19
2.752
84
1.560
62
2.450
40
2.691
18
2.753
83
1.622
61
2.472
39
2.696
17
2.754
82
1.684
60
2.493
38
2.700
16
2.757
81
1.7-29
59
2.515
37
2.705
15
2.759
80
1.774
58
2.536
36
2.708
14
2.762
79
1.820
57
2. 553
35
2.711
13
2.764
78
1.865
56
2.576
34
2.714
12
2.767
11
1.910
55
'2.594
33
2.717
11
2.766
76
1.952
54
2.611
32
2.720
10
2.764
75
1.994
53
2.629
31
2.723
9
2.763
74
2.037
52
2.647
30
2.726
8
2.761
73
2.079
51
2.654
29
2.728
7
2.760
72
2.121'
50
2.660
28
2.731
71
2.167
49
2.667
27
2.734
70
2.214
48
2.673
26
2.737
69
2.260
47
2.680
25
2.740
68
2.307
46
2.680 ,
24
2.744
67
2.353
45
2.681
23
2.747
66
2.372
44
2.681
22
2.750
Digitized
byV^OOQ IC
492
TABLE XXI.
Value of £1 per Annum dnring the joint Continuance of Two Livev.
(Carlisle 3^ per Cent.)
Older Age Eighty-Eight Years.
Ag6.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
88
1.315
65
2.317
42
2.597
19
2.661
87
1.369
64
2.338
41
2.600
18
2.662
86
1.424
63
2.360
40
2.604
17
2.664
85
1.478
62
2.378
39
2.607
16
2.6B6
84
1.533
61
2.396
38
2.611
15
2.668
83
1.587
60
2.414
37
2.615
14
2.670
82
1.635
59
2.432
36
2.618
13
2.672
81
1.683
58
2.450
35
2.622
12
2.673
80
1.730
57
2.470
34
2.625
11
2.674
79
1.778
56
2.490
33
2.629
10
2.674
78
1.826
55
2.509
32
2.631
9
2.675
77
1.862
54
2.529
31
2.633
8
2.676
76
1.898
53
2.549
30
2.63-1
75
1.934
52
2.5.38
29
2.636
74
1.970
51
2.566
28
2.638
73
2.006
50
2.575
27
2.642
72
2.05.%
49
2.583
26
2.646
71
2.104
4S
2.592
25
2.649
70
2.154
47
2.592
24
2.653
69
2.203
46
2.592
23
2.657
68
2.252
45
2.593
22
2.658
67
2.274
44
2.593
21
2.659
66
2.295
43
2.593
20
2.660
Older Age Eighty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
89
1.235
66
2.207
43
2.493
20
2.555
88
1.284
65
2.231
42
2.496
19
2.556
87
1.333
64
2.256
41
2.498
18
2.557
86
1.382
63
2.271
40
2.501
17
2.559
85
1.431
62
2.286
39
2.503
16
2.560
84
1.4S0
61
2.301
38
2.507
15
2.562
83
1.527
60
2.316
37
2.511
14
2.563
82
1.575
59
2.331
36
2.516
13
2.565
81
1.622
58
2.352
35
2.520
12
2.567
80
1.670
57
2.373
34
2.524
11
2.370
79
1.717
56
2.395
33
2.525
10
2.572
78
1.751
55
2.416
32
2.526
9
2.574
77
1.785
54
2.437
31
2.528
76
1.818
53
2.447
30
2.5v!9
75
1.852
52
2.457
29
2.530
74
1.886
51
2.467
28
2.534
73
1.935
50
2.477
27
2.538
72
1.985
49
2.487
26
2.542
71
2.034
48
2.483
25
2.546
70
2.084
47
2.489
24
2.550
69
2.133
46
2.489
23
2.551
68
2.158"
45
2.490
22
2.552
67
2.182
44
2.491
21
2.554
Digitized by VjOOQ IC
TABLE XXI.
f ^'4*r
Valua of £1 per Annum during the joint Continuance of Two Lives.
(Carlijile 3^ per Cent.)
Older Age Ninety Years.
V.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
90
1.077
€7
2.043
44
2.337
21
2.394
89
1.126
66
2.071
43
2.338
20
2.396
88
1.175
65
2.099
42
2.340
19
2.397
S7
1.223
64
2.112
41
2.341
IS
2.398
86
1.272
63
2.125
40
2.342
17
2.399
85
1.321
62
2.139
39
2.346
16
2.400
84
1.371
61
2.152
38
2.350
15
2.401
83
1.421
60
2.165
37
2.355
14
2.403
82
1.470
59
2.186
36
2.359
13
2.406
81
1.520
58
2.207
35
2.363
12
2.408
80
1.570
57
2.229
34
2.365
11
2.411
79
1.603
56
2.250
33
2.366
10
2.413
78
1.636
55
2.271
32
2.368
77
1.669
54
2.282
31
2.369
76
1.702
53
2.293
3Q
2.371
76
1.735
52
2.305
29
2.374
74
1.780
51
2.316
28
2.378
73
l.fe25
50
2.327
27
2.381
72
1.869
49
2.329
26
2.385
71
1.914
48
2.331
25
2.388
70
1.959
47
2.332
24
2.390
69
1.987
46
2.334
23
2.391
68
2.015
45
2.336
22
2.393
Older Age Ninety-One YearB.
Ace.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
91
1.039
68
1.996
45
2.319
22
2.376
90
1.080
67
2.030
44
2.320
21
2.378
89
1.120
65
2.065
43
2.320
20
2.379
88
1.161
65
2.079
42
2.321
19
2.379
87
1.201
64
2.093
41
2.321
18
2.380
86
1.242
63
2.108
40
2.325
17
2.380
85
1.294
62
2.122
39
2.329
16
2.381
84
1.346
61
2.136
38
2.334
15
2.383
83
1.398
6i
2.156
37
2.338
14
2.386
82
1.450
59
2.176
36
2.342
13
2.383
81
1.502
58
2.196
35
2.344
12
2.391
80
1.539
57
2.216
34
2.346
11
2.393
79
1.575
56
2.236
33
2.349
78
1.612
55
2.249
32
2.351
77
1.648
54
2.262
31
2.353
76
1.685
53
2.275
30
2.356
75
1.726
52
2.288
29
2.359
74
1.768
51
2.301
28
2.361
.
73
1.809
50
2.305
27
2.364
72
1.851
49
2.308
26
2.367
71
1.892
48
2.312
25
2.369
70
1.927
47
2.315
24
2.371
69
1.961
46
2.319
23
2.374
byGOQg
494
TABLE XXL
Value of £1 per Annum darings the joint Continuftnee of Two Livef .
(Carlisle 3^ per Cent)
Older .
Age Ninety-Two Years.
Age.
92
Value.
Age.
72
Value.
AgP.
62
Value.
A««.
Value.
1.108
1 .913
2.383
32
2.445
91
1.133
71
1.955
51
2.389
31
2.447
90
1.157
70
1.997
50
2.394
30
2.449
89
1.182
69
2.040
49
2.400
29
2.451
88
1.206
68
2.082
48
2.405
28
2.453
87
1.231
67
2.124
47
2.411
27
2.455
86
1.287
66
2.141
46
2.411
26
2.458
85
1.344
65
2.158
46
2.411
25
2.461
84
1.400
64
2.175
44
2.410
24
2.464
83
1.457
63
2.192
43
2.410
23
2.667
82
1.513
62
2.209
42
2.410
22
2.470
81
1.555
Gl
2.228
41
2.414
21
2.471
80
1.596
60
2.247
40
2.41S
20
2.471
79
1.638
59
2.265
39
2.422
19
2.472
78
1.679
58
2.284
38
2.426
18
2.472
n
1.721
67
2.303
37
2.430
17
2.473
76
1.759
56
2.319
36
2.433
16
2.475
75
1.798
65
2.335
36
2.436
15
2.477
74
1.836
54
2.351
34
2.439
14
2.480
73
1.875
53
2.367
33
2.442
13
12
2.482
2.484
CHder Age Ninety-Three Years.
Age.
93
92
9]
90
89
88
87
86
85
84
a3
82
81
80
79
78
77
76
75
74
Value.
1.212
1.221
1.230
1.240
1.249
1.258
1.313
1.367
1.4*22
1.476
1.531
1.579
1.627
1.676
1.724
1.772
1.808
1.843
1.879
1.914
Age.
Value.
1.960
1.999
2.048
2.097
2.146
2.195
2.216
2.237
2.257
2.278
2.299
2.316
2.332
2.349
2.365
2.382
2.401
2.420
2.440
2.469
Age.
63
52
61
50
49
48
47
46
46
44
43
42
41
40
39
38
37
36
35
34
Value.
2.478
2.486
2.494
2.501
2.609
2.517
2.617
2.516
2.516
2.616
2.616
2.518
2.522
2.525
2.529
2.532
2.636
2.539
2.543
2.646
Age.
Value.
2.650
2.561
2.553
2.664
2.55C
2.557
2.561
2.566
2.668
2.672
2.676
2.577
2.678
2.578
2.679
18 2.530
17 2.582
16 2.684
15 2.585
14 2.587
13 2.589
TABLE XXI.
495
Value of £1 per Annum during; the joint Continuance of Two LiTes.
(Carlisle 3^ per Cent.)
Older
Age Ninety-Four Years.
Age.
V.lne.
Aire.
74
Value.
Age.
Value.
Age.
Value.
94
1.287
1.956
54
2.520
34
2.599
93
1.280
73
2.008
53
2.529
33
2. GOO
92
1.273
72
2.060
52
2.5.-38
32
2.601
91
1.267
71
2.113
51
2.548
31
2.602
90
1.260
70
2.165
50
2.557
30
2.603
89
1.253
69
2.217
49
2.566
29
2.604
83
1.306
68
2.242
48
2.566
28
2.608
87
1.359
67
2.266
47
2.566
27
2.612
86
1.413
66
2.291
46
2.566
26
2.616
85
1.466
65
2.315
45
2.566
25
2.620
84
1.519
64
2.340
44
2.566
24
2.624
83
1.571
63
2.354
43
2.568
23
2.625
82
1.623
62
2.368
42
2.570
22
2.626
81
1.674
61
2.382
41
2.573
21
2.6-28
80
1.726
60
2.396
40
2.675
20
2.629
79
1.778
59
2.410
39
2.577
19
2.630
78
1.814
58
2.432
38
2.581
18
2.631
77
1.849
^7
2.454
37
2.r>86
17
2.633
76
1.885
56
2.476
36
2.590
16
2.634
75
1.920
b5
2.498
35
2.595
15
14
2.636
2.637
Older Age Ninety-Five Years.
Ago.
Value.
Age.
7b
Value.
Age.
Value.
Age.
Value.
95
1.368
1.967
55
2.537
35
2.623
94
1.335
74
2.017
54
2.548
34
2.624
93
1.302
73
2.067
53
2.558
33
.2.626
92
1.270
72
2.117
52
2.569
32
2.627
91
1.237
71
2.167
51
2.579
31
2.629
90
1.204
70
2.217
50
2.590
30
2.630
89
1.262
69
2.246
49
2.591
29
2.634
88
1.319
68
2.27<)
48
2.692
28
2.637
87
1.377
67
2.305
47
2.592
27
2.641
86
1.434
66
2.335
46
2.593
26
2.644
85
1.492
65
2.364
45
2.594
25
2.648
84
1.550
64
2,376
44
2.595
24
2.650
83
1.609
63
2.388
43
2.596
23
2.651
82
1.667
62
2.399
42
2.597
22
2.653
81
1.726
61
2.411
41
2.598
21
2.654
80
1.784
60
2.423
40
2.599
20
2.656
79
1.821
59
2.446
39
2.604
19
2.657
78
1.857
58
. 2.469
38
2.609
18
2.657
77
1.894
57
2.491
37
2.613
17
2.658
76
1.930
56
2.514
36
2.618
16
2.658
2.659
Digitized by VjOOQIC
490
TABLE XXr.
Value of £1 per Annum during the joint Coniiauance of Two Lives.
(Carlisle 3^ per Cent.)
Older Age Ninety-
Six Years
Age.
Value.
Age.
76
Value.
Age.
5fi
Value.
Age.
Value.
96
1.409
1.936
2.488
36
2.578
95
1.367
75
1.980
65
2.499
35
2.r>80
94
1.325
74
i>.024
54
2.511
34
2.681
93
1.282
73
2.068
53
2.522
33
2.583
92
1.240
72
2.112
52
2.531
32
2.584
91
1.198
71
2.156
51
2.545
31
2.586
90
1.247
70
2.190
50
2.547
30
2.589
89
1.296
69
2.224
49
2.549
29
2.592
88
1.344
68
2.259
48
2.551
28
2.595
87
1.393
67
2.293
47
2.553
27
2.598
86
1.442
66
2.327
46
2.555
26
2.601
85
1.502
65
2.333
45
2.555
25
2.603
84
1.662
64
2.350
44
2.555
24
2.605
83
1.622
63
2.361
43
2.555
23
2.606
62
1.682
62
2.373
42
2.555
22
2.608
81
1.742
61
2.384
41
2.555
21
2.610
80
1.781
60
2.405
40
2.560
20
2.610
79
1.820
59
2.426
39
2.564
19
2.611
78
1.658
58
2.446
38
2.569
18
2.611
V
1.897
57
2.467
37
2.573
17
16
2.612
2.612
Older Age Ninety-Seven Years.
Age.
Value.
AgP.
Value.
Age.
Value.
Age.
97
1.380
n
1.853
57
2.354
37
96
1.347
76
1.888
56
2.366
36
95
1.315
75
1.923
55
2.378
35
94
1.282
74
1.959
54
2.390
34
93
1.250
73
1.994
53
2.402
33
92
1.217
72
2.029
52
2.414
32
91
1.246
71
2.066
51
2.417
31
90
1.276
70
2.103
50
2.420
30
89
1.305
69
2.141
49
2.423
29
8S
1.335
68
2.178
48
2.426
28
87
1.364
67
2.215
47
2.429
27
86
1.423
66
2.226
46
2.4-28
26
85
1.482
65
2.237
45
2.428
26
84
1.542
64
2.248
44
2.427
24
83
1.601
63
2.259
43
2.427
23
82
1.660
62
2.270
42
2.426
22
81
1.699
61
2.287
41
2,430
21
80
1.737
60
2-304
40
2.434
20
79
1.776
59
2.320
39
2.438
19
78
1.814
68
2.337
38
2.442
18
17
Value.
2.446
2.448
2.450
2.452
2.454
2.456
2.458
2.460
2.461
2.463
2.465
2.467
2.470
2.472
2.475
2.477
2.477
2.477
2.477
2.477
17 2.477 _T^
Ul^itizedbyVjOOglC
TABLB XXI.
497
Value of £1 per Annam during the joint Continoance of Two Lives.
(Carlisle ^ per Gent.)
Older Age Ninety-Eight Years.
Age.
Volue.
Age.
Valae.
Age.
Value.
Age.
Value.
98
1.3C2
78
1.763
53
2.199
38
2.291
97
1.340
77
1.790
57
2.212
37
2.293
96
1.317
76
1.817.
56
2.224
36
2.295
95
1.295
75
1.844
55
2.237
35
2.297
94
1.272
74
1.871
54
2.249
34
2.299
93
1.250
73
1.898
53
2.262
33
•2.301
92
1.263
72
1.935*
52
2.266
32
2.302
91
1.276
71
1.972
51
2.270
31
2.303
90
1.290
70
2.010
50
2.273
30
2.304
89
1.303
69
2.047
49
2.277
29
2.305
88
1.316
68
2.084
48
2.281
28
2.306
87
1.367
67
2.095
47
2.280
27
2.309
86
1.418
66
2.106
46
2.279
26
2.311
85
1.469
65
2.117
45
2.278
25
2.314
84
1.520
64
2.128
44
2.277
24
2.316
83
1.671
63
2.139
43
2.276
23
2.319
82
1.609
62
2.151
42
2.279
22
2.319
81
1.648
61
2.163
41
2.282
21
2.319
80
1.686
60
2.175
40
2.285
20
2.820
79
1.725
59
2.187
89
2.288
;i9
18
2.320
2.320
Older Age Ninety-Nine Years.
Age.
Valns.
Age.
Value.
Age.
Value.
Age.
Value.
99
1.283
79
1.606
59
1.969
39
2.052
98
1.271
78
1.627
58
1.981
38
2.054
97
1,259
77
1.648
57
1.993
37
2.056
96
1*247
76
1.670
56
2.005
36
2.058
95
1.235
75
1.691
55
2.017
35
2.060
94
1.223
74
1.712
54
2.029
34
2.062
93
1.223
73
1.745
53
2.033
33
2.062
92
1.223
72
1.779
52
2.036
32
2.063
91
1.222
71
1.812
51
2.040
31
2.063
90
1.222
70
1.846
50
2.043
30
2.064
89
1.222
69
1.879
49
2.047
29
2.064
88
1.265
68
1.889
48
2.046
28
2.066
87
1.308
67
1.899
47
2.045
27
2.069
86
1.351
66
1.909
46
2.045
26
2.071
85
1.394
65
1.919
45
2.044
25
2.074
84
1.437
64
1.929
44
2.043
24
2.076
83
1.471
63
1.937
43
2.045
23
2.076
82
1.505
62
1.945
42
2.047
22
2.076
81
1.538
61
1.953
41
2.048
21
2.077
80
1.572
60
1.961
40
2.050
20
19
2.077
2.077
Digitiz
ed%V^*-^Xl^
498
TABLE XXI.
Value of £1 per Annixm during the joint Continaance of Two Livei.
(CariiileSi per Gent.)
Older Age One Hundred Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
100
0.984
79
1.320
58
1.582
37
1.632
99
- 1.000
78
1.335
57
1.591
36
1.633
98
1.016
17
1.351
56
1.601
35
1.635
97
1.031
76
1.366
55
1.610
34
1.635
96
1.047
75
1.381
54
1.613
33
1.636
95
1.063
74
1.405
53
1.616
32
1.636
94
1.045
73
1.429
52
1.619
31
1.637
93
1.026
72
1.452 -
51
1.622
30
1.637
92
1.008
71
1.476
50
1.625
29
1.639
91
0.989
70
1.500
49
1.625
28
1.640
90
0.971
69
1.508
48
1.624
27
1.642
89
1.009
68
1.517
47
1.624
26
1.643
88
1.047
67
1.525
46
1.623
35
1.645
87
1.085
66
1.534
45
1.623
24
1.645
86
1.123
65
1.542
44
1.624
23
1.645
85
1.161
64
1.546
43
1.625
22
1.646
84
1.190
63
1.550
42
1.625
21
1.646
83
1.219
62
1.555
41
1.626
20
1.646
82
1.247
61
1.559
40
1.6-27
81
1.276
60
1.563
39
1.629
80
1.305
59
K572
38
1.630
Older Age One Hundred and One Years.
Age.
101
100
99
98
97
96
95
94
93
92
91
90
89
88
87
85
84
83
82
81
Value.
0.683
0.715
0.748
0.780
0.813
845
82)
806
787
767
0.748
0.773
0.798
0.823
0.848
0.873
0.894
0.915
0.935
0.9:i6
0.977
Age.
80
79
78
77
76
76
74
73
72
71
70
69
68
67
65
64
63
62
61
60
Value.
0.988
0.999
.l.OOd
1.020
1.031
1.046
1.060
1.075
1.089
1.104
1.111
1.118
l.lL'5
1.132
1.139
1.142
1.144
1.147
1.149
1.152
1.158
Age.
Value.
1.164
1.170
1.176
1.182
1.184
1.186
1.188
1.190
1.192
1.192
1.192
1.192
1.192
1.192
1.192
1.192
1.193
1.193
1.193
1.194
1.195
Age.
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
Value.
1.196
1.197
1.198
1.198
1.199
1.199
1.200
1.200
1.201
1 .202
1.203
1.204
1.205
1.205
1.205
1.206
1.206
1.206
jitiTPrlliy Google
TABLE XXI.
499
Valae of £1 per Annum during the joint Continoance'of Two LiveB.'
(Caxliile 3^ per Gent)
Older Age One Hundred and Two Years.
Age.
Value.
Age.
Value.
Ag«.
Value.
A«e.
Value.*
102
.385
81
.640
60
.737
39
• 754
101
.421
80
•647;
59
.740
38
.755
100
»4d7
79
.653
58
.743
37
•755
99
.493
78
.660
57
.746
36
.755
98
.629
77
.666
56
• 747
35
.756
97
.565
76
.673
55
.748
34
.756
96
.555
75
.680
54
.750
33
.757
95
.546
74
•687
53
.751
32
.757
94
.536
73
•694
52
.752
31
.757
93
•527
72
.701
51
.752
30
.758
92
.517
71
•706
50
.752
29
.758
91
.527
70
.710
49
•753
28
.759
90
.538
69
.715
48
.753
27
.759
89
.548
68
.719
47
.753
26
.759
88
.559
67
.724
46
.753
25
.769
87
.569
66
.725
45
• 753
24
.760
86
• 582
65
.727
44
.753
23
.760 -
85
.595
64
.728
43
.753
22
.760
84
.608
63
• 730
.42
.753
83
• 621
62
.731
41
.753
82
•634
61
.734
40
.754
.
Older Age One Hundred and Three Years.
Age.
Value.
Age.
Value.
Age.
61
Value.
.312
Affik
Value.
103
^107
82
.276
40
.317
102
.136
81
.279
60
.312
39
.317
101
.165
80
.281
59
.313
38
.317
100
.195
79
.284
68
•314
37
•317
99
.224
78
.287
57
•315
36
.318
98
.253
77
.289
56
•315
85
.318
97
•250
76
.291
55
.316
34
.319
96
.247
75
.293
54
.316
33
.319
95
.245
74
.295
53
.317
32
.319
94
.242
73
.297
52
.317
31
.319
93
.239
72
.299
51
.317
30
.319
92
.241
71
.301
50
.317
29
.319
91
.244
70
.303
49
.317
28
.319
90
.246
69
.305
48
.317
27
.319
89
.249
68
.307
47
.317
26
.319
88
.251
67
.308
46
.317
26
.320
87
.25^
66
.308
45
.317
24
.320
86
.260
65
.309
44
.317
23
.320
85
.264
64
.309
43
.317
84
.269
63
.310
42
.317
83
.273
62
•311
41
.317
'^oooIp
i
n^^ o " ^ O'^
300
TABLE XXr.
Value of £1 per Annum during the joint CuntiuUance of Two LWes.
(Carlisle 4^ per Cent.)
Older Age 0 Years.
Older Ag
e One Year.
Age.
Value.
Age.
I
0
Value.
0
8.259
11.056
8.871
Older Age Two Years.
Older Age Three Years.
Age.
Value.
Age.
Value.
2
1
0
12.669
11.492
9.484
3
2
1
0
14.141
12.981
11.928
10.096
Older Age Four Years.
Older Age Five Years.
Age.
ValuA.
Age.
Value.
4
3
2
1
0
14.966
14.322
13.294
12.364
10.709
5
4
3
2
1
0
15.578
15.063
14.503
13.606
12.800
11.321
Older Age Six Years.
Older Age Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value
6
5
4
3
15.874
15.604
15.160
14.683
2
1
0
13.919
13.236
11.339
7
6
5
4
16.004
15.857
15.630
15.257
3
2
1
0
14.864
14.231
13.220
11.357
TABLE XXI.
501
Value of £1 per Annum during the joint Continuance of Two Liyes.
(Carlisle 4) per Cent)
Older Age Eight Years.
Older Age Nine Years.
Age.
Valtta.
Age.
Value.
Age.
Valae.
Age.
Value.
8
7
6
5
4
16.022
15.960
15.840
15.656
15.354
3
2
1
0
15.045
14.190
13.204
11.375
9
8
7
6
5
15.966
15.963
15.916
15.822
15.682
4
3
2
1
0
15.451
14.987
14.149
13.189
11.393
Older Age
Ten Years.
Older Age Eleven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
10
9
8
7
6
5
15.855
15.898
15.903
15.873
15.805
15.708
4
3
2
1
0
15.383
14.929
14.109
13.173
11.411
11
10
9
8
7
6
15.718
15.785
15.831
15.844
15.829
15.788
5
4
3
2
1
0
15.636
15.315
14.871
14.068
13.157
11.358
Older Age Twelve Years.
Older Age Thirteen Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
12
11
10
9
8
7
15.585
15.625
15.665
15.705
15.745
15.785
15.716
5
4
3
2
1
0
15.564
15.246
14.813
14.027
13.096
11.305
13
12
11
10
9
8
7
15.450
15.505
15.560
15.615
15.670
15.725
15.715
6
5
4
3
2
1
0
15.645
15.491
15.178
14.755
13.963
13.035
11.252
le
502
TABLE XXI.
Value of £1 per Annum during; the joint Continuance of Two Lives.
(Carlisle 4} per Gent)
Older Age Fourteen Years.
Agt.
14
13
12
11
10
9
•8
7
Valae.
15.314
15.377
15.440
15.502
15.565
15.628
15.657
15.645
Afe.
Value.
15.573
15.419
15.110
14.689
13.899
12.974
11.199
Older Age Fifleen Years.
Age.
15
14
13
12
11
10
9
8
Value.
15.182
15.247
15.312
15.376
15.441
15.506
15.562
15.590
Ago.
Value.
15.576
15.502
15.347
15.044
14.623
13.835
12.913
11.146
Older Age Sixteen Yeaiis.
Older Age Seventeen Years.
Age.
ValuA
Age.
Value.
Age.
Value.
Age.
Value.
16
15.063
7
15.506
17
14.954
8
15.400
15
15.126
6
15.430
16
15.015
7
15.436
14
15.189
5
15.280
15
15.075 i
6
15.361
13
15.252
4
14.977
14
15.136
5
15.213
12
15.315
3
14.557
13
15.196
4
14.911
11
15.378
2
13.771
12
15.257
3
14.491
IQ
15.441
1
12.852
11
15.293
2
13.707
9
15.496
0
11.097
10
15.329
1
12.794
8
15.522
9
15.364
0
11.048
-Older Age Eighteen Years.
Older Age Nineteen Years.
Age.
18
17
16
15
14
13
12
11
10
9
Value.
14.846
14.904
14.962
15.019
15.077
15.135
iri.185
15.236
15.286
15.337
Age.
Value.
15.387
15.363
15.292
15.146
14.844
14.425
13.641
12,735
10.999
Ago.
19
18
17
16
15
14
13
12
11
10
Value.
14.732
14.788
14.843
14.899
14.954
15.010
15.068
15.126
15.183
15.241
Age.
4 14.778
3 14.351
13.575
12.677
10^950
Diqitizeb by VjiDU V LC
Value.
15.299
15.310
15.290
15.224
15.079
TABLB XXI.
Value of £1 per Annum during the joint Continuance of Two Jayw.
(Carlisle 4^ per Cent.)
Older Age Twenty
Yean.
Age.
Valne.
Age.
Valae.
Age.
Value.
Age.
Valae.
20
19
18
17
16
15
14.613
14.667
14.721
14.776
14.830
14.884
14
13
12
11
10
9
14.944
15.004
15.063
15.123
15.183
15.218
8
7
6
5
4
3
15.233
15.218
15.155
15.012
14.697
14.276
2
1
0
13.508
12.618
10.901
• 1
Older Age Twenty-One Years.
Age,
V^lue.
Age.
Value.
Age.
Valae.
Age.
Value.
21
20
19
18
17
16
14.489
14.544
14.598
14.653
14.707
14.762
15
14
13
12
11
10
14.820
14.878
14.935
14.993
15.051
15.097
9
8
7
6
5
4
15.137
15.156
15.145
15.086
14.925
14.616
3
2
1
0
14.202
13.442
12.560
10.838
Older Age Twenty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
22
21
20
19
18
17
14.353
14.410
14.467
14.525
14.582
14.639
16
15
14
13
12
11
14.694
14.749
14.805
14.860
14.915
14.946
10
9
8
7
6
5
14.978
15.009
15.041
15.072
14.993
14.837
4
3
2
1
0
14.535
14.127
13.376
12.482
10.775
Older Age Twenty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
23
22
21
20
14.211
14.271
14.332
14.392
16
15
14
13
14.617
14.670
14.722
14.774
Q
8
7
6
14.956
15.002
14.974
14.900
2
1
0
13.288
12.404
10.711
19
18
17
14.453
14.513
14.565
12
11
10
14.820
14.865
14.911
5
4
3
14.750
14.454
14.053
^Google
504
TABLE XXI.
Value of £1 per Aanum during the joint Contmoanbe of Two LWes.
(Gariiile 4^ per Cent)
Older ^e Twenty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
A««.
Value.
24
23
22
21
20
19
18
14.062
14.126
14.189
14.253
14.316
14.380
14.430
17
16
15
14
13
12
11
14.480
14.530
14.580
14.630
14.683
14.735
14.788
10
9
8
7
6
5
4
14.840
14.893
14.901
14.877
14.807
14.662
14.373
3
2
1
U
13.956
13.199
12.325
10.648
Older Age Twenty-Five Years.
. Ago.
Value.
Age.
Value.
Age,
Value.
Age.
Value.
25
13.905
18
14.338
11
14.701
4
14.272
24
13.972
17
14.387
10
14.755
3
13.859
23
14.040
16
14.435
9
14.791
2
13.111
*22
14.107
15
14.483
8
14.799
1
12.247
21
14.175
14
14.537
7
14.779
0
10.585
20
14.242
13
14.592
6
14.714
19
14.290
12
14.646
5
14.575
Older Age Twenty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Agi.
Value.
26
13.746
19
14.196
12
14.550
5
14.474
25
13.817
18
14.244
11
14.602
4
14.171
24
13.837
17
14.293
10
14.655
3
13.762
23
13.958
16
14.341
9
14.689
2
13.022
22
14.028
15
14.393
8
14.698
1
12.169
21
14.099
14
14.445
7
14.682
0
10.512
20
14.147
13
14.498
6
14.621
Older Age Twenty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
27
26
25
24
23
22
21
13.579
13.652
13.726
13.799
13.873
13.946
13.997
20
19
18
17
16
15
14
14.048
14.098
14.149
14.200
14.249
14.299
14.348
13
12
11
10
9
•8
7
14.398
14.447
14.474
14.502
14.529
14.557
14.584
6
5
4
3
2
1
0
14.521
14.372
14.069
13.665
12.934
12.085
10.439
■ LJis
TABLE XXI.
505
ValiM of £1 per Annum daring the joint Continoance of Two Liree.
(CarUale 4^ per Cent)
Older Age Twenty-Eight Years.
Age.
Value.
Asp.
Volae.
Age.
Value.
Age.
Value.
28
13.413
20
13.952
12
14.333
4
13.968
27
13.469
19
14.006
11
14.373
3
13.568
26
13.565
18
14.059
10
14.414
2
12.846
25
13.640
17
14.106
9
14.454
1
12.001
24
13.716
16
14.152
8
14.495
0
10.365
23
13.792
15
14.199
7
14.486
22
13.845
14
14.245
6
14.421
21
13.899
13
14.292
5
14.271
Older Age Twenty-Nine Years.
Older Age Thirty Years.
Older Age Thirty-One Years.
Age.
Valae.
Age.
Value.
Age.
Value.
Age.
Value.
29
13.264
21
13.811
13
14.192
5
14.169
28
13.340
20
13.868
12
14.240
4
13.867
27
13.415
19
13.924
11
14.287
3
13.475
26
13.491
18
13.968
10
14.335
2
12.758
25
13.566
17
14.012
9
14.382
1
11.918
24
13.642
16
14.057
8
14.398
0
10.292
23
13.698
15
14.101
7
14.388
22
13.755
14
14.145
6
14.320
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
30
13.137
22
13.679
14
14.060
6
14.220
29
13.210
21
13.739
•13
14.109
5
14.068
28
13.282
20
13.799
12
14.158
4
13.769
27
13.355
19
13.841
11
14.207
3
13.382
26
13.427
18
13.884
10
14.256
2
12.669
25
13.500
17
13.926
9
14.283
1
ll.a34
24
13.560
16
13.969
8
14.301
0
10.219
23
13.620
15
14.011
7
14.289
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
31
13.010
23
13.545
15
13.930
7
14.191
30
13.079
22
13.608
14
13.977
6
14.120
29
13.148
21
13.671
13
14.023
5
13.963
28
13.218
20
13.713
12
14.070
4
13.672
27
13.287
19
13.756
11
14.117
3
13.290
26
13.356
18
13.798
10
14.152
2
12.581
25
13.419
17
13.841
9
14.184
1
11.750
24
13.482
16
13.883
8
14.204
0
10.143
Digitized by ^^UUV
le
506
TABLB XXI.
Value of C\ per Annum during the joint Gontinnanoe of Two Liret.
(Carlisle 4} per Gent)
Older Age Thirty-Two Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
32
12.877
23
13.468
14
13.889
5
13,858
31
12.943
22
13.534
13
13.933
4
13.574
30
13.009
21
13.578
12
13.977
3
13.197
29
13.074
20
13.623
11
14.000
2
12.493
28
13.140
19
13.667
10
14.023
1
11,656
27
13.206
18
13.712
9
14.047
0
10.068
26
13.272
17
13.756
8
14.070
25
13.337
16
13.800
7
14.093
24
13.403
15
13.844
6
14.007
Older Age Thirty-Three Yeare.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
33
12.733
24
13.321
15
13.747
6
13.895
32
12.797
23
13.389
14
13.788
5
13.752
31
12.860
22
13.436
13
13.829
4
13.477
30
12.924
21
13.483
12
13.865
3
13.104
29
12.987
20
13.529
11
13.901
2
12.386
28
13.051
19
13.576
10
13.938
I
11.562
27
13.119
18
13.623
9
13,974
0
9.992
26
13.186
17
13.664
8
14.010
25
13.254
16
13.705
7
13.974
Older Age Thirty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
Ago.
Value.
34
12.578
23
13.167
16
13.597
7
13.854
33
12.642
24
13.234
15
13.636
6
13.782
32
12.706
23
13.284
14
13.674
6
13.647
31
12.769
22
13.333
13
13.717
4
13.379
30
12.833
21
13.383
12
13.759
3
12.985
29
12.897
20
13.432
11
13.802
2
12.279
28
12.964
19
13.482
10
13.844
1
11.469
27
13.032
18
13.520
9
13.887
0
9.917
26
13.099
17
13.559
8
13.885
^
TABLBXXI.
5or
Value of £1 per Anniim during ihe joint Continuance of Two Lives.
(Carlisle 4^ per Cent.)
Older Age Thirty-Five Yean.
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
Volne.
35
12.415
26
13.007
17
13.443
8
13.760
34
12.482
25
13.071
16
13.479 .
7
13.735
33
12.549
24
13.123
15
13.516
6
13.670
312
12.617
23
13.176
14
13.560 .
5
13.542
31
12.684
22
13.228
13
13.604
4
13.252
30
12.751
21
13.281
12
13.648
3
12.867
29
12.815
20
13.333
11
13.692
2
12.173
28
12.879
19
13.370
10
13.736
1
11.375
27
12.943
18
13.406
9
13.757
0
9.841
Older Age Thirty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
36
12.244
26
12.902
16
13.360
6
13.557
35
12.315
25
12.957
15
13.402
5
13.409
34
12.386
24
13.012
14
13.443
4
13.125
33
12.458
23
13.068
13
13.485
3
12.748
32
12.529
22
13.123
12
13.526
2
12.066
31
12.600
21
13.178
11
13.568
1
11.281
30
12.660
20
13.214
10
13.603
0
9.746
29
12.721
19
13.251
9
13.627
28
12.781
18
13 287
8
13.635
27
12.842
17
13.324
7
13.615
Older Age Thirty-Seven Years.
Age.
Vidue.
Age.
Value.
Age.
Value.
Age.
Value.
37
12.069
27
12.728
17
13.205
7
13.496
36
12.144
26
12.785
16
13.244
6
13.421
35
12.219
25
12.843
15
13.283
5
13.275
34
12.295
24
12.900
14
13.321
4
12.997
33
12.370
23
12.958
13
13.360
3
12.630
32
12.445
22
13.015
12
13.399
2
11.959
31
12.502
21
13.033
11
13.418
1
11.168
30
12.558
20
13.091
10
13.433
0
9.650
29
12.615
19
13.129
9
13.457
28
13.671
18
13.167
8
13.477
iyPdfi
Google
508
TABLE XXI.
Value of £1 per Annum during the joint Continuance of IVo Lives.
(Carlisle 4^ per Cent.)
Older Age Thirty-Eight Years.
Age.
Value.
Age.
Valne.
Age.
Valae.
Age.
Value.
3d
11.890
28
12.551
18
13.048
8
13.385
37
11.969
27
12.610
17
13.084
7
13.360
36
12.047
26
12.669
16
13.120
6
13.286
35
12.126
25
12.729
15
13.155
5
13.142
34
12.204
, 24
12.788
14
13.191
4
12.87U
33
12.283
23
12.847
13
13.227
3
12.511
32
12.337
22
12.887
12
13.259
2
11.838
31
12.390
21
12.927
11
13.290 .
1
11.055
30
12.444
20
12.968
10
13.322
0
9.555
29
12.497
19
13.008
9
13.353
Older Age Thirty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Ago.
Value.
39
11.708
29
12.331
19
12.886
9
13.238
38
11.789
28
12.439
18
12.919
8
13.250
37
11.870
27
12.498
17
12.952
7
13.224
36
11.950
26
12.556
16
12.985
6
13.150
35
12.031
25
12.615
15
13.018
5
13.008
34
12.112
24
12.673
14
13.051
4
12.743
. 33
12.166
23
12.716
13
13.088
3
12.383
32
12.220
22
12.758
12
13.126
2
11.716
31
12.273
21
12.801
11
13.163
1
10.943
30
12.327
20
12.843
10
13.201
0
9.459
Older Age Forty Years.
Age.
Valttf.
Age.
Value.
Age.
18
Value.
Age.
Value.
40
11.531
29
12.279
12.786
7
13.088
39
11.613
28
12.334
17
12.817
6
13.015
38
11.695
27
12.388
16
12.848
5
12.875
37
11.776
26
12.443
15
12.879
4
12.611
36
' 11.858
25
12.498
14
12.918
3
12.255
33
11.940
24
12.543
13
12.956
2
11.595
34
11.997
23
12.588
12
12.995
1
10.830
33
12.054
22
12.634
11
13.033
0
9.364
32
12.110
21
12.679
10
13.072
31
12.167
20
12.724
9
13.104
30
12.224
19
12.755
8
13.115
^
TABLE XXI.
509
Value of £1 per Annum dnring the joint Continuance of Two livet.
(Carliile 4} per Cent)
Older Age Forty-One Years.
A«e.
Value.
A«e.
Valae.
Ag«.
Vidao.
Age.
Value.
41
11.369
30
12.125
19
12.629
8
12.979
40
11.450
29
12,176
18
12.659
7
12.952
39
11.531
28
12.228
17
12.690
6
12.879
38
11.611
27
12.279
16
12.721
5
12.740
37
11.692
26
12.330
15
12.757
4
12.480
36
11.773
25
12.377
14
12.794
3
12.127
35
11.833
24
12.425
13
12.830
2
11.473
34
11.893
23
12.472
12
12.867
1
10.717
33
11.954
22
12.520
11
12.903
0
9.267
32
12.014
21
12.567
10
12.937
31
12.074
20
12.598
9
12.969
Older Age Forty-Two Yean.
Ag«.
Valte.
Age.
ValM.
Age.
Value.
Age.
Value.
42
11.215
31
11.973
20
12.473
12.785
41
11.294
30
12.020
19
12.506
12.800
40
11.372
29
12.068
18
12.538
12.816
39
11.451
28
12.115
17
12.570
12.736
38
11.529
27
12.162
16
12.604
12.604
37
11.608
26
12.211
15
12.637
12.848
36
11.672
25
12.261
14
12.671
11.999
35
11.735
24
12.310
13
12.704
2
11.352
34
11.799
23
12.360
12
12.738
1
10.600
33
1U862
22
12.409
11
12.754
0
9.171
32
11.926
21
12.441
10
12.769
Older Age Forty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
43
11.064
32
11.818
21
12.313
10
12.655
42
11.140
31
11.862
20
12.352
9
12.682
41
11.215
30
11.907
19
12.386
8
12.709
40
11.291
29
11.951
18
12.420
7
12-667
39
11.866
28
11.996
17
12.451
6
12.597
38
11.442
27
12.047
16
12.481
5
12.469
37
11.508
26
12.098
15
12.512
4
12.217
36
11.574
25
12.148
14
12.542
3
11.871
35
11.641
24
12.199
13
12.573
2
11.220
34
11.707
23
12.250
12
12.600
1
10.483
33
U.77S
22
12.284
11
12.627
0
9.074
MO
TABLE XXI.
Value of £1 per Annam during the joint Continuanee of Two Lifet.
(Carligla4^perCeat)
Older Age Forty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
44
10.906
32
11.700
20
12.227
8
12.550
43
10.979
31
11.744
19
12.263
7
12.519
42
11.052
30
11.788
18
12.291
6
12.455
41
11.125
29
11.832
17
12.319
5
12.833
40
11.198
28
11.682
16
12.347
4
12.085
39
11.271
27
11.932
15
12.375
3
11.722
38
H.339
26
11.982
14
12.403
2
11.088
37
11.407
25
12.032
13
12.436
1
10.367
3G
11.476
24
12.082
12
12.468
0
8.978
35
11.544
23
12.118
11
12.501
34
11.612
22
I2.ir)4
10
12.533
33
11.656
21
12.191
9
12.566
Older Age Forty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
45
10.742
33
11.536
21
12.061
9
12.895
44
10.813
32
11.582
20
12.099
8
12.392
43
10.885
31
11.629
19
12.125
7
12.370
42
10.956
30
11.675
18
12.151
6
12.314
41
U.028
29
11.721
17
12.177
5
12.198
40
11.099
28
11.768
16
12.203
4
11.919
39
11.168
27
11.814
15
12.229
3
11.573
38
11.237
26
11.861
14
12.263
2
10.955
37
11.305
25
11.907
13
12.296
1
10.250
36
11.374
24
11.945
12
12.330
0
8.881
35
11.443
23
11.984
11
12.363
34
11.489
22
12.022
10
12.397
Older Age Forty-Six Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
46
10.565
34
11.362
22
11.885
10
12.212
45
10.638
33
11.412
21
11.925
9
12.224
44
10.710
32
11.461
20
11.9:)0
8
12.233
43
10.783
31
11.510
19
11.976
7
12.222
42
10.855
30
ll.5:)3
18
12.001
6
12.173
41
10.928
29
11.595
17
12.027
5
12.014
40
10.995
28
11.638
16
12.052
4
11.753
39
11.062
27
11.680
15
12.083
3
11.423
38
11.130
26
11.723
14
12.115
2
10.823
37
11.197
25
11.763
13
12.146
1
10.133
36
11.264
24
11.804
12
12.178
0
8*751
35
11.313
23
11.844
U
12.209
TOOgle
TABLE XXL
511
Value of £1 per Annum during the joint Contimiance of Two Llres.
(Garlbie 4^ per Cent.)
Older Age Forty-Seven Years.
Age.
Value.
Age.
Valae.
Age.
Value.
Age.
Value.
47
10.375
35
11.179
23
11.695
11
12.025
46
10.451
34
11.231
22
n.737
10
12.037
45
10.526
33
11.283
21
11.764
9
12.049
44
10.602
32
11.335
20
11.790
8
12.061
43
10.677
31
11.373
19
11.817
7
12.073
43
10.753
30
11.412
18
11.843
6
11.971
41
10.817
29
11.450
17
11.870
5
11.830
40
10.882
28
11.489
16
11.899
4
11.587
39
10.946
27
11.527
15
11.927
3
11.274
38
11.011
26
11.569
14
11.956
2
10.691
37
11.075
25
11.611
13
11.984
1
9.967
36
11.127
24
11.653
12
12.013
0
8.620
Older Age Forty-Eight Yean.
Age.
Value. .
Age.
Value.
Age.
Value.
Age.
Value.
48
10.166
35
11.036
22
11.563
9
11.893
47
10.247
34
11.090
21
11.591
8
11.916
46
10.328
33
11.144
20
11.619
7
11.854
45
10.408
32
11.179
19
11.647
6
11.768
44
10.489
31
11.214
18
11.675
5
11.645
43
10.570
30
11.250
17
11.701
4
•11.421
42
10.631
29
11.285
16
11.726
3
11.125
41
10.692
28
11.320
15
11.752
2
10.498
40
10.7.52
27
11.363
14
11.777
1
9.800
39
10.813
26
11.406
13
11.803
0
8.490
38
10.874
25
11.449
12
11.826
37
10.928
24
11.492
11
11.848
36
10.982
23
11.535
10
11.871
Oldc
sr Age Forty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
49
9.926
36
10.820
23
11.341
10
11.684
48
10.014
35
10.875
22
11.371
9
11.712
47
10.102
34
10.930
21
11.400
8
11.684
46
10.191
33
10.9G4
20
11.430
7
11.635
4)
)0.'279
32
10.999
19
11.460
6
11.566
44
10.367
31
11.033
18
11.483
5
11.461
43
10.424
30
11.068
17
11.506
4
11.255
42
10.482*
29
11.102
16
11.526
3
10.907
41
10.539
28
11.144
15
11.551
2
10.305
40
10.597
27
11.186
14
11.574
1
9.634
39
10.654
26
11.227
13
11.602
0
8.359
38
10.709
25
11.269
12
11.629
37
10.764
24
11.311
11
11,657
512
TABLE XXI.
Value of £1 per Annum duriu^ the joint Continuaace of Tiro Lives.
(Carlisle ^ per Cent)
Older Age Fifty Years.
Ase.
Valu«.
Age.
Valu«.
Age.
Valaa.
Age.
Value.
50
9.663
37
10.589
24
11.102
11
i 1.445
49
9.760
36
10.644
23
11.133
10
11.473
48
9.837
35
10.699
22
11.165
9
11.469
47
9.955
34
10.735
21
11.196
8
11.451
46
10.052
33
10.771
20
11.228
7
11.417
45
10.149
32
10.807
19
11.249
6
11.363
44
10.204
31
10.843
18
11.269
5
11.277
43
10.259
30
10.879
17
11.290
4
11.020
42
10.313
29
10.917
16
11.310
3
10.689
41
10.368
28
10.955
15
11.331
2
10.111
40
10.423
27
10.994
14
11.359
1
9.467
39
10.478
26
11.032
13
11.388
0
8.229
38
10.533
25
11.070
12
11.416
Older Age Fifty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
51
9.374
38
10.344
25
10.845
12
11.181
50
9.481
37
10.397
24
10.878
11
11.207
49
9.589
36
10.450
23
10.911
10
11.222
48
9.696
•35
10.488
22
10.944
9
11.226
47
9.804
34
10.526
21
10.977
8
11.219
46
9.911
33
10.565
20
10.997
7
11.198
45
9.966
32
10.603
19
11.017
6
11.161
44
10.021
31
10.641
18
11.037
5
11.028
43
10.076
30
10.675
17
11.057
4
10.785
42
10.131
29
10.709
16
11.077
3
10.472
41
10.186
28
10.744
15
11.103
2
9.918
40
10.239
27
10.778
14
11.129
1
9.301
39
10.292
26
10.812
13
11.155
0
8.053
Older Age Fifty-Two
Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
52
9.082
39
10.098
26
10.581
13
10.915
51
9.199
38
10.147
25
10.616
12
10.938
50
9.316
37
10.197
24
10.650
11
10.946
49
9.432
36
10.237
23
10.685
10
10.^54
48
9.549
35
10.277
22
10.719
9
10.963
47
9.666
34
10.318
21
10.740
6
10.971
46
9.723
33
10.358
20
10.760
7
10.979
45
9.779
32
10.398
19
10.781
6
10.902
44
9.836
31
10.428
18
10.801
5
10.779
43
9.892
SO
10.458
17
10.822
4
10.550
42
9.949
29
10.487
16
10.845
3
10.254
41
9.999
28
10.517
15
10.868
2
9.725
40
10.048
27
10.547
14
10.892
1
0
9.089
7.877
TABLE XXI.
513
Value of £1 per Annam during the joint Continuance of Two Lives.
(Carlisle 4^ per Cent) /
Older Age Fifty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
53
8.786
42
.9.757
31
10.199
20
10.520
9
10.736
52
8.911
41
9.803
30
10.226
19
10.542
8
10.754
51
9.035
40
9.848
29
10.252
18
10.564
7
10.712
50
9.160
39
9.894
23
10.279
17
10.534
6
10.644
49
9.284
38
9.939
27
10.314
16
10.604
5
10.530
48
9.409
37
9.980
26
10.349
15
10.625
4
10.315
47
9.470
36
10.022
25
10.384
14
10.645
3
10.036
46
9.530
35
10.063
24
10.419
13
10.665
2
9.490
45
9.591
34
10.105
23
10.454
12
10.683
1
8.877
44
9.651
33
10.146
22
10.476
11
10.701
0
7.700
43
9.712
32
10.173
21
10.498
10
10.718
Older A
ge Fifty-Four Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
10
Value.
54
8.485
43
9.509
32
9.937
21
10.252
10.476
53
8.615
42
9.551
31
9.963
20
10.276
9
10.498
52
8.745
41
9.592
30
9.988
19
10.299
8
10.480
51
8.875
40
9.634
29
10.014
18
10.317
7
10.445
50
9.005
39
9.675
28
10.048
17
10.334
6
10.385
49
9.135
38
9.717
27
10.081
16
10.352
5
10.281
48
9.202
37
9.759
26
10.115
15
10.369
4
10.080
47
9.268
36
9.802
25
10.148
14
10.387
3
9.780
46
9.335
35
9.844
24
10.182
13
10.409
2
9.254
45
9.401
34
9.886
23
10.205
12
10.431
1
8.665
44
9.468
33
9.912
22
10.229
11
10.454
0
7.524
Older Age Fifty-Five Years.
Age.
Value.
Age.
Value.
9.292
Age.
31
Value.
Age.
Value.
Age.
Value.
55
8.174
43
9.723
19
10.040
7
10.177
54
8.308
42
9.331
30
9.750
18
10.056
6
10.127
53
8.442
41
9.369
29
9.780
17
10.071
5
10.032
52
8.576
40
9.408
28
9.810
16
10.087
4
9,814
51
8.710
39
9.450
27
9.841
15
10.102
3
9.524
50
8.844
38
9.491
26
9.871
14
10.125
2
9.019
49
8.918
37
9.533
25
9.901
13
10.148
1
8.453
48
8.992
36
9.574
24
9.926
12
10.170
0
7.34S
47
9.067
35
9.616
23
9.951
11
10.193
46
9.141
34
9.643
22
9.975
10
10.216
45
9.215
33
9.C70
21
10.000
9
10.221
44
9.254
32
9.696
20
10.025
8
10.206
Digiti;
3d i^ Google
514
TABLE XXI.
Value of £1 per Annum during^ the joint Continuance of Two Livei.
(Carligle 4^ per Cent)
Older Age Fifty-Six YeaiB.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
56
7.856
41
9.143
26
9.613
11
9.919
55
7.993
40
9.182
25
9.639
10
9.943
54
8.129
39
9.221
24
9.665
9
9.9J5
63
8.266
38
9.260
23
9.691
8
9.931
52
8.402
37
9.299
22
9.717
7
9.910
51
8.539
36
9.338
21
9.743
6
9.868
50
8.622
35
9.367
20
9.758 -
5
: 9.763
49
8.705
34
9.395
19
9.773
4
9.547
48
8.787
33
9.424
18
9.787
3
9.269
;47
8.870
32
9.452
17
9.802
2
8.783
;46
8.953
31
9.481
16
9.817
1
8.241
'45
8.991
30
9.507
15
9.837
0
7.157
'44
9.029
29
9.534
14
9.858
43
9.067
28
9.660
13
9.878
42
9.105
27
9.587
12
9.899
Older Age Fifty -Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age,
Value.
57
7.531
42
8.875
27
9.316
12
9.618
56
7.670
41
8.911
26
9.343
n
9.623
55
7.810
40
8.947]
25
9.370
10
9.628
54
7.949
39
8.982
24
9.397
9
9.633
53
8.089
38
9.018
23
9.424
8
9.638
52
8.228
37
9.054
22
9.451
7
9.643
51
8.318
36
9.084
21
9.466
6
9.607
50
8.409
35
9.114
20
9.482
5
9.494
49
8.499
34
9.143
19
9.497
4
9.281
48
8.590
33
9.173
18
9.513
3
9.013
47
8.680
32
9.203
17
9.528
2
8.548
46
8.719
31
9.226
16
9.546
1
8.026
45
8.758
30
9.248
15
9.564
0
6.965
44
8.797
29
9.271
14
9.582
43
8.836
28
9.293
13
9.600
Digitized by LjOOQ iC
TABLE XXI.
515
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 4) per Cent)
Older Age Fifty-Eight Years.
Age.
Vslue.
Age.
Value.
Agi".
Value.
Age.
Value.
58
7.210
43
8.611
28
9.021
13
9.317
57
7.352
42
8.643
27
9.043
12
9.330
56
7.493
41
8.674
26
9.076
11
9.343
55
7.635
40
8.706
25
9.103
10
9.357
54
7.776
39
8.737
24
9.131
9
9.370
53
7.918
38
8.769
23
9.158
8
9.383
52
8.015
37
8.800
22
9.174
7
9.393
51
8.112
36
8.831
21
9.191
6
9.345
50
8.208
35
8.861
20
9.207
5
9.224
49
8.305
34
8.892
19
9.224
4
9.014
48
8.402
33
8.923
18
9.240
3
8.757
47
8.444
32
8.943
17
9.255
2
8.328
46
8.486
31
8.962
16
9.271
1
7.811
45
8.527
30
8.982
15
9.286
0
6.774
44
8.569
29
9.001
14
9.302
Older Age Fifty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
59
6.912
44
8.358
29
8.745
14
9.029
58
7.053
43
8.386
28
8.771
13
9.046
57
7.194
42
8.414
27
8.798
12
9.063
56
7.336
41
8.441
26
8.824
11
9.081
55
7.477
40
8.469
25
8.851
10
9.098
54
7.618
39
8.497
24
8.877
9
9.115
53
7.719
38
8.528
23
8.894
8
9.145
52
7.821
37
8.559
22
8.912
7
9.143
51
7.922
36
8.591
21
8.929
6
9.084
50
8.024
35
8.622
20
8.947
5
8.955
49
8.125
34
8.653
19
8.964
4
8.748
48
8.172
33
8.671
18
8.977
3
8.535
47
8.218
32
8.690
17
8.990
2
8.108
46
8.265
31
8.708
16
9.003
1
7.597
45
8.311
30
8.727
15
9.016
0
6.582
Digitgel^big^UU
gte
516
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Tiro Lives.
(Carlisle 4^ per Cent.)
Older Age Sixty Yean.
Age.
Value.
Age.
Viilue.
Age.
Value.
Age.
Value.
6')
6.650
44
8.148
28
8.5^5
12
8.817
59
6.787
43
8.173
27
8.568
11
8.834
58
6.923
42
8.198
26
8.592
10
8.852
57
7.060
41
8.223
25
8.615
9
8.884
56
7.196
40
8.248
24
8.634
8
8.907
55
7.333
39
8.279
23
8.653
7
8.894
54
7.438
38
8.309
22
8.671
6
8.822
53
7.54 i
37
8.340
21
8.690
5
8.686
52
7.649
36
8.370
20
8.709
4
8.526
51
7.754
35
8.401
19
8.720
3
8.313
50
7.859
34
8.420
18
8.731
2
7.889
49
7.912
33
8.440
17
8.742
1
7.382
48
7.965
32
8.459
16
8.753
0
6.391
47
8.017
31
8.479-
15
8.764
46
8.070
30
8.498
14
8.782
45
8.123
29
8.521
13
8.799
Older Age Sixty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
61
6.439
45
7.939
29
8.322
13
8.582
60
6.566
44
7.963
28
8.343
12
8.598
59
6.693
43
7.987
27
8.363
U
8.614
58
6.820
42
8.011
26
8.383
10
8.623
57
6.947
41
8.035
25
8.403
9
8.654
56
7.074
40
8.063
24
8.423
8
8.669
55
7.182
39
8.092
23
8.443
7
8.644
54
7.290
38
8.120
22
8.463
6
8.561
53
7.397
37
8.149
21
8.483
5
8.460
52
7.505
36
8.177
20
8.493
4
8.304
51
7.613
35
8.198
19
8.504
3
8.092
50
7.673
34
8.219
18
8.514
2
7.669
49
7.734
33
8.240
17
8.525
1
7,167
48
7.794
32
8.261
16
8.535
0
6.232
47
7.855
31
8.282
15
8.551
46
7.915
30
8.302
14
8.567
Digitized by VjOOQ IC
TABLE XSL
617
Value of £1 per Annnm during the joint Continuance of Two Lives.
(Carlisle 4^ per Cent)
Older Age Sixty-Two Years.
Age.
Value.
Ag*'.
Valae.
Ag«.
Value.
Ag«.
Value.
62
6.238
42
7.830
22
8.258
2
7.449
61
6.353
41
7.855
21
8.269
1
6.976
60
6.469
40
7.881
20
8.280
0
6.073
59
6.584
39
7.906
19
8.291
6S
6.700
38
7.932
18
8.302
57
6.815
37
7.957
17
8.313
56
6.926
36
7.979
16
8.327
55
7.037
35
8.001
15
8.340
54
7.148
34
8.024
14
8.354
53
7.259 •
33
8.046
13
8.367
52
7.370
32
8.068
12
8.381
51
7.437
31
8.085
11
8.384
50
7.505
30
8.102
10
8.386
49
7.672
29
8.119
9
8.389
48
7.640
28
8.136
8
8.391
47
7.707
27
8.153
7
8.394
46
7.732
26
8.174
6
8.326
45
7.756
26
8.195
5
8.235
44
7.781
24
8.216
4
8.082
43
7.805
23
8.237
3
7.870
Older Age Sixty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
63
6.035
43
7.624
23
8.028
3
7.648
62
6.139
42
7.646
22
8.040
2
7.233
61
6.243
41
7.668
21
8.052
1
6.783
60
6.348
40
7.689
20
8.063
0
6.913
59
6.452
39
7.711
19
8.075
58
6.556
38
7.733
18
8.087
57
6.670
37
7.756
17
8.098
56
6.784
36
7.779
16
8.110
55
6.897
35
7.803
15
8.121
54
7.011
34
7.826
14
8.133
53
7.125
33
7.849
13
8.144
62
7.198
32
7.863
12
8.151
51
7.271
31
7.877
11
8.164
50
7. 345
30
7.892
10
8.173
49
7.418
29
7.906
9
8.183
48
7.491
28
7.920
8
8.193
47
7.618
27
7.942
7
8.147
46
7.544
26
7.963
6
8.091
45
7.571
25
7.98:>
6
8.009
44
7.597
24
8.006
4
7.860
Digitized by VjOOQIC
518
TABLB XXI.
Value of £1 per Annum during the jobt Gontinninee of Tiro liret.
(Carlisle ^ per Cent.)
Older Age Sixty-Four Yean.
'Age.
Valoe.
Age.
Valve
Age.
Value.
Age.
ValiUL
64
5.818
44
7,407
24
7.785 .
4
7.638
63
5.914
43
7.425
23
7.798
3
7.408
62
6.011
42
7.443
22
7.811
2
7.016
61
6.107
41
7.461
21
7.823
1
6.590
60
6.204
40
7.479
20
7.836
0
5.754
59
6.300
39
7.497
19
7.849
58
6.414
38
7.521
18
7.858
57
6.527
37
7.544
17
7.868
56
6.^41
36
7.568
16
7.877
55
6.754
35
7.591
15
7,887
54
6.868
34
7.615
14
7,896 J
53
6.945
33
7,628
13
7.909
^
52
7.022
32
7.641
12
7.922
""
51
7.100
31
7.655
\l
7.936
50
7.177
30
7.668
10
7.949
49
7.254
29
7.681
9
7.962
48
7.285
28
7.702
8
7.934
47
7.315
27
7.723
7
7.901
46
7.346
26
7.743
6
7.856
45
7.376
25
7.764
5
7.784
Older Age Sirty-Five Years.
Age.
V«Iae.
Ago.
Value.
Age.
Value.
Age.
Value.
65
5.594
45
7.182
T 25
7.532
5
7.558
64
5.686
44
7.197
^ 24
7.546
4
7.379
63
5.779
43
7.212
23
7.560
3
7.167
62
5.871
42
7.227
22
7.574
2
6.800
61
5.964
41
2.242
21
7.588
1
6.398
60
6.056
40
7.257
20
7.602
0
5.595
59
6.165
39
7.280
19
7.610
58
6.275
38
7.303
18
7.617
57
6.384
37
7.326
17
7.625
56
6.494
36
7.349
16
7.632
«
55
6.6031
35
7.372
15
7.640
54
6.683
34
7.386
14
7.654
53
6.763
33
7.400
13
7.668
52
6.844
32
7.414
12
7.681
51
6.924
31
7.428
11
7.695
50
7.004
30
7.442
10
7.709
49
7.040
29
7.460
9
7.692
48
7.075
28
7.478
8
7.676
47
7.111
27
7.496
7
7.654
46
7.146
26
7.514
6
7.621
Digitized by VjUUVIC
TABLE XXI.
519
Valu0 of £1 per Annum during the joint Continuance of Two Livoi*
(CarHile4i pet Cent)
Older Age Sizty*Siz Yean.
Age.
Valae.
Age.
Valutt.
Age.
Value.
Age.
Value.
66
5.357
46
6.944
26
7.269
6
7.386
65
5.451
45
6.958
25
7.284
5
7.282
64
5.545
44
6.972
24
7.299
4
7.120
63
5.640
43
6.985
23
7.313
3
6.927
62
5.734
42
6.999
22
7.328
2
6.583
61
5.828
41
7.013
21
7.343
1
6.206
60
5.928
40
7.034
20
7.350
0
5.399
59
6.028
39
7.055
1»
7.3:)7
58
6.127
38
7.075
18
7.364
57
6.227
37
7.096
17
7.371
56
6.327
36
7.117
16
7.378
55
6.409
35
7.132
15
7.390
54
6:491
34
7.147
14
7.402
53
6.573
33
7.163
13
7.415
52
6.655
32
7.178
12
7.427
51
6.737
31
7.193
n
7.439
50
6.778
30
7.208
10
7.428
49
6.820
29
7.223
9
7.422
43
6.861
28
7.239
8
7.417
47
6.903
27
7.254
7
7.408
Older Age Sixty-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
67
5.106
47
6.693
27
6.992
7
7.161
66
5.204
46
6.707
26
7.008
6
7.095
65
5.302
45
6.720
25
7.024
5
7.006
64
5.401
44
6.734
24
7.039
4
6.861
63
5.499
43
6.747
23
7.055
3
0.686
62
5.597
42
6.761
22
7.071
2
6.367
61
5.685
41
6.779
21
7.078
1
5.967
60
6.774
40
6.797
20
7.085
0
5.204
59
5.862
39
6.814
19
7.093
58
5.951
38
6.832
18
7.100
57
6.039
37
6.850
17
7.108
56
6.123
36
6.866
16
7.117
55
6.207
35
6.882
15
7.127
54
6.291
34
6.899
14
7.137
53
6.375
33
6.915
13
7.148
52
6.459
32
6.931
12
7.158
51
6.506
31
6.943
11
7.159
50
6.553
30
6.955
10
7.159
49
6.599
29
6.968
9
7.160
48
6.646
28
6.980
8
7.160
Digitized by VjOOQ iC.
520
TABLB XXI.
Value of £1 per Annum daring the joint Continoanee of Two Lives.
(Carliile 4} per Gent.)
Older Age Sixty-Eight Yean.
Ajje.
Value.
Age.
ValiM.
Age.
ValM.
Age.
Value.
68
4.843
48
6.427
28
6.706
8
6.900
67
4.946
47
6.442
27
6.722
7
6.862
66
5.049
46
6.457
26
6.738
6
6.803
65
5.153
45
6.471
25
6.754
5
6.729
64
5.256
44
6.486
24
6.770
4
6.602
63
5,359
43
6.501
23
6.786
3
6.446
62
5.436
42
6.515
22
6.794
2
6.105
61
5.513
41
6.530
21
6.802
1
5.729
60
5.591
40
6.544
20
6.810
0
5.0C8
59
5.668
39
6.559
19
6.818
53
5.745
38
6.573
18
6.826
57
5.831
37
6.590
17
6.834
56
5.916
36
6.607
16
6.842
55
6.002
35
6.623
15
6.851
54
6.087
34
6.640
14
6.859
53
6.173
33
6.657
13
6.867
52
6.2-24
32
6.667
12
6.874
51
6.275
31
6.677
11
6.880
50
6.325
30
6.686
10
6.887
49
6.376
29
6.696
9
6.893
Older Age Sixty-Nine Years.
Age.
Value.
Age.
Value.
Age.
Valup.
Age.
Value.
69
4.566
49
6.143
29
6.414
9
6.612
68
4.674
48
6.160
28
6.429
8
6.602
67
4.782
47
6.178
27
6.444
7
6.563
66
4.890
46
6.195
26
6.460
6
6.512
65
4.998
45
6.213
25
6.475
5
6.453
64
5.106
44
6.230
24
6.490
4
6.343
63
5.175
43
6.241
23
6.499
3
6.169
62
5.244
42
6.252
22
6.507
2
5.842
61
5.314
41
6.263
21
6.516
1
5.490
60
5.383
40
6.274
20
6.524
0
4.813
59
5.452
39
6.285
19
6.533
58
5.537
38
6.302
18
6.539
57
5.622
37
6.319
17
6.545
56
5.706
36
6.336
16
6.552
55
5.791
35
6.353
15
6.558
54
5.876
34
6.370
14
6.564
53
5.929
3)
6.379
13
6.574
52
5.983
32
6.388
12
6.583
51
6.036
31
6.396
11
6.593
50
6.090
30
6.405
10
6.602
[_
Digitized by LjOOQ IC
TABLB XXI.
521
Value of £1 per Anaum during the joint Continuance of Two lire^*
(Carlisle 4^ per Cent.)
Older Age Seventy
Years.
Ak«.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
70
4.278
50
5.845
30
6.118
10
6.303
69
4.391
49
5.866
29
6.131
9
6.324
68
4.504
48
5.887
28
6.144
8
6.304
67
4.618
47
5.907
27
6.157
7
6.264
66
4.731
46
5.928
26
6.170
6
6.220
65
4.844
45
5.949
25
6.183
5
6.177
64
4.908
44
5.957
24
6.192
4
6.067
63
4.973
43
5.965
23
6.202
3
5.892
62
5.037
42
5.974
22
6.211
2
5.580
61
5.102
41
5.982
21
6.221
1
5.252
60
5.166
40
5.990
20
6.230
0
4.617
59
5.246
39
6.006
19
6.235
58
5.327
38
6.023
18
6.240
57
5.407
37
6.039
17
6.244
56
5.488
36
6.056
16
6.249
55
5.568
35
6.072
15
6.254
54
5.623
34
6.081
14
6.264
53
5.679
33
6.090
13
6.274
52
5.734
32
6.100
12
6.283
51
5.790
31
6.109
11
6.293
Older Age Seventy-One Years.
Ago.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
71
3.970
51
5.528
31
5.811
11
5.977
70
4.089
50
5.553
30
5.822
10
6.037
69
4.208
49
5.578
29
5.832
9
6.036
68
4.328
48
5.604
28
5.843
8
6.006
67
4.447
47
5,629
27
5.853
7
5.965
66
4.566
46
5.654
26
5.864
6
5.929
65
4.631
45
5.661
25
5.874
5
5.916
64
4.696
44
5.668
24
5.884
4
5.791
63
4.760
43
5.674
23
5.894
3
5.616
62
4.825
42
5.681
22
5.904
2
5.317
61
4.890
41
5.688
21
5.914
1
5.013
60
4.962
40
5.702
20
5.918
0
4.429
59
5,033
39
5.717
19
5.922
58
5.105
38
5.731
18
5.9-26
57
5.176
37
5.746
17
5.930
56
5.248
36
5.760
16
5.934
55
5.304
35
5.770
15
5.943
54
5.360
34
5.780
14
5.951
53
5.416
33
5.791
13
5.960
.
52
5.472
32
5.801
12
5.968
Digitized by
Googk
522
TABLE XXI.
Value of £1 per Annum daring the Joint ContinuaDce of Tiro Lires*
(Cailitto^perCent.)
Older Age Seventy-Two Years.
AgB.
Value.
Age.
Value.
Age.
\m\w.
Age.
Value.
72
3.684
52
5.227
32
5.518
12
5.669
71
3.806
51
5.256
31
5.526
11
5.668
70
3.928
50
5.285
30
5.534
10
5.668
69
4.051
49
5.314
29
5.543
9
5.667
6S
4.173
48
5.343
28
5.551
8
5.667
67
4.295
47
5.372
27
5.559
7
5.666
66
4.362
46
5.378
26
5.570
6
5.689
65
4.429
45
5.384
25
5.580
5
5.654
64
4.497
44
5.391
24
5.591
4
5.516
63
4.564
43
5.397
23
5.601
3
5.339
62
4.631
42
5.403
22
5.612
2
5.055
61
4.693
41
5.415
21
5.616
1
4.815
60
4.754
40
5.427
20
5.621
0
4.241
59
4.816
39
5.440
19
5.6-25
58
• 4.877
38
5.452
18
5.630
57
4.939
37
5.464
17
5.634
56.
4.997
36
5.475
16
5.641
55
5.054
35
5.486
15
5.648
54
5. 112
34
5,496
14
5.655
53
5.169
33
5.507^
13
5.662
Older Age Seventy-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
13
Value.
73
3.433
53
4.952
33
5.252
5.389
72
3.554
52
4.984
32
6.258
12
5. 393
71
3.676
51
5,017
31
5.264
11
5.397
70
3.797
50
5.049
30
5.271
10
5.402
69
3.919
49
5.082
29
5.277
9
5.406
68
4.040
48
5.114
28
5.283
8
5.410
67
4.111
47
5.121
27
5.294
7
5.448
66
4.182
46
5.128
26
5.305
6
5.449
65
4.253
45
5.134
25
5.316
5
5.393
64
4.324
44
5.141
24
5.327
4
5.240
63
4.395
43
5.148
23
5.338
3
5.062
62
4.447
42
5.157
22
5.343
2
4.863
61
4.500
41
5.167
21
5.348
1
4.617
60
4.552
40
5.176
20
5.352
0
4.054
59
4.605
39
5.186
19
5.357
58
4.657
38
5.195
18
5.362
57
4.716
37
5.206
17
5.367
56
4.775
36
5.218
16
5.373
55
4.834
35
5.229
15
5.378
54
4.893
34
5.241
14
5.384
Digitized by LjOOQ iC
TABLB XXI.
a23
Valtid of £l per Annum during the joiut Continiiance of Two LiYes.
(Cailisle.4^ per Cent)
Older Age Sevaity-Four Years.
Age.
Value.
Age.
Valae.
Age.
Valoe.
Age.
Value.
74
3.221
54
4.705
34
5.013
14
5.140
73
3.337
53
4.740
33
5.019
13
5.147
72
3.454
52
4.775
32
5.024
12
5.153
71
3.570
51
4.809
31
5.030
11
5.160
70
3.687
50
4.844
30
5.035
10
5.166
69
3.803
49
4.879
29
5.041
9
5.173
68
3.878
48
4.888
28
5.052
6
5.209
67
3.954
47
4.896
27
5.062
7
5.230
66
4.029
46
4.905
26
5.073
6
5.209
65
4.105
45
4.913
25
5.083
5
5.131
64
4.180
44
4.922
24
5.094
4
4.964
63
4.226
43
4.929
23
5.099
3
4.876
62
4.272
42
4,935
22
5.104
2
4.672
61
4.316
41
4.942
21
5.110
1
4.419
60
4.364
40
4.948
20
5.115
0
3.866
59
4.410
39
4.955
19
5.120
58
4.469
38
4.967
18
5.124
57
4.528
37
4.978
17
5.128
56
4.587
36
4.990
16
5.132
55
4.646
35
5.001
15
5.136
Older Age Seventy-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
75
3.066
55
4.497
35
4.817
15
4.937
74
3.172
54
4.534
34
4.823
14
4.944
73
3.277
53
4.571
33
4.829
13
4.951
72
3.383
52
4.607
32
4.835
12
4.958
71
3.488
51
4.644
31
4.841
11
4.965
70
3.594
50
4.681
30
4.847
10
4.972
69
3.675
49
4.692
29
4.856
9
4.979
68
3.756
48
4.704
28
4.865
8
5.009
67
3.838
47
4.715
27
4.874
7
5.013
66
3.919
46
4,727
26
4.883
6
4.969
65
4.000
45
4.738
25
4.892
5
4.870
64
4.043
44
4.742
24
4.898
4
4.778
63
4.085
43
4.746
23
4.904
3
4.689
62
4.128
42
4.751
22
4.910
2
4.480
61
4.170
41
4.755
21
4.916
I
4.221
60
4.213
40
4.759
20
4.922
0
3.678
59
4.270
39
4.771
19
4.925
58
4.327
38
4.782
18
4.928
57
4.383
37
4.794
17
4,931
56
4.440
36
4.805
16
4.934
Digitized by VjOOQ iC
524
TABLBXXI.
Value of £1 per Annum during the joint Gouttnuance of Two Liret
(Carlisle 4| per Cent)
Older Age Seventy-Six Yean.
Aga.
Value.
Age.
Value.
Age,
Value.
Age.
Value.
76
2.917
56
4.291
36
4.624
16
4.740
75
3.009
55
4.329
35
4.631
15
4.746
74
3.101
54
4.367
34
4.637
14
4.752
73
3.194
53
4.406
33
4.644
13
4.758
72
3.286
52
4.444
32
4.650
12
4.764
71
3.378
51
4.482
31
4.657
11
4.770
70
3.466
50
4.497
30
4.664
10
4.779
69
3.555
49
4.512
29
4.672
9
4.784
68
3.643
48
4.526
28
4.679
8
4.808
67
3.732
47
4.541
27
4.687
7
4.795
66
3.820
46
4.556
26
4.694
6
4.729
65
3.863
45
4.559
25
4.701
5
4.681
64
3.906
44
4.562
24
4.708
4
4.592
63
3.950
43
4.565
23
4.714
3
4.503
62
3.993
42
4.563
22
4.721
2
4.289
61
4.036
41
4.571
21
4.728
I
4.023
60
4.087
40
4.562
20
4.730
0
3.542
59
4.138
39
4.592
19
'4.733
56
4.189
38
4.603
18
4.735
57
4.240
37
4.613
17
4.738
Older
Age Seventy-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
77
2.788
57
4.096
37
4.444
17
4.558
76
2.867
56
4.136
36
4.4)1
16
4.563
75
2.945
55
4.176
35
4.459
15
4.568
74
3.024
54
4.217
34
4.466
14
4.574
73
3.102
53
4.257
33
4.474
13
4.579
72
3.181
52
4.297
32
4.481
12
4.564
71
3.274
51
4.315
31
4.487
11
4.583
70
3.367
50
4.333
30
4.492
10
4.581
69
3.461
49
4.332
29 •
4.498
9
4.580
68
3.554
48'
4.370
28
4.503
8
4.578
67
3.647
47
4.388
27
4.509
7
4.577
66
3.693
46
4.390
26
4.516
6
4.534
65
3.739
45
4.392
25
4.524
5
4.491
64
3.784
44
4.395
24
4.531
4
4.406
63
3.830
43
4.397
23
4.539
3
4.316
62
3.876
42
4.399
22
4.546
2
4.097
61
3.920
41
4.408
21
4.548
1
3.862
60
3.964
40
4.417
20
4.551
0
3.407
59
4.008
39
4.426
19
4.553
58
4.052
38
4.435
18
4.556
Digitized by VjOOQ IC
TABLB XXI.
52
Value of £1 per Annttm during the joint Continuance of Two Livei*
(Carlisle 4} per Cent.)
Older Age Seventy-Eight Years.
Age.
Value.
Age.
Value.
Age.
V&lue.
Age.
Value.
78
2.657
58
3.897
38
4.260
18
4.374
77
2.725
57
3.939
37
4.268
17
4.378
n
2.793
56
3.982
36
4.276
16
4.382
75
2.861
55
4.024
35
. 4.284
15
4.385
74
2.929
54
4.067
34
4.292
14
4.389
73
2.997
53
4.109
33
4.300
13
4.393
72
3.091
52
4.130
32
4.304
12
4.396
7\
3.186
51
4.151
31
4.308
11
4.399
70
3.280
50
4.171
30
4.312
10
4.401
69
3.375
49 •
4.192
29
4.316
9
4.404
68
3.469
48
4.213
28
4.320
8
4.407
67
3.518
47
4.216
27
4.328
7
4.378
66
3.567
46
4.218
26
4.336
6
4.339
65
3.616
45
4.221
25
4.344
5
4.302
64
3.665
44
4.223
24
4.352
4
4.220
63
3.714
43
4.226
23
4.360
3
4.130
62
3.751
42
4.233
22
4.363
2
3.922
61
3.787
41
4.240
21
4.366
1
3.701
60
3.824
40
4.246
20
4.368
0
3.271
59
3.860
39
4.253
19
4.371
Older Age Seventy-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
79
2.496
59
3.683
39
4.051
19
4.165
78
2.559
58
3.726
38
4.060
18
4.168
77
2.622
57
3.769
37
4.068
17
4.170
76
2.686
56
3.811
36
4.077
16
4.173
75
2.749
55
3.854
35
4.085
15
4.175
74
2.812
54
3.897
34
4.094
14
4.178
73
2.903
53
3.920
33
4.097
13
4.183
72
2.993
52
3.942
32
4.100
12
4.187
71
3.084
51
3.965
31
4.104
11
4.192
70
3.174
50
3.987
30
4.107
10
4.196
69
3.265
49
4.010
29
4.110
9
4.201
68
3.318
48
4.014
28
4.118
8
4.205
67
3.370
47
4.018
27
4.126
7
4.180
66
3.423
46
4.021
26
4.133
6
4.143
65
3.475
45
4.025
25
4.141
5
4.112
64
3.528
44
4.029
24
4.149
4
4.034
63
3.559
43
4.033
23
4.152
3
3.943
62
3.590
42
4.038
22
4.155
2
3.748
61
3.621
41
4.042
21
4.159
1
3.541
60
3.652
40
4.047
20
4.162
0
3.136
Digitized by VjOOQ
Te
52«
TABLB XXL
Value of £1 per Ammni daring the joint CoDtinuanee of Tiro Livet.
(Cariisle ^ per Cent.)
Older Age Eighty
Years.
Age.
Value.
Ag«.
Value.
Age.
Value.
Age.
Value.
80
2.356
59
3.534
38
3.877
17
3.977
79
2.417
58
3.575
37
3.885
16
3.979
78
2.479
57
3.617
36
3.894
15
3.981
77
2.540
56
3.658
35
3.902
14
3.986
76
2.602
55
3.699
34
3.906
13
3.991
75
2.663
54
3.723
33.
3.909
12
3.996
74
2.744
53
3.747
32
3.91^
11
4.001
73
2.826
52
3.771
31
3.916
10
4.006
72
2.907
51
3.795
30
3.92Q
9
4.002
71
2.989
50
3.819
29
3.927
8
4.003
70
3.070
49
3.825
28
3.933
7
3.981
69
3.127
48
3.830
27
3.940
6
3.948
68
3.184
47
3.836
26
3.946
5
3.923
67
8.242
46
3.841
25
3.953
4
3.844
66
8.299
45
3.847
24
3.957
3
3.755
65
3.356
44
3.850
23
3.961
2
3.573
64
3.383
43
3.852
22
3.964
I
3.380
63
3.411
42
3.855
21
3.968
0
3.000
62
3.438
41
3.857
20
3.972
61
3.466
40
3.860
19
3.974
60
3.493
39
3.868
18
3.976
Older Age Eighty-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value,
81
2.192
61
3.300
41
3.653
21
3.759
80
2.254
60
3.336
40
3.661
20
3.760
79
2.316
59
3.372
39
3.668
19
3.762
78
2.379
58
3.409
,18
3.676
18
3.763
77
2.441
57
3.445
37
3.683
17
3.765
76
2.503
56
3.481
36
3.691
16
3.766
75
2.573
55
3.506
35
3.695
15
3.770
74
2.643
54
3.531
34
3.699
14
3.775
73
2.712
53
3.556
33
• 3.704
13
8.779
72
2.782
52
3.581
32
3.708
12
3.784
71
2.852
51
3.606
31
3.712
11
3.788
70
2.914
50
3.614
*30
3.717
10
3.806
69
2.977
49
3.622
29
8.722
9
3.804
68
3.039
48
3.630
28
3.728
8
3.801
67
3.102
47
3.638
27
3.733
7
3.783
66
3.164
46
3.646
26
3.738
6
3.753
65
3.191
45
3.647
25
3.742
5
3.727
64
8.218
44
3.649
24
3.746
4
3.654
63
3.246
43
3.650
23
3.751
3
3.568
62
3.273
42
3.652
22
3.755
2
1
3.399
3.219
Digitized by ^^UUV
le
TABLE XXI.
527
Value of £1 per Annum during the joint Conlinuanee of Tvo Lives.
(Carlisle 4} per Cent)
Older Age Kighty-Two Yean.
Age.
Value.
Age.
Value.
Age.
Valne.
Age.
Value.
82
2.053
62
3.129
42
3.469
22
3.567
81
2.116
61
3.159
41
3.475
21
3.568
80
2.179
60
3.190
40
3.482
20
3.570
79
2.241
59
3.220
39
3.488
19
3.571
78
2.304
58
3.251
38
3.495
18
3.573
77
2.367
57
3.281
37
3.501
17
3.574
76
2.425
56
3.307
36
3.506
16
3.578
75
2.483
55
3.334
35
3.510
15
3.581
74
2.640
54
3.360
34
3.515
14
3.585
73
2.598
53
3.387
33
3.519
13
3.588
72
2.656
52
3.413
32
3.524
12
3.592
71
2.722
51
3.423
31
3.528
11
3.590
70
2.788
50
3.434
30
3.532
10
3.589
69
•2.854
49
3.444
29
3.535
9
3.587
68
2.920
48
3.455
28
3.539
8
3.586
67
2.986
47
3.465
27
3.543
7
3.584
66
3.015
46
3.466
26
3.548
6
3.562
65
3.043
45
3.467
25
3.5.'>3
5
3.532
64
3.072
44
3.467
24
3.557
4
3.464
63
3.100
43
3.468
23
3.562
3
2
3.380
3.224
Older Age Eighty-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
83
1.905
63
2.953
43
3.280
23
3.369
82
1.969
62
2.978
42
3.285
22
3.370
81
2.033
61
3.002
4\
3.290
21
3.372
80
2.096
60
3.027
40
3.294
20
3.373
79
2.160
59
3.0JI
39
3.299
19
3.875
78
2.224
58
3.076
38
3.304
18
3.376
77
2.272
57
3.104
37
3.309
17
3.379
76
2.321
56
3.132
36
3.314
16
3.382
75
2.369
55
3.159
35
3.320
15
3.384
74
2.418
54
3.187
34
3.325
14
3.387
73
2.466
53
3.215
33
3.330
13
3.390
72
2.533
52
3.227
32
3.332
12
3.391
71
2.600
51
3.239
31
3.335
11
3.393
70
2.666
50
3.252
30
3.337
10
3.394
69
2.733
49
3.264
29
3.340
9
3.396
68
2.800
48
3.276
28
3.342
8
3.397
67
2.831
47
3.277
27
3.347
7
3.401
66
2.861
46
3.278
26
3.353
6
3.371
65
2.892
45
3.278
25
3. aw
5
3.336
64
2.922
44
3.279
24
3.364
4
3
3.274
3.193
Digitized by VjVJiJ
gle
528
TABLE XXI.
Value of £1 per Annum during the joint Contmuaaoe of Two Livei.
(Carlisle 4) per Cent)
Older Age Eighty-Four Years.
Age.
Value.
Age.
Value.
Age.
Vaine.
Age.
Value.
84
1.762
64
2.779
44
3.096
24
3.175
83
1.824
63
2.799
43
3.099
23
3.177
82
1.886
62
2.819
42
3.102
22
3.179
81
1.948
61
2.839
41
3.106
21
3.180
80
2.010
60
2.859
40
3.109
20
3.182
79
2.072
59
2.879
39
3.112
19
3.184
78
2.116
58
2.908
38
3.118
18
3.1S6
77
2.160
57
2.936
37
3.123
17
3.188
76
2.204
56
2.965
36
3.129
16
3.189
75
2.248
55
2.993
35
3.134
15
3.191
74
. 2.292
54
3.022
34
3.140
14
3.193
73
2.356
53
3.035
33
3.142
13
3.196
72
2.421
52
3.049
32
3.144
12
3.199
71
2.485
51
3.062
31
3.145
11
3.202
70
2.550
50
3.076
30
3.147
10
3.205
69
2.614
49
3.089
29
3.149
9
3.208
68
2.647
48
3.090
28
3.154
8
3.236
67
2.680
47
3.092
27
3.159
7
3.219
66
2.713
46
3.093
26
3.165
6
3.181
65
2.746
45
3.095
25
3.170
5
4
3.141
3.084
Older Age Eighty-Five Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
85
1.601
65
2.596
45
2.904
25
2.972
84
1.665
64
2.613
44
2.906
24
2.974
83
1.729
63
2.630
43
2.907
23
2.977
82
1.792
62
2.647
42
2.909
22
2.979
81
1.856
61
2.664
41
2.910
21
2.982
80
1.920
60
2.681
40
2.912
20
2.984
79
1.962
59
2.708
39
2.918
19
2.985
78
2.004
58
2.736
3d
2.923
18
2.986
77
2.045
57
2.763
37
2.929
17
2.987
76
2.087
56
2.791
36
2.934
16
2.988
75
2.129
55
2.818
35
2.910
15
2.989
74
2.186
54
2.833
34
2.942
14
2.992
73
2.243
53
2.847
33
2.944
13
2.996
72
2.301
52
2.862
32
2.946
12
2.999
71
2.358
51
2.876
31
2.948
11
3.003
70
2.415
50
2.891
30
2.950
10
3.006
69
2.451
49
2.894
29
2.954
9
3.066
68
2.487
48
2.896
28
2.959
8
3.075
67
2.324
.47
2.899
27
2.963
7
3.036
66
2.560
46
2.901
26
2.968
6
5
2.990
2.945
Digitized by ^^UUV
F
TABLE XXL
529
Value of XI per Annum during the joint Coutinuanee of Two Lifcc
(Carlisle 4.} per Cent.)
Older Age Eighty-Six Yean.
Ag«.
Valoe.
Ag*..
Valae.
Age.
Value.
Age.
Valut.
86
1.460
64
2.464
42
2.738
20
2.808
85
1.522
63
2.480
41
2,739-
19
2.809
84
1.584
62
2.497
40
2.744
13
2.809
83
1.645
61
2.514
39
2.749
17
2.810
82
1.707
60
2.538
3S
2.754
16
2.811
81
1.769
59
2.563
37
2.759
15
2.814
80
1.812
58
2.587
36
2.764
14
2.817
79
1.854
57
2.612
35
2.767
13
2.820
78
1.897
56
2.636
34
2.7«9
12
2.823
77
1.939
53
2.651
33
2.772
11
2.826
76
1.982
54
2.667
♦32
2.774
10
5.869
75
2.031
53
2.682
31
2.777
9
2.924
74
2.080
52
2.698
30
2.780
8
2.915
73
2.129
51
2.713
29
2.784
7
2.854
72
2.178
50
2.717
28
2.787
6
2.799
71
2.227
49
2.722
27
2.791
70
2.268
48
2,726
26
2.794
69
2.308
47
2.731
25
2.797
68
2.349
46
2.735
24
2.799
67
2.389
45
2.736
23
2.802
66
2.430
44
2.737
22
2.804
65
2.447
43
2.737
21
2.807
Older Age Eighty-Seven Years.
Afe.
Value:
Age.
Vain*.
Ag*.
ValiM.
As..
Value.
87
1.346
65
2.324
43
2.598
21
2.664
86
1.406
64
2.342
42
2.598
20
2.664
85
1.466
63
2.360
41
2.602
19
2.665
84
1.527
62
2.378
40
2.607
18
2.665
83
1.587
61
2.400
39
2.611
J7
2.666
82
1.647
60
2.420
38
2.616
16
2.669
81
1.690
59
2.440
37
2.620
15
2.671
80
1.734
58
2.461
36
2.623
14
2.674
79
1.777
57
2.482
35
2.626
13
2.676
78
1.821
56
2.500
34
2.629
12
2.679
77
1.864
55
2.516
33
2.632
11
2.677
76
1.904
54
2.532
32
2.635
10
2.676
75
1.945
53
2.549
31
2.637
9
2.674
74
1.985
52
2.566
30
2.6J0
8
2.673
73
2.026
51
2.572
29
2.642
7
2.671
72
2.066
50
2.578
28
2.645
71
2.110
49
2.585
27
2.647
70
2.155
48
2.591
26
2.650
69
2.199
47
2.597
25
2.653
68
2.244
46
2.597
24
2.657
67
2.288
45
2.597
23
2.660
66
2.306
44
2.598
22
2.663
igitiza ajivjoogle
530
TABLK XXI.
Value of £1 per Atttkum during the joint Continutnce of Two LWct.
(Carlitle 4} per Gent.) >
Older Age Eighty-Eight Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
88
1.290
65
2.253
42
2.518
19
2.579
87
1.343
64 .
2.274
41
2.521
18
2.580 .
86
1.396
63
2.294
40
2.525
17
2.5S2
85
1.449
62
2.311
39
2.628
16
2.584
84
1.502
61
2.326
38
2.531
15
2.585
83
1.555
60
2.346
37
2.535
14
2.587
82
1.601
59
2.363
36
2.538
13
2.589
81
1.647
58
2.380
35
2.542
12
2.590
80 .
1.692
57
2.399
34
2.545
11
2.591
79
1.738
56
2.418
33
2.549
10
2.591
78
1.784
55
2.436
%32
2.551
9
2.592
77
1.*^18
64
2.455
31
2.552
8
2.593
76
1.853
53
2.474
30
2.554
75
1.887
52
2.482
29
2.555
74
1.922
51
2.490
28
2,557
73
1.956*
- 50
2.498
27
2.561
72
2.003
49
2.5U6
26
2.564
71
2.050
48
2.514
25
^2.568
70
2.098
47
2.514
24
2.571
69
2.145
46
2.514
23
2.576
68
2.192
45
2.515
22
2.576
67
2.212
44
2.515
21
2.577
66
2.238
43
2.516
20
2.578
Older Age Eighty-Nine Yean.
Age.
Valuei
Age.
Value.
Age.
Value.
Age.
Value.
89
1.215
66
2.149
43
2.420
20
2.479
88
1.262
65
2.172
42
2.422
19
2.480
87
1.310
64
2.195
41
2.425
18
2.481
86
K357
63
2.209
40
2.427
17
2.482
85
1.405
62
2.224
39
2.429
16
2.484
84
1.452
61
2.238
38
2.433
15
2.485
83
1.498
60
2.253
37
2.437
14
2.486
82
1.544
59
2.257
36
2.441
13
2.488
81
1.589
58
2.287
35
2.445
12
2.490
80
1.635
57
2.307
34
2.449
11
2.493
79
1.681
56
2.328
33
2.450
10
2.496
78
1.713
55
2.348
32
2.451
9
2.497
77
1.74J
54
2.368
31
2.453
76
1.778
63
2.377
30
2.454
76
1.810
52
2.387
29
2.455
74
1.842
51
2.396
28
2.459
73
1.889
50
2.406
27
2.463
72
1.937
49
2.415
26
2.466
71
1.984
48
2.416
25
2.470
70
2.032
47
2.416
24
2.474
69
2.079
46
2.417
23
2.475
68
2.102
45
2.417
22
2.476
67
2.125
44
2.418
21
2.478
Digitized by VjUUV LC
TABLE XXI.
531
Vftlue of £1 per Annom diiriog the Joint ContinYiaiice of Two life*.
(Carlisle 4^ per Cent)
Older Age Ninety Years.
Age*
Value.
Age.
Valae.
Age.
Valtte.
Age.
Velw.
90
1.049
67
1.972
44
2.248
21
2.303
89
1.096
66
1.999
' 43
2.250
20
2.304
88
1.143
65
2.025
42
2.251
19
2.305
87
1.190
64
2.037
41
2.253
IS
2.306
86
1.237
63
2.050
40
2.254
17
2.306
85
1.284
62
2.062
39
2.258
16
2.307
84
1.332
61
2.075
38
2.262
15
2.308
83
1.380
60
2.087
37
2.265
14
2.310
82
1.427
59
2.107
36
2.269
13
2.313
81
1.475
58
2.127
35
2.273
12
2.3151
80
1.523
hi
2.147
34
2.275
n
2.318
79
1.554
56
2.167
33
2.276
10
2.320
78
1.585
55
2.187
32
2.278
n
1.617
54
2.197
31
2.279
76
1.648
53
2.208
30
2.281
7b
1.679
52
2.218
29
2.284
74
1.722
51
2.229
28
2.287
73
1.765
50
2.239
27
2.291
72
1.807
49
2.241
26
2.294
• 71
1.850
48
2.242
25
2.297
70
1.893
47
2.244
24
2.298
69
1.919
46
2.245
23
2.300
68
2.946
45
2.247
22
2.301
Older Age Ninety-One Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Valuer
91
1.018
68
1.938
43
2.245
22
2.300
90
1.058
67
1.971
44
2.246
21
2.302
89
1.097
66
2.004
43
2.246
20
2.302
88
1.137
65
2.017
42
2.247
19
2.303
87
1.176
64
2.031
41
2.247
18
2.303
86
1.216
63
2.044
40
2.251
17
2.304
85
1.266
62
2.058
39
2.255
16
2.304
84
1.316
61
2.071
38
2.260
15
2.306
83
1.367
60
2.090
37
2.264
14
2.309
82
1.417
59
2.110
36
2.268
13
2.311
81
1.467
58
2.129
35
2.270
12
2.314
80
1.502
57
2.149
34
2.272
11
2.316
79
1.537
56
2.168
33
2.274
78
1.572
55
2.180
32
2.276
77
1.607
54
2.192
31
2.278
76
1.642
53
2.205
30
2.281
75
1.682
52
2.217
29
2.283
74.;
1.721
51
2.229
28
2.286
73
1.761
50
2.232
27
2.288
72
1.800
49
2.235
26
2.291
71
1.840
48
2.239
25
2.293
70
1.873
47
2.242
24
2.295
69
1.906
46
2.245
23
2.298
T
Digi^erl b
yj^uuvlt:
532
TABLK XXL
Value of £1 per Annum during the joint Continuance of Two Livci.
(Carlisle 4^ per Cent)
Older Age Ninety-Two Years.
Age.
Value.
Age.
72
Value.
Ag.^.
52
Valne.
Age.
Valus.
92
1.084
1.86 1'
2.309
32
2.367
91
1.108
71
1.901
51
2.314
31
2.369
90
1.132
70
1.942
50
2.319
30
2.371
89
1.157
69
1.982
49
2.324
29
2.373
88
1.181
68
2.023
48
2.329
28
2.375
87
1.205
67
2.063
47
2.334
27
2.377
86
1.260
66
2.079
46
2.334
26
2.330
85
1.314
65
2.095
45
2.334
25
2.383
84
1.369
64
2.111
44
2.a34
24
2.385
83
1.423
63
2.127
43
2.334
23
2.388 .
82
1.478
62
2.143
42
2.334
22
2.391
81
1.518
61
2.161
41
2.338
21
2.392
80
1.55S
60
2.179
40
2.342
20
2.392
79
1.597
59
2.197
39
2.345
19
2.393
78
1.637
53
2.215
38
2.349
18
2.393
ii
1.677
57
2.233
37
2.353
17
2.394
76
1.714
56
2.243
36
2.356
16
2.396
75
1.751
55
2.263
.35
2.359
15
2.398 •
74
1.787
54
2.279
34
2.361
14
2.400
73
1.824
53
2.294
33
2.364
13
12
2.402
2.404
Older Age Ninety-Three Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
93
1.186
73
1.898
53
2.402
33
2.470
92
1.195
72
1.945
52
2.409
32
2.471
91
1.204
71
1.992
51
2.416
31
2.473
90
1.214
70
2.039
50
2.424
30
2.474
89
1.223
69
2.086
49
2.431
29
2.476
88
1.232
68
2.133
48
2.438
28
2.477
87
1.285
67
2.153
47
2.438
27
2.481
86
1.337
66
2.172
46
2.437
26
2.484
85
1.390
65
2.192
45
2.437
25
2.488
84
1.442
64
2.211
44
2.436
24
2.491
83
1.495
63
2.231
43
2.436
23
2.495
82
1.541
62
2.247
42
2.439
22
2.496
81
1.588
61
2.263
41
2.443
21
2.497
80
1.634
60
2.278
40
2.446
20
2.497
79
1.681
59
2.294
39
2.450
19
2.498
78
1.727
58
2.310
38
2.453
18
2.499
n
1.761
57
2.328
37
2.456
17
2.501 •
7^
1.795
56
2.347
36
2.460
16
2.502
75
1.830
55
2.365
35
2.463
15
2.504
74
1.864
54
2.334
34
2.467
14
13
2.50.1
2.507
Digitized by ^^UUS! IC
TABLE XXI.
533
Value of £1 per Annum during the joint Continuance of Two Livet.
(Carlisle 4^ per Cent.)
Older
Age Ninety- Four Years
Age.
Value.
Age.
74
Value.
Age.
-54
Value.
Age.
34
Value.
94
].2:)8
1.905
2.445
i2.520
93
1.252
73
1.9J5
53
2.454
33
2.521
92
1.246
72
2.005
bl
2.462
32
2.522
91
1.239
71
2.05.>
51
2.471
31
2.523
90
1.233
70
2.105
50
2.479
30
2.524
89
1.227
69
2.155
49
2.488
29
2.525
88
1.279
68
2.179
48
2.488
28
2.529
87
1.330
67
2.202
47
2.488
27
2.533
86
1.382
66
2.226
46
2.488
26
2.536
83
1.433
65
2.249
45
2.488
25
2.540
84
1.485
64
2.273
44
2.488
24
2.544
83
1.535
63
2.236
43
2.490
23
2.545
82
1.585
62
2.300
42
2.492
22
2.546
81
1.634
61
2.313
41
2.495
21
2.548
80
1.684
60
2.327
40
2.497
20
2.549
79
1.734
59
2.340
39
2.499
19
2.5.50
78
1.763
58
2.361
38
2.503
18
2.551
77
1.802
&7
2.382
37
2.507
17
2.552
76
1.837
56
2.403
36
2.512
16
2.554
75
1.871
55
2.424
35
2.516
15
14
2.555
2.556
Older Age Ninety-Five Years.
Age.
95
94
93
92
91
90
89
88'
87
86
85
84
83
82
81
80
79
78
77
76
Value.
1.338
1.306
1.274
1.243
1.211
1.179
1.235
1.291
1.347
1.403
1.459
1.515
1.572
1.628
1.685
1.741
1.776
1.811
1.847
1.882
Age.
Value.
1.917
1.965
2.013
2.062
2.110
2.158
2.186
2.214
2.242
2.270
2.298
2.309
2.321
2.332
2.344
2.355
2.377
2.399
2.421
2.443
Age.
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
Value.
2.465
2.475
2.485
2.495
2.505
2.515
2.516
2.517
2.517
2.518
2 519
2.520
2.521
2.522
2.523
2.524
2.529
2.533
2.538
2.542
Agf.
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
Value.
2.547
2.54S
2.549
2.551
2.552
2.553
2.5.36
2.560
2.563
2.567
2.570
2.572
2.573
2.575
2.576
2.578
2.579
2.579
2.580
2.580
2.581
Digitijod by ^jOO^ IC
534
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two Lives.
(Carlisle 4^ per Cent)
Older Age Ni
QCty-
Six YeaiB
•
Age.
Value.
Age.
76
Valne,
Age.
Value.
Ag6.
Value.
96
1.379
1.888 .
56
2.421
36
2.507
95
1.338
75
1 931
55
2.432
35
2.509
94
1.297
74
1.974
54
2.443
34
2.510
93
1.255
73
2.016
63
2.453
33
2.512
92
1.214
72
2.069
52
2.464
32
2.513
91
1.173
71
2.102
51
2.475
31
2.515
90
1.221
70
2.135
50
2.477
30
2.518
89
1.268
69
2.168
49
2.479
29
2.521
88
1.316
68
2.200
48
2.481
28
2,523
87
1.363
67
2.233
47
2.483
27
2.526
86
1.411
66
2.266
46
2.485
26
2.529
85
1.469
65
2.277
45
2.485
25
2.531
84
1.527
64
2.288
44
2.485
24
2.533
83
1.586
63
2.299
43
2.485
23
2.534
82
1.644
62
2.310
42
2.485
22
2.536
81
1.702
61
2.321
41
2.485
21
2.538
80
1.739 .
60
2.341
40
2.489
20
2.538
79
1.776
59
2.361
•39
2.494
19
2.539
78
1.814
58
2.381
38
2.498
18
2.539
11
1.851
57
2.401
37
2.503
17
16
2.540
2.540
Older Age Ninety-Seven Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
37
Value.
97
1.352
n
1.811
57
2.295
2.384
96
1.320
76
1.845
56
2.307
36
2.38fi
95
1.288
7&
1.879
55
2.318
35
2.388
94
1.257
74
1.914
54
2.330
34
2.389
93
1.225
73
1.948
53
2.341
33
2.391
92
1.193
72
1.982
52
2.353
32
2.393
91
1.222
71
2.018
51
2.356
31
2.395
90
1.251
70
2.054
50
2.359
30
2.397
89
1.279
69
2.089
49
2.361
29
2.398
88
1.308
68
2.125
48
2.364
28
2.400
87
1.337
67
2.161
47
. 2.367
27
2.402
86
1.394
66
2.172
46
2.367
26
2.404
85
1.432
65
2.182
45
2.366
25
2.406
84
1.509
64
2.193
44
2.366
24
2.409
83
1.567
63
2,203
43
2.365
23
2.411
82
1.624
62
2.214
42
2.365
22
2.413
81
1.661
61
2.230
41
2.369
21
2.413
80
1.699
60
2-246
40
2.373
20
2.413
79
1.736
59
2.263
39
2.376
19
2.414
78
1.774
58
2.279
38
2.380
18
17
2.414
2.414
Digitized by VjUUV IC
TABLB XXI.
535
Value of £1 per Annum during the joint Continuance of TVo Lires.
(CarliBle 4^ per Cent.)
Older Age Ninety-Eight Yean.
Ar.
Value.
A.e.
Value.
Afe.
Value.
A«e.
Value.
98
1.336
78
1 .726
53
2.149
38
2.238
97
1.314
77
1.752
57
2.161
37
2.240
9fi
1.292
76
1.778
56
2.173
36
2.242
95
1.270
75
1.805
55
2.186
35
2.244
94
1.248
74
1.831
54
2.198
34
2.246
93
1.226
73
1.857
53
2.210
33
2.248
92
1.239
72
1.893
52
2.214
32
2.249
91
1.252
71
1.929
51
2.217
31
2.;;50
90
1.266
70
1.966
50
2.221
30
2.250
89
1.279
69
2.002
49
2.224
29
2.251
88
1.292
68
2.038
48
2.228
23
2.252
87
1.341
67
2.048"
47
2.227
27
2.255
86
1.391
66
2.059
46
2.2:6
26
2.257
85
1.440
65
2.069
45
2.226
25
2.260
84
1.490
64
2.080
44
2.225
24
2.262
83
1.539
63
2.090
43
2.224
23
2.265
82
1.576
62
2.102
42
2.227
22
2.265
81
1.614
61
2.114
41
2.230
21
2.265
80
1.651
60
2.125
40
2.232
20
2.266
79
1.689
59
2.137
39
2.235
19
18
2.266
2.266
Older Age Ninety-Nine Years.
Age.
Value.
Age.
Value.
Age.
Value.
Age.
Value.
99
1.261
79
1.576
59
1.929
39
2.010
98
1.249
78
1.597
58
1.941
38
2:012
97
1.237
77
1.617
57
1.953
37
2.014
96
1.226
76
1.638
56
1.964
36
2.016
95
1.214
75
1.658
55
1.976
35
2.018
94
1.202
74
1,679
54
1.988
34
2.020
93
1.202
73
1.712
63
1.991
33
2.020
92
1.202
72
1.744
52
1.995
32
2.021
91
1.202
71
1.777
51
1.998
31
2.021
90
1.202
79
1.809
50
2.002
30
2.022
89
1.202
69
1.842
49
2.005
29
2.022
88
1.244
68
1.852
48
2.004
28
2.024
87
1.286
67
1.862
47
2.003
27
2.027
86
1.327
66
1.871
46
2.003
26
2.029
85
1.369
65
. 1.881
45
2.002
25
2.032
84
1.411
64
1.891
44
2.001
H
2.034
83
1.444
63
1.899
43
2.003
23
2.034
82
1.477
62
1.906
42
2.005
22
2.034
81
1.510
61
1.914
41
2.006
21
2.035
80
1.543
60
1.921
40
2.008
20
19
2.035 .
2.035
«
Digitized by VjiOOQlC
536
TABLE XXI.
Value of £1 per Annum during the joint Continuance of Two LiTCi.
(Carlisle 4} per Cent.)
Older Age One Hundred Years,
Age.
Value.
Aur.
Vala«.
Age
Valne.
Age.
Value.
100
0.969
79
1.298
58
1.534
37
1.603
99
0.984
78
1.313
57
1.564
36
1.605
98
1.000
77
1 .328
.'>6
1.573
35
1.607
97
1.015
76
1.343
55
1.582
34
1.607
96
1.031
75
1.S58
54
1.585
33
1.607
95
1.046
74
1.331
53
1.583
32
1.608
94
1.028
73
1.404
52
1.591
31
1.608
93
1.010
72
1.428
51
1.594
30
1.608
92
0.992
71
1.451
50
1.597
29
1.610 .
91
0.974
70
1.474
49
1.596
28
1.611 ^
90
0.956
69
1.482
48
1.596
27
1.613
89
0.993
68
1.490
47
1.595
26
1.614
E8
1.030
67
1.499
46
1.595
25
1.616
87.
1.058
66
1.507
45
1.594
24
1.616
86
1.105
65
1.515
44
1.595
23
1.616
85
1.142
64
1.519
43
1.596
22
1.617
84
1.170
63
1.523
42
1.596
21
1.617
83
1.198
62
1.528
41
1.597
20
1.617
82
1.227
61
1 .532
40
1.598
81
1.255
60
1.536
39
1.600
80
1.283
59
1.545
38
1.002
•
Older Age One Hundred and One Years.
•
Age.
\9\W.
Age.
Valuta.
Age.
Value.
Age.
Value.
101
0.674
80
0.974
59
1.147
38
1.180
100
0.706
79
0.985
58
1.153
37
1.181
99
0.738
78
0,995
57
1.159
36
1.162
98
0.770
77
1.006
.56
1.1G5
35
1.182
.»7
0.802
76
1.017
55
1.167
34
1.182
96
0.834
75
1.031
54
1.169
33
1.183
95
0.815
74
1.046
53
1.170
32
1.183
94
0.796
73
1.060
52
1.172
31
1.183
93
0.776
72
1.075
51
1.174
30
1.184
92
0.757
71
1.089
50
1.174
29
1.185
91
0.738
70
1.096
49
1.174
28
1.185
90
0.763
69
1.103
48
1.174
27
1.186
89
0.787
68
1.109
47
1.174
26
1.187
88
0.812
67
1.116
46
1.174
25
1.187
87
0.835
66
1.123
45
1.174
24
1.187
86
o.8ni
65
1.125
44
1.175
23
1.188
85
0.881
64
1.1::8
43
1.175
22
1.188
84
0.902
63
1.130
42
1.176
21
1.18J
83
0.922
62
1.133
41
1.176
82
0.943
61
1.135
40
1.177
81
0.963
60
1.141
39
1.178
Digitized by VjUUVIC
TABLK XXI.
M7
Value of £1 per Annttm dimug the joint Continuance of Two Lives.
(Carlisle 4^ per Cent)
Older Age One Hundred and Two Years.
Affe.
Value.
Age.
ViiUie.
Age.
60
Value.
Age.
39
Value. -
102
.381
81
.633
.728
.746
101
.417
80
.639
59
.731
38
.746
100
.452
79
.646
58
.734
37
.747
9!)
.488
78
.652
57
.737
36
.747
9S
.523
77
.658
56
.738
35
.747
97
.559
76
.665
55
.739
34
.748
96
.549
75
.672
54
.741
33
.748
05
.540
74
.678
53
.742
32
.748
9^
.530
73
.685
52
.743
31
.748
>.. 93
.521
72
.692
51
.743
30
.749
92
.511
71
.697
50
.743
29
.749
91
.521
70
.702
49
.741
28
.750
90
.531
69
.706
48
.744
27
.750
89
.542
68
.711
47
.744
26
.750
86
.552
67
.716
46
.744
25
.750
87
.562
66
.717
45
.744
24
.751
86
.575
65
.718
44
.744
23
.751
85
.588
64
.720
43
.744
22
.751
84
.601
63
.721
42
.744
83
.614
62
.722
41
.745
82
.627
61
.725
40
.745
Older Age One Hundred and Three Yean.
Age.
Value.
Age.
Value.
Age.
61
Value.
.309
Age,
Value.
103
.106
82
.274
40
.315
102
.135
81
.276
60
.309
39
.315
101
.164
80
.279
59
.310
38
.315
100
.193
79
.281
58
.311
37
.315
99
.222
78
.284
57
.312
36
.315
98
•251
77
.286
56
.312
35
.316
97
.248
76
.288
55
.313
34
.316
96
.245
75
.290
54
.313
33
.316
95
.242
74
.292
53
.314
32
.316
94
.239
73
.294
52
.314
31
.316
93
.236
72
.296
51
.314
30
.316
92
.239
71
.298
50
.315
29
.316
91
.241
70
.300
49
.315
28
.316
90
.244
69
.3<'2
48
.315
27
.316
89
.246
68
.304
47
.315
26
.316
88
.249
67
.305
46
.315
25
.316
87
.253
66
.305
45
.314
24
.316
86
.258
65
.306
44
.314
23
.316
85
.262
64
.306
43
.314
84
.267
63
.307
42
.314
83
.271
62
«308
41
.314
Digitized by VjUUVi'C
53B
TABLE XXIL
Showing the present Value of £1 to be leeeiTed at the end of the Year in which i
aMigned Life may £aiU (CaiUsle Rate of Mortality.)
Age.
8 per Cent
3i per Ccut.
4 per Genu
4k per Cent.
0
.46641
.43621
.41224
.39289
1
.38587
.35171
.32483
.30336
2
.34463
.30826
•27976
.25713
3
.31021
.27178
.24173
,21793
4
.29267
.25294
.22187
.19728
5
.28079
.23997
.20800
.18268
6
.27633
.23474
.20211
.17624
7
.27572
.23355
.20038
.17402
8
.27764
.23499
.20137
.17463
9
.28125
.23820
•20419
.17703
10
.28606
.24269
.20833
.18084
11
.29145
.24781
.21313
.18532
12
,29681
.2.11288
.21789
.18975
13
.30222
.25802
.22272
. 19426
14
.30771
.26323
.22762
.19885
15
.31315
.26840
.23249
.20340
16
.31833
.27330
.23706
.20763
17
.32334
.27802
.24150
.21171
18
.32841
.28279
.24590
.21581
19
•33362
.28773
.25052
.22009
20
.33901
.29285
.25532
.22456
21
.34455
.29814
.26031
.22922
22
.35037
.30374
.26562
.23422
23
.35637
.30954
.27115
•23944
24
.36252
.81555
.27690
•24489
25
.36808.
.32179
.28289
.25060
26
.37548
.32813
.«8901
.25644
27
.38218
.33471
.29538
,26255
28
.38890
.34132
.30176
.26868
29
.39531
.34759
.30781
.27446
30*
.40129
.35340
.31338
.27973
31
.40734
.35929
.31903
.28509
32
.41357
.36539
.32491
.29069
33
.42010
.37182
.33113
.29664
34
.42694
.37858
.33771
.30298
35
.43399
.38560
.34457
.30961
36
.44117
.39287
".,35170
.31653
37
.44870
.40029
•35901
.32364
38
.45624
.40787
.36649
.3.3094
39
•46393
.41562
.37416
.33844
40
.47156
.42332
.38178
.34590
41
.47893
.43073
.38911
.35306
42
.48621
.43806
.39636
.36013
43
.49352
.44543
.40364
,36724
44
.50108
.45304
.41120
.37465
45
.50885
.46092
.41905
.38237
46
.51694
.46919
.42734
.39055
47
.52542
.47788
.43607
.39922
48
.53439
.48711
.44542
.40855
49
.54406
.49715
.45565
.41884
60
.55429
.50782
.46658
.42988
51
•56509
.51914
.47824
.44174
Digitized by CjOOQTC
TABLE XXII.
689
Showing the pieient Value of £1 to be received at the end of the Tear in which
an assigned Life mvy fail, (Carlisle Bate of Mortality.)
Age.
5 per Cent.
.6 per Cent.
7 per Cent.
8 per Cent.
0
.37700
.35251
.33421
.32015
1
.28595
• .25974
.24079
.22674
2
.23891
.21179
.19258
.17867
3
.19886
.17065
.15097
.13696
4
.17757
.14857
.12847
.11430
5
.16238
.13255
.11198
.09748
6
.15548
•12491
.10387
.08904
7
.15286
.12163
.10007
.08489
8
.15305
.12117
.09916
.08363
9
•15514
.12264
.10021
.08430
10
.15862
.12558
.10263
.08637
11
.16281
.12921
.10577
.08919
12
.16695
.13277
.10891
.09193
13
.17114
.13640
.11211
.09474
14
.17543
.14013
.11538
.09763
15
•17967
.14381
•11859
.10045
16
.18362
.14715
.12147
.10289
17
.18733
.15026
.12408
.10511
18
.19110
.15343
.12677
•10733
19
.19505
.15677
.12958
.10970
20
.19919
.16028
.13259
.11222
21
.20352
.16402
.13579
.11496
22
.20819
.16809
.13933
.11807
23
.21310
.17240
.14312
.12141
24
.21824
.17692
.14711
.12496
25
.22367
* 18174
.15136
.12874
26
.22919
.18672
.15581
.13267
27
.23500
.19198
.16052
.13689
28
.24086
.19725
.16529
.14119
29
.24633
.20211
.16962
.14504
30
.25129
.20642
.17335
.14830
31
.25633
.21083
.17714
.15155
32
.26162
.21547
.18120
.15504
33
.26729
.22051
.18564
.15889
34
.27333
.22594
.19049
.16319
35
.27967
.23172
.19565
.16778
36
.28633
.23783
.20115
.17274
37
.29319
.24411
.20684
.17793
38
.30024
.25062
.21279
.18326
39
.30752
.25736
.21894
.18889
40
.31477
.26404
.22509
.19444
41
.32167
.27038
.23085
.19963
42
.32852
.27666
.23648
.20467
43
.33538
.28294
.24210
.20971
44
.34257
•28957
.24805
.21504
45
.35010
.29653
.25440
.22074
46
.35810
.30400
.26127
.22696
47
.36662
.31204
.26873
.23378
48
.37586
.32087
.27697
.24141
49
.38610
.33077
.28639
.25030
60
.39714
.34164
.29679
.26022
51
.40905
.35347
.30831
.27126
Digitized by VjUUV IC
540
TABLE XXII.
Showing the present Value of £1 to be received at the end of the Year in which
an assigned Life may fail. (Caiiide lUte of Mortality.)
Age.
3 per Ceut.
3^ per Crot
i per Cent.
A\ per CeoU
52
.57598
.53060
.49008
.45381
53
.58699
.54222
.50211
.46611
54
.59812
.55399
.51436
.47867
55
.60948
.56605
.52694
.49162
56
.62096
.57830
.53977
.50487
57
.63260
.59077
.55286
.51844
58
.64413
.60315
•56591
.53199
59
.65512
.61494
.57833
.54491
60
.66531
.62589
.58987
.55691
61
.67436
.63559
.60007
.56748
62
.68325
.64513
.61012
.57791
63
.69222
.65480
.62033
•58853
64
.70157
.66490
.63103
.59970
65
.71112
.67526
.64203
.61122
66
.72103
.68599
.65347
.62325
67
.73122
.69713
.66539
•63582
68
.74168
.70859
.67770
.64884
69
.75246
.72041
.69043
.66236
70
.76340
•73248
.70349
.67626
71
.77465
.74496
.71701
.69072
72
.78525
.75671
.72979
.70441
73
.79483
.76733
.74136
•71681
74
.80334
.77675
.75161
.72781
75
.81033
.78458
.76004
•73683
76
.81717
.79211
.76831
.74569
n
.82352
.79915
.77597
.75391
78
.82996
.80631
.78378
.76230
79
.83713
.81433
.79256
.mn
80
.84374
.82172
.80066
.78051
81
.85090
.82976
.80950
•79008
82
.85734
.83698
.81745
.79869
83
.86392
.84439
.82561
.80756
84
.87027
.85154
.83352
.81617
85
.87682
.85894
.84173
.82513
86
.88253
.86542
.84891
.83298
87
.88719
.87071
.85477
.83939
■ 88
.89002
.87390
.85833
.84328
89
.89325
.87758
.8«242
.84777
90
.89809
.88308
.86861
.85453
91
.89861
.8S371
.86929
.85535
92
,89582
.880:>0
.86569
.85138
93
.89261
.87683
.86156
.84677
94
.89118
.87515
.85962
.84461
95
.89057
.37437
.85868
•84349
96
.89212
.67605
.86047
• .84536
^7
.89633
.88079
.86569
•85101
98
.90132
.88637
.87184
.85768
99
.90880
.89487
.88127
.86799
100
.92185
.90979
.89797
.88639
101
.93511
.92496
.91500
.90521
102
.94842
.94027
.93224
.92433
103
.96144
.9o5'29
•94921
.94320
TABLE XXIL
541
Showing the present Value of £1 to be received at the end of the Year ia which an
assigned Life may fail (Carlisle Rate of Mortality.)
Aire.
6 per Cent.
6 per Cent.
7 per Cent
8 per Cent.
52
.42124
.36558
.32015
.28267
53
.43371
.37804
.33238
.29459
54
.44643
.39039
,34507
•30696
55
•45967
.40431
.3.>842
.32007
56
.47319
.41812
.37229
.33370
57
.48710
.43243
.38668
.34800
58
.50105
.44687
.40121
.36252
59
.51433
.46062
.41514
.37644
60
.52667
.47336
.42803
.38926
61
.53752
.48445
.43922
.40036
62
.54824
.49549
.45027
.41133
63
.55914
.50676
.46105
.42259
64
.57067
•51875
.47389
.43481
65
.58262
.53126
• 48664
.44763
66
.59510
.54440
•50012
.46133
67
.60824
.55332
.51451
.47593
68
.62186
.57287
.52969
.49141
69
.63603
.58809
.54565
•50793
70
.65067
.60389
.56234
.52519
71
.66595
.62053
.58000
.54371
72
.68043
.63638
.59687
.56134
73
.69357
.63075
.61225
.57748
74
.70524
. 66355
.62586
.59178
75
.71481
.67396
.63598
.60333
76
.72419
.68421
.64791
.61481
77
.73291
.69377
.65805
.62548
78
.74181
.70351
.66851
.63645
79
.75191
.71472
.68055
.64919
80
.76119
.72502
.69167
.66096
81
.77148
.73645
.70410
•67422
82
•78067
.74675
•71529
.68615
83
,79019
.75740
•72693
.69859
84
.79948
.76781
.73838
.71089
8>
•80910
.77874
.75042
.72393
86
.81762
.78836
.76108
.73548
87
.82452
.79628
.76978
.74496
88
.82870
.80101
.77502
•75067
89
.83357
.80653
.79078
.75733
90
.84103
.81513
.79196
.76793
91
.84186
.81615
.78634
.76926
92
.83752
.81111
.77973
.76311
93
.83248
.80528
.77633
.75o78
94
.83005
.80234
.77633
.75185
95
.82876
.80064
.77424
.74941
96
.83071
.80268
.77626
.75126
97
.83676
.80936
.78352
.75904
98
.84391
.81734
.79216
.76822
99
.85500
.82996
.80609
.78326
100
.87505
.85306
•83193
.81163
101
.89562
.87689
.85875
.84133
102
.91653
.90128
.88650
.87207
103
.93728
.92562
.91417
•90304
Digitized by VjOOQIC
548
TABLB XXIII.
Preient Value of £1 per Annum during the joint Continuance of Two Hale Lifes.
(ChokUi 3 per Cent.)
A|M.
Value
AgM.
Vulne
Agtt.
Value
AgM.
■ ' ■
Valne
AfM.
i
i
i
1
i
v«i«
1
of the
1
orth«
1
oftlM
^
of the
i §
of the
i
Annuity.
8
Annnity.
g
Aanoity.
75
g
Annuity.
Anaaity.
5
>«
'
40
>*
30
60
>•
30
30
6.131
o >*
85 75
■
"o
0
9.213
12.771
8.917
3.212
5
0
12.873
35
12.216
35
8.668
35
6.009
80
2.934
5
18.048
40
11.605
40
8.361
40
5,662
85
2.739
10
0
12.958
45
0
9.081
45
8.061
45
5.718
90
0
2.467
5
18.183
5
12.736
50
7.723
50
5.560
5
3.265
10
18.346
10
12.993
55
7.299
55
5.362
10
3.360
15
0
12.444
15
12.664
60
6.590
60
4.934
15
3.327
5
17.468
20
12.416
65
0
6.062
65
4.807
20
3.298
10
17.652
25
12.204
5
8.403
70
4.117
25
3.282
15
17.013
30
11.988
10
8.620
76
S.940
30
3.294
20
0
12.004
35
11.511
15
8.458
80
0
3.839
35
3.260
5
16.860
4U
10.977
20
8.345
5
5.2*24
40
3.214
10
17.064
45
10.432
25
8.269
10
5.372
45
3.168
15
16.475
50
0
8.367
30
8.221
15
5.294
50
3.125
20
15.984
5
11.717
35
8.011
20
5.238
55
3.081
25
0
11.585
10
11.971
40
7.766
25
5.208
60
2.908
5
16.280
15
11.688
45
7.521
30
5.209
66
2.913
10
16.503
20
11.480
50
7.245
35
6.120
70
2.607
15
15.963
25
11.312
55
6.902
40
5.010
75
2.537
20
15.518
30
11.147
60
6.269
45
4.905
80
2.356
25
15.102
35
10.744
65
6.026
50
4.792
85
2.235
30
0
11.146
40
10.290
70
0
4.917
55
4.651
90
1.901
5
15.666
45
9.823
5
6.764
60
4.315
95
0
1.863
10
15.907
50
9.305
10
6.943
65
4.235
5
2.417
15
15.417
55
0
7.599
15
6.824
70
3.667
10
2.486
20
15.020
5
10.611
20
6.740
75
3.527
15
2.469
25
14.652
10
10.855
•25
6.688
80
3.190
20
2.452
30
14.259
15
10.618
30
6.664
85
0
3.310
25
2.439
35
0
10.472
20
10.448
35
6.514
5
4.464
30
2.450
5
14.713
25
10.317
40
6.338
10
4.594
35
2.434
10
14.964
30
10.199
45
6.163
15
4.536
40
2.409
15
14.531
35
9.868
50
5.969
20
4.492
45
2.384
20
14.188
40
9.492
55
5.723
25
4.468
50
2.357
25
13.877
45
9.109
60
5.241
30
4.479
55
2.349
30
13.544
50
8.675
65
5.071
35
4.416
60
2.232
35
12.912
55
8.150
70
4.322
40
4.335
65
2.260
40
0
9.770
60
0
6.606
75
0
4.512
45
4.259
70
2.067
5
13.717
5
9.194
5
6.187
50
4.180
75
2.023
10
13.973
10
9.417
10
6.357
55
4.089
80
1.906
15
13.594
15
9.225
15
6.255
60
3.819
85
1.840
20
13.301
20
9.090
20
6.183
65
3.792
90
1.614
25
13.042
25
6.994
25
6.142
70
3.317
95
1.483
Digitized by VjUUV LC
TABLE XXIII.
543
Present Value of £1 per Annum during the joint Continuance of Two Female Lives*
.'(Chester 3 per Cent)
A get.
Ages.
A gee.
Age..
Age..
i
Valae
c
Value
,.
Valoc
1
Value
1
Value
1
of the
1
?
of the
1
M
of the
jj
of the
1
of the
g
Annaliy.
§
Anuuity.
1
Annaily.
J
o
AnDoity.
f
Aanuily.
s
PH
o
>*
o
>*
c
>«
o
>•
0
0
11.002
40
30
14.144
60
30
9.859
75
30
6.002
85
75
3.328
6
0
14.628
35
13.730
35
9.694
35
6.936
80
2.803
5
19.512
40
13.260
40
9.522
40
6.872
85
2.907
10
0
14.532
45
0
10.762
45
9.313
45
5.802
90
0
3.058
5
19.399
5
14.383
50
9.031
50
5,725
6
3.884
10
19.315
10
14.464
55
8.531
55
5.544
10
3.953
15
0
14.019
15
14.138
60
7.699
60
6.146
16
3.920
5
18.724
20
13.886
65
0
6.889
65
4.939
20
3.904
10
18.669
25
13.546
Tj
9.108
70
4.232
25
3.861
15
18.076
30
13.409
lu
9.221
75
3.866
30
3.862
ieo
0
13.570
35
13.065
r>
9.077
80
0
3.795
35
3.835
5
18.132
40
12.674
-'!
8.975
5
4.903
40
3.809
10
18.105
45
12.186
11 ^
8.811
10
4.979
45
3.784
15
17.558
50
0
9.974
.JO
8.795
15
4.922
50
3.769
20
17.088
5
13.319
■j'?
8.667
20
4.886
55
3.723
S5
0
13.023
10
13.414
JO
8.539
25
4.812
60
3.537
5
17.408
15
13.135
J.V
8.390
30
4.816
65
3.519
10
17.407
20
12.922
M*
8.190
35
4.768
70
3.126
15
16.909
25
12.628
yy
7.817
40
4.7*23
75
2.942
20
16.487
30
12.532
i:o
7.130
45
4.677
80
2.521
25
15.942
35
12.252;
'■'■'
6.705
50
4.623
85
2.597
30
0
12.653
40
11.942
7«.
n
5.467
55
4.503
90
2.446
5
16.918
45
11.549
.%
7.171
60
4.211
95
0
1.911
10
16.940
50
11.029
lU
7.270
65
4.078
5
2.357
15
16.482
55
0
8.988
].;j
7.169
70
3.530
10
2.400
20
16.102
5
11.974
■Jii
7.099
75
3.233
15
2.385
2j
15.605
10
12.082
■J,j
6.978
80
2.747
20
2.382
30
15.318
15
11.850
m
6.975
85
0
3.779
•25
2.354
35
0
12.074
20
11.678
:i3
6.888
5
4.891
30
2.362
5
16.145
25
11.432
m
6.801
10
4.972
35
2.351
10
16.188
30
11.369
\o
6.704
15
4.919
40
2.339
15
15.775
35
11.151
50
6.584
20
4.886
45
2.328
20
15.440
40
10.914
55
6.334
25
4.813
50
2.321
25
14.999
45
10.619
60
5.841
30
4.822
55
2.316
30
14.764
50
10.219
65
5.563
35
4.778
60
2.221
35
14.282
55
9.564
70
4.694
40
4.736
G5
2.243
40
0
11.456
60
0
7.763
75
0
4.709
46
4.696
70
2.053
5
15.316
5
10.296
5
6.136
50
4.659
75
1.981
10
15.378
10
10.405
10
6.227
5^
4.557
80
1.753
15
15.009
15
10.224
15
6.149
60
4.283
85
1.761
20
14.717
io
10.091
20
6.098
65
4.183
90
1.750
25
14.327
25
9.894
25
5.999
70
3.619
96
1.401
Digitized by ^^UUV
Fe
544
TABLE XXIII.
Present Value of £1 per Annum during the joint Continuance of a Mule and Female
Life, when the Female is the Younger Life.
(Chester 3 per Cent.)
Agps.
\ge9.
H
■■.
Aw^
Ab?*'
J
Vnln*
Value
^
' V^DB
i
ValM
4
Yuliie
^
I
af lli*j;
«
ofilm
*
Dfth*
.
utihe
jt
i
oTilift
1
Anauity.
1
I
ADbuity.
is
Auuuity.
*
g
Abbuiiy. 1
E
Aunaiijr.
PL
i±i
S
£
00 30
9.020
X
k.
^ -
0
0
10*060
40,
30
53,115
7^
7o
6,158 85
75
3.206
5
0
14.050
35
12.705
35
8.8M
35
5.088
30
2.:i9
5
18*751
40
}^^-37I
40
8,722
40
6.021
^
2. SOS
10
0
14.124
45
0
9.800
^5
6. 53d
45:
5.950
»0
0
2.624
5
is.ao4
5
13,071
50
8.292
50
5.862
5, 3.310
10
la.feoa
10
13.163
'^5
1
7.853
Ki
5.674
10
3.368
15
0
13p544
15
12-Sfi2
60
7.113
60
5,2C1
15
3.342
5
18,094
20
12.667
G5
0
6.501
&j
5.051
20
3.329
10
18,065
25
12.370
5
8.581
70
4,289
25
3.286
15
17,518
30
12,263
10
8.689
75
3.897
30
3.295
2D
0
13.047
;J:'>
11.973
15
8.554
80
U
4,099
.'55
3.273
5
17.437
4U
11.647
20
3.460
5
5,314
40
3.252
10
17.433
45
11.245
iS
8,306
10
5.398
45
3.232
Ih
IG,031
r>o
0
9.016
30
8.292
15
5,337
:>o
3.220
20
16.507
6
12.013
3^
8.174
20
5.297
5.^
3.163
25
D
12.574
10
12.105
40
8,054
i5
5.216
GO
3.033
5
16,810
!5
11.870
4.7
7.JJ14
30
6.222
!i5
3,019
10
!6,fi30
W
11,680
50
7.729
35
5.170
70
2.700
Id
16.371
25
11.433
5.1
7,382
40
5.121
75
2.351
20
I6.nd
30
n.35r
fiO
6.739
45
5.073
30
2,207
25
15.403
35
11.120
65
6.352
50
5-019
83
2.257
30
0
12.0S0
lu
10.859
70
0
5,264
5:1
4,890
110
2.147
5
16.151
45
111.533
5
6.897
60
4.575
115
0
1.978
10
16.103
511
10.106
10
6.991
Cj
4.436
h
2.446
15
15.77C
5^
U
8,173
15
6.893
70
3.B19
lu
2,491
20
15.437
fi
10.864 i
:o
6.826
T'^
3.500
15
2.475
25
14.989
JO
10.969
25
6.710
SJ
2.952
20
2.472
30
14.751
15
10.760^
30
6.705
8:i
LI
3.528
i5
2.443
35
0
11.333
2U
10.619
35
6.622
5
4.535
:^0
2.450
5
15.145
25
10.402
40
6.539
10
4.612
15
2.439
10
15,206
30
10.352
45
6.445
15
4.566
40
2.427
15
14.a?&
35
10.162
50
6.326
20
4.540
15
2.415
20
14.544
40
9.958
55
6. 085
it
4.474
50
2.408
26
14.152
45
9.707
60
5.605
3t»
4.484
i5
2.403
JO
13.962
50
9.369
65
5.332
35
4.446
riO
2.302
35
13.548
55
8.811
70
4.501
40
4.419
m
2.326
40
0
10.557
60
0
7.097
75
0
4.825
45
4.376
;o
2.125
5
14.101
5
9.400
5
6.302
50
4.345
73
2.051
10
14.178
10
9.r)03
10
6.395
55
4.266
80
1.811
15
13.854
15
9.343
15
6.313
60
4.0-22
85
1.819
20
13.602
20
9.320
20
6.258
65
3.954
00
1.808
25
13.260
25
9.049
25
6.156
70
3.453
OS
1.437
Digitized by VjOOQ IC
TABLE XXIII.
545
Present Value of £1 per Annum during the joint Continuance of a Male and Female
Life, when the Male is the Younger Life.
(Chester 3 per Cent.)
Age..
Valoa
Agi
s.
Value
Agee.
Value
Age..
Value
Agpj.
1
i
^
Value
.
ofUiA
•5
.
of the
•5
.
or the
-
.
uTthe
^
d
of the
•s
Annaity.
§
•a
Antiaity.
g
^
Annuity.
g
•5
Annuity.
t
i
Annuity.
iS
s
£
s
£
S
(S
a
i
^
"o
0
10.060
40
30
14.721
60
30
9.772
75
30
5.976
85
75
3.348
5
0
13.382
35
13.078
35
9.446
35
5.860
!iO
3.038
5
18.751
40
12.372
40
9.112
40
5.721
85
2.089
10
0
13.314
45
0
9.960
45
8.771
45
5.583
90
0
2.875
5
18.669
5
13.996
50
8.389
50
5.433
5
3.827
10
18.808
10
14.263
55
7.906
55
5.259
10
3.942
15
0
12.863
15
13.897
60
7.113
60
4.836
is'
3.901
5
18.048
20
13.593
65
0
6.422
65
4.730
1
:^0
3.866
10
18.209
/5
13.338
5
8.918
70
4.064
J5
3.846
15
,17.518
30
13.067
10
9.147
75
3.897
JO
3.861
20
0
12.470
35
12.508
15
8.972
80
0
3.554
25
3.818
5
17-506
40
11.884
20
8.851
5
4.821
4U
3.761
10
17.690
45
11.245
25
8.772
10
4.953
45
3.704
15
17.048
50
0
9.243
30
8.719
15
4.882
lO
3.652
20
16.507
5
12.979
35
8.492
20
4.832
y^
3.597
25
0
11.985
10
13.249
40
8.229
25
4.803
m
3.384
5
16.836
15
12.922
45
7.967
30
4.892
i.&
3.391
10
17 040
20
12.698
50
7.669
35
4.719
70
3.009
15
16.452
25
12.478
55
7.299
40
4.618
75
2.929
20
15.960
30
12.272
60
6.624
45
4.521
so
2.707
25
15.493
35
11.797
65
6.352
50
4.413
Sh
2.560
30
0
11.664
40
11.267
70
0
5.106
55
4.283
90
2.147
5
16.389
45
10.718
5
7.033
60
3.975
95
U
1.801
10
16.616
50
10.106
10
7.221
65
3.895
5
2.330
15
16.074
55
0
8.347
15
7.097
70
3.319
10
2.395
20
15.628
5
11.687
•20
7.009
75
3.256
15
2.379
25
15.205
10
11.950
25
6.956
80
2.952
20
2.364
30
14.751
15
11.678
30
6.932
85
0
3.542
a
2.351
35
0
11.142
20
11.484
35
6.778
5
4.811
:\Q
2.362
5
15.672
25
11.355
40
6.598
10
4.951
J5
2.346
10
15.909
30
11.186
45
6.413
15
4.883
40
2.322
15
15.422
35
10.803
50
6.215
20
4.833
■15
2.298
20
15.028
40
10.369
55
5.959
25
4.807
\U
2.272
25
14.661
45
9.927
60
5.462
30
4.815
\5
2.265
30
14.265
50
9.423
65
5.289
35
4.740
ut
2.154
35
13.548
55
8.811
70
4.501
40
4.646
65
2.179
40
0
10.586
60
0
7.213
75
0
4.406
45
4.557
7fl
1.997
5
14.882
5
10.066
5
6.025
50
4.466
73
1.955
10
15.151
10
10.307
10
6.191
55
4.350
9t
1.844
15
14.707
15
10.090
15
6.095
60
4.049
^
1.787
20
14.365
20
9.939
20
6.026
65
3.998
90
1.567
25
14.054
25
9.832
25 5.985
70
3.468
D5
1.437
Digitizedl^OOgle
546
TABLE XXIII.
Present Value of £1 per Annum during the joint Continuance of Two Male Lives.
(Chester 5 per Cent.)
A|«.
ViJw
Agui.
V«kl!
A«M.
Vol lie
A^ei.
Vnluc^
Ajfci.
1
t
^
r
^
Value
i
axhm
1
^
^jfihrt
i:
fe
af (ha
1
of the
j;
•
of Lim
AuDuky.
1
AuDatty-
-c
g
Antluitf.
3
Anauii}'.
S
1
Anniiit),
3
>
c
T,
eo'
30
o
>
s
>,
^
0
G*D17
40
10.401
7.679
75
30
5.485
83
75
2,998
b
0
0.649
2!>
10,075
35
7.430
35
5.383
80
2-748
5
13.511
4U
9.043
40
7.248
40
3.272
85
2.575
10
0
9.70G
45
0
7^443 ;
45
7.016
45
1 5J41
90
0
2.316
5
13,707
U
10.390
50
0.737
50
5.010
5
3.05fi
10
13p917
lU
I0.02t
5!i
6.431
hb
4.850
10
3-143
15
0
9.J80 '
\5
10.370
GO
5,844
60
4.481
15
3.04^1
5
13.275
2(»
9,708
65
0
5.290
0?i
4 387
20
3 0S7
10
13,490
■IS
9.650
5
7.298 ,
70
3.7ai
2iV
3.072
15
13.083
,iu
9-046
10
7.492
73
3.030
30
3,083
20
0
9.-22&
r^
9,5S7
15
7.360
80
0
3.139
35
3.053
b
I 2. 92 J
4l^
9.033
20
7.267
3
4w27
40
3.0U
10
13,144
45
S.SIO
25
7.203
10'
4-y61
45
2.969
15
12.76fi
50
{►
6,004
30
7.179
15
4.794
50
2-930
20
12.465 1
5
9.705
35
7,013
lO
4.745
55
2,692
25
0
S,900
JO
9.931
40
5.817
23
4.71S
601
2.733
^
12.G03
i:.
9.717
45
6.623
30
4.722
66
2.740
10
12.&3U
w
S».5fi3
50
6.407 ,
35
4.G46
70
2.460
n
12.475
23,
9.447)
55
6.139
40
4.553
75
2.428
20
12.194
30
9.342
GO
5.608
45
4.462
80
2.230
25
1KU47
3j
9<049
65
5.423
50
4.367
85
2,119
30
0
B.764
40
S.713
70
0
4.357
55
4.250
90
1.813
5
12.S71
45
8.370
a
5. 964
60
3.954
95
0
1.778
10
la. 505
Ui)
7.989
10
0.124
65
3.895
3
2,302
15
13.J73
55
0
6,413
15
6.026
70
3.302
10
2.367
20
11,915 ,
li
S.932
20
5,956
75
3.:'G7
15
2.352
25
1LC91
10
9. 151
25
5.yi4
m.
11.971
XO
2.336
30'
n.4G3
15
3p96G
30
5.900
85
0
3,053
25
2.323
35
0
8.33S
20
8.635
35
5w79
5
4.101
30
2.334
5
11.674
2*1
8.741
40
5,639
10
l/llH
35
2.319
lU
11.909
30
8.067
45
5.493
15
4J70
40
2.29^
i:j
11. GOO
35
8.418
50
5.336
20
4.130
45
2.ii72
20
11,378
40
s.in
53
5.141
25
4J0^
50
2.246
25
11.133
45
7.843
60
4.729
30
4.ny
fi5
2.239
30
10.987
50
7,518 ,
fi5
4.002
33
4.004
60
2.129
35
10*556
55
7.121
70
3.953
40
.^,yy3
05
2.155
40
0
7.693
eo
0
5.076
75
0
4.043
43
3.926
^0
1.974
5
10.032
5
7.860
6
r>.5l8
50
:i,&57
75
1 .932
10
11,200
10
8.059
10
5.671
55
3w80
SO
1 -822
15
10,'>95
15
7.900
15
5,.i8.-)
GO
3,:m
H5
1.759
1^0
10.792
2^^
7.79Q
20
5.324
05
3,519
m
1.54Ei
25
10.624
25
j.rii
25
5.489
70
3,093
93
1.421
Digitized by'
JUVIC
TABLE XXIir.
647
Preaent Value of £1 pe< Annum during the joint Continuance of Twro Female Lives.
(Cheater tj per Cent)
Age*.
Age..
Age..
Age..
Ages.
1
Value
1
Value
i
Valae
i
Value
^
Value
.
of the
1
oftlie
1
of the
^
of the
1
&
of the
•S
g
Aonuity.
§
Annuity.
i
Annuity.
•V
g
Annuity.
s
9
Annuity.
o
;S
_o
^
60
?
_5
>t
s
^
0
0
8.135
40
30
11.365
30
8.424
75
30
5.381
85
75
3.097
5
0
10.804
35
11.084
35
8.297
35
6.a26
80
2.61.9
5
14.398
40
10.792
40
8.169
40
6.273
85
2.712
10
0
10.816
45
0
8.683
45
8.016
45
5.216
90
0
2.859
5
14.416
6
11.556
50
7.813
50
5.152
6
3.620
10
14.444
10
11.647
55
7.437
55
6.012
10
3.684
15
0
10.522
15
11.413
60
6.770
60
4.673
15
3.656
5
14.023
20
11.237
65
0
6.992
65
4.629
20
3.641
10
14.061
25
10.987
7.886
70
3.895
26
3.592
15
13.700
30
10.910
i;;
8.073
75
3.579
30
3.602
20
0
10.277
35
10.661
i^
7.875
80
0
3.445
35
3.578
5
13.696
40
10.416
■2V
7.795
6
4.432
40
3.554
10
13.743
4;')
10.093
2%
7.659
10
4.502
45
3.531
15
13.402
50
0
8.185
M)
7.651
16
4.453
50
3.618
20
13.123
5
10.889
■ i'f
7.550
20
4.423
55
3.478
25
0
9.959
10
10.988
j('
7.449
25
4.358
60
3.308
5
13.271
15
10.781
j;.
7.336
30
4.363
65
3.295
10
13.327
20
10.627
r^i)
7.189
35
4.322
70
2.937
15
13.008
25
10.404
j5
6.902
40
4.284
75
2.771
20
12.714
30
10.349
flO
6.339
46
4.245
80
2.384
25
12.402
35
10.150
rir>
6.015
50
4.202
85
2.449
30
0
9.783
40
9.936
70
0
4.841
56
4.104
90
2.318
5
13.036
45
9.668
5
6.321
60
3.851
95
0
1.824
10
13.102
50
9.314
10
6.412
65
3.748
6
2.246
15
12.799
55
l»
7.523
10
6.329
70
3.259
10
2.287
20
12,559
^
10.085
20
6.274
75
3.009
15
2.273
25
12.231
lu
10.083
26
6.171
80
2.669
20
2.270
30
12.082
15
9.907
30
6.171
85
0
3.468
25
2.244
35
0
9.454
2ii
9.791
36
6.100
6
4.458
30
2.251
5
12.595
ri
9.586
40
6.029
10
4.632
36
2.241
10
12.669
IW
9.549
46
6.954
16
4.486
40
2.230
15
12.369
5[>
9.388
50
5.862
20
4.458
45
2.219
20
12.170
H]
9.217
56
5.667
25
4.393
50
2.213
25
11.868
45
9.009
60
6.234
30
4.402
56
2.209
30
11.743
50
8.729
65
5.040
36
4.363
60
2.119
33
11.438
55
8.248
70
4.290
40
4.326
65
2.109
40
0
i,m
60
0
6.614
n
0
4.229
46
4.292
70
1.961
5
1«.114
5
8.743
6
6.485
50
4.261
76
1.894
It
12.199
10
8.847
10
5.504
66
4.175
80
1.679
15
11.939
15
8.705
15
5.463
60
3.932
85
1.681
20
11.741
20
8.603
20
6.443
65
3.853
90
1.677
25
11.4155
25
8.444
23
5.3/7
70
3.351
95
1.344
2
N
"^
548
TABLE XXIXI.
Present Value of £1 per Annum during the joint Continuance of Two Lives (Male
end Female) Female the Younger.
(Chester 5 per Cent.)
A
«"•
Value
Ag«t.
Value
Axes.
Value
Ages.
Valoe
Agea.
a'
£
•
,
i
Value
i
1
of the
•
of the
.
"S
of the
^
1
of the
i
or the
Annuity.
1
Annuity.
1
J
Annuity.
1
S
1
Annuity.
1
Annuity.
0
0
7.498
40
30
10.673
60
30
7.744
75
30
5.504
85
75
2.998
5
0
10.462
35
10.439
35
7.636
35
5.446
80
2.'i53
5
13.942
40
10.181
40
7.521
40
5.390
85
2.632
10
0
10.603
45
0
8.013
45
7.386
45
5.332
90
0
2.463
5
14.134
5
10.644
50
7.209
50
5.264
5
3.097
10
14.172
10
10.739
55
6.879
55
5,113
10
3.147
15
0
10.264
15
10.534
60
6.284
60
4.761
15
3.127
5
13.677
20
10.388
65
0
5.666
65
4.600
20
3.116
10
13.724
25
10.116
5
7.445
70
3.938
25
3.076
15
13.384
30
10.099
10
7.545
75
3.600
30
3.084
20
0
9.984
35
9.898
15
7.437
80
0
3.723
35
3.065
5
13.304
40
9.678
20
7.363
5
4.806
40
3.045
10
13.429
45
9.408
25
7.418
10
4.883
45
3.027
15
13.039
50
0
7.489
30
7.228
15
4.830
50
3.016
20
12.781
5
9.932
35
7.135
20
4.797
55
2.985
23
0
9.728
10
10.031
40
7.041
25
4.726
60
2.8'J6
5
12.963
1&
9.851
45
6.934
30
4.732
65
2.836
10
13.028
20
9.719
50
6.798
35
4.688
70
2.546
15
12.726
25
9.522
55
6.532
40
4.646
76
2.410
20
12.487
30
9.479
60
6.005
45
4.604
80
2.093
25
12.161
35
9.308
65
5.710
50
4.561
85
2.135
30
0
9.465
40
9,126
70
0
4.659
55
4.455
90
2.042
5
12.609
45
8.895
5
6.076
60
4.180
95
0
1.886
10
12.G84
50
8.607
10
6.162
65
4.072
5
2.329
15
12.^03
55
0
6.903
15
6.082
70
3.529
10
2.372
20
12.183
5
9.132
20
6.029
75
3.252
15
2.357
25
11.879
10
9.234
25
5.930
80
2.755
20
2.354
30
11.754
15
9.079
30
5.929
85
0
3.252
25
2.327
35
0
9.003
20
8.908
35
5.861
5
4.164
30
2.3.34
5
11.984
25
8.796
40
5.794
10
4.236
35
2.323
10
12.068
30
8.768
45
6.720
15
4.195
40
2.312
15
11.812
35
8.626
50
5.630
20
4.173
45
2.301
20
11.616
40
8.478
55
5.441
25
4.114
50
2.294
25
11.341
4.'>
8.300
60
5.042
30
4.123
55
'2.290
30
11.238
50
8.062
65
4.833
36
4.090
60
2.280
35
10.970
55
7.649
70
4.116
40
4.058
65
2.217
40
0
8.508
60
0
6.080
75
0
4.320
45
4.028
70
2.029
5
11.315
5
8.026
5
5.617
50
4.002
75
1.959
10
11.403
IjO
8.124
10
6.702
55
3.936
80
1.733
15
11.174
15
7.998
15
5.633
60
3.717
85
1.738
20
11.000
20
7.908
20
5.589
65
3.665
90
1.731
25
10*753
25
7.764
S5
5.501
70
3.217
95
1.378
' Digitized by ^^OOQlC
TABLE XXIII.
549
Preient Value of £1 per Annum during the joint Continuance of Two Lives (Malt
and Female) Male the Younger.
(Chester 5 per Cent.)
u^*.
Vnlue
Ast*-
Vftlue
Agw.
Valiw
Ages.
Value
Ages.
i
9
i
VeLw
^
of the
4
►
orth«
JB
.
of the
•5
•
of the
£
of tlie
Annnhj.
=
AnDuhy. .
•s
Annuity.
g
•5
Annuity.
g
i
Annuity.
£
z
it
4l>
:jo
£
a
£
s
85
X
0
0
7.498
11.109
60
30
8.343
7b
30
5.363
75
3.109
6
0
9.956
J5
10.669
35
8.118
35
5.267
80
2.832
5
13.942
4U
10.181
40
7.859
40
5.150
85
2.632
10
0
9.974
45
a
8.056
45
7.597
45
5.035
90
0
1.712
5
13.969
5
11.269
50
7.304
50
4.912
5
3.570
10
14.172
10
11.510
55
6.933
55
4.763
10
3.675
15
0
9.711
15
11.235
60
6.284
60
4.405
15
3.638
5
13.600
20
11.027
65
0
5.693
65
4.329
20
3.606
10
13.808
23
10.863
6
7.730
70
3.743
25
3.5S7
15
13.384
3(1
10.697
10
7.934
75
3.600
30
3.601
20
0
9.493
^6
10.304
15
7.792
80
0
3.723
35
3.563
5
13.293
4CI
9.861
20
7.693
5
4.360
40
3.511
10
13.508
15
9.408
25
7.631
10
4.481
45
3.460
15
13.105
5n
fl
7.609
30
7.599
15
4.420
50
3.412
20
12.781
5
10.631
35
7.420
20
4.376
55
3.364
25
0
9.310 !
JO
10.871
4a
7.209
25
4.350
60
3.169
5
12.893
n
10.627
45
7.001
30
4.352
66
3.178
10
13.112
10
10.450
50
6.769
35
4.286
70
2.831
15
12.735
2S
10.311
55
6.478
40
4.197
7b
2.757
20
12.412 ;
3i\
10.183
60
5.913
45
4.114
80
2.553
25
12.161
35
9.839
65
5.710
50
4.023
85
2.420
30
0
9.051
40
9.451
70
0
4.1>27
55
3.916
90
2.042
5
12.676
Ab
9.053
5
6.204
60
3.616
95
0
1.719
10
12.905
:>o
8.607
10
6.374
65
3.588
5
2.221
15
12.547
55
0
7,000
15
6.271
70
a. 139
10
2.282
20
12.264
h
9.754
20
6.197
75
8.024
15
2.268
25
12.012
in
9.987
25
6.154
80
2.755
20
2.239
30
11.754
\'a
9.778
30
6.141
85
0
3.243
25
2.241
3d
0
8.754
ti)
9.630
35
6.016
5
4.386
30
2.251
5
12.259
25
9.521
40
6.866
10
4.515
35
2.237
10
12.493
M
9.429
45
5.718
15
4.455
40
2.214
15
12.161
35
9.144
60
5.558
20
4.415
45
2.192
20
11.904
4i)
8.817
55
5.354
25
4.387
50
2.167
25
11.679
45
8.486
60
4.931
30
4.396
55
2.160
30
11.448
50
8.110
65
4.802
35
4.332
60
2.0.^6
35
10.970
55
7.649
70
4.116
40
4.247
65
2.080
40
0
8.431
GO
0
6.163
75
0
8.960
45
4.171
70
1.909
5
11.803
5
8.558
5
6.390
50
4.092
75
1.868
10
12.041
iO
8.773
10
6.540
55
3.994
80
1.764
15
11.737
li
8.601
15
6.459
60
3.727
85
1.705
20
11.505
20
8.482
20
5.400
65
3.689
90
1.504
25
11.308
25
8.402
25
5.365
70
3.216
95
1.378
D\l
jrft2i
'CTtT^
950
TABLE XXIV.
Showing, out of the Number entering upon any Year, the Proportion which die in
that Year or sunriTe it, according to the Carlisle Rate of Mortality.
A«e.
which di«.
Proportion
which •urriTC
Radpcoeal
of ditto.
Age.
Proportioa
which die.
Proportion
whiou aorvire.
Rrciprocftl
of ditto.
0
.153900
.846100
M8189
52
,015201
.984799
1.01544
1
.080605
.919395
1.08767
53
•016148
.983852
1.01641
2
.064918
.935082
1.06942
54
.016896
.983104
1.01719
3
.037943
.962057
1.03944
55
.0179-23
.982077
1.01425
4
.028723
.971277
1.02957
56
.019000
.981000
1.01937
5
.017802
.982198
1.01812
57
.020897
.979103
1.02134
6
.012283
.987717
1.01244
58
.024206
.975794
1.02481
7
.008796
.991204
1.00887
59
.028274
.971726
1.02910
8
.006579
.993421
1.00662
60
.033489
.966511
1.03465
9
.005082
,9949ia
1.00511
61
.035785
.964:^15
1.03711
10
.004489
.995511
1.00451
62
.037408
.962592
1.03886
11
.004820
.995180
1.00484
63
.038250
.961750
1.03977
)2
.005000
.995000
1.00503
64
.039771
.960229
1.04142
13
.005182
.994818
1.00521
65
.041087
.958913
1.04285
14
.005525
.994475
1.00556
66
.042502
.957498
1.04439
15
.006191
.993809
1.00623
67
.044388
.955612
1.04645
16
.006703
.993292
1.00675
68
.046450
.953550
1.04871
17
.006914
.993086
1.00696
69
.049109
.950891
K05165
18
•006962
.993038
1.00701
70
.051645
.943355
1.05446
19
.007011
.992989
1.00706
71
.058849
.941151
1.06253
20
.007061
•992939
1.00711
72
.068129
.931871
1.07311
21
.006946
.993054
1.00699
73
.U78117
.921883
1.08474
22
.006994
.993006
1.00704
74
.090168
.909832
1.09910
23
.007043
.992957
1.00709
75
.095522
.904478
1.10561
24
.007093
.992907
1.00714
76
.102970
.897030
1.11479
25
.007314
.992686
1.00736
n
.107432
.892568
1.12036
26
.007368
.992632
1.00742
78
.108821
.891179
1.12211
27
.007768
.992232
1.00783
79
.118409
.881591
1.13431
28
.008699
.991301
1.00878
80
.121721
.878279
1.13859
29
.009828
.990172
1.00993
81
.133811
.866189
1.15448
30
.010103
.989897
1.01021
82
.140690
.859310
1.16372
31
.010206
.989794
1.01031
83
.150883
.849117
1.17769
32
.010130
.989870
1.01023
84
.158790
.841210
1.18876
33
.010051
.989949
1.01015
85
.175281
.824719
1.21253
34
.010153
.989847
1.01026
86
.193461
.806539
1.23987
35
.010257
.989743
1.01036
87
.216216
.783784
1.27586
36
.010552
.989448
1.01066
88
.219828
.780172
1.28177
37
.010655
.989145
1.01097
89
.215470
.784530
1.27465
38
.011167
.988833
1.01129
90
.260563
.739437
1.35238
39
.011877
.988123
1.01202
91
.285714
.714286
1.40000
40
.013005
.986995
1.01318
92
.280000
.720000
1.38889
41
.013775
.986225
1.01397
93
.259259
.740741
1.35000
42
.014373
.985627
1.01458
94
.250000
.750000
1.33333
43
.014:)82
.985418
1.01480
95
.233333
.766667
1.30435
44
.014798
.985202
1.01502
96
.217391
.782609
1.27778
45
.014809
.985191
1.01503
97
.222222
.777778
1.28571
46
.014816
.985184
1.01504
98
.214286
.785714
1.27273
47
.014603
.985397
1.01482
99
.181818
.818182
1.22222
48
.013935
.986065
1.01413
100
.222222
J7777H
1.28571
49
.013683
.986317
1.01387
101
.285714
.714286
1.40000
50
.013418
.986582
1.01380
102
.400000
.600000
1.66667
51
.014293
.985708
1.01450
103
.666666
.333334
3.00000
Digitized by VjOOQ IC
TABLE XXV-
W
Jibe Loganthm and iU Arithmetical Complement of the Fraction which :
the Probability that a Life of an assigned Age will survive One Tear^ according
to the Carlisle Table of Mortality.
Arithmetical
Arithmeckal
Age.
Logarithm.
Ckimplemdnt of
ailto.
Age.
Logarithm.
<ttto.
0
1.9274217
0.0725783
52
T.9933475
0.0066525
1
.963502)
0.0364979
53
.9929297
.0070703
2
.9708495
.0291505
54
.9925995
.0074005
3
.9832006
.0167994
55
.9921456
.0078544
4
•9973434
•012656G
56
.9916690
.0083310
5
.9921990
.0078010
57
.9908284
.0091716
6
•9946326
.0053674
58
.9893580-
.0106420
7
.9961631
;0038369
59
.98754.38
.0124562
S
.9971334
.002S666
60
•9852068
.0147932
9
.9977871
.0022129
61
.9841738
.0158262
10
.9930460
.0019540
62
.9834422
.0165578
11
.9979015
.•0020985
63
.9830624
•0169376
12
.9978230
.0021770
64
.9823748
.0176252
13
.9977436
.0022564
65
.9817793
.0182207
14
.9975939
.0024061
66
.9811380
.0188620
15
.9973032
.0026968
67
.9802815
.0197185
16
.9970769
.00-29231
68
.9793434
.0206566
17
.9969867
.0030133
69
.9781308
.0218692
18
.9969657
.0030343
70
.9769708
•0230292
19
.9969443
.0030557
71
.9736592
.0263408
20
.9969227
.0030773
72
.9693559
.0306441
21
.9969730
.0030270
73
.9646757
.0353243
22
.9969518
.0030482
74
•9589610
•0410390
23
.9969303
.0030697
75
.9563978
.0436022
24
.9969084
•0030916
76
•9528069
.0471931
25
.9968118
.0031882
'77
.9606413
.0493587
26
.9967882
.0032118
78
.9499649
.0500351
27
.9966133
•0033867
79
.9452672
.054732^
28
.9962056
.0037944
80
.^36326
.0563674
29
.9957107
.0042893
81
.9376125
.0623875
30
.9955901
.0044099
82
.9341500
•0658500
31
.9955448
.0044552
S3
.9289677
•0710323
32
.9955781
.0044219
84
.9249043
.0750957
33
.9956127
.0043873
85
.9163061
.0836939
34
.9955680
.0044320
86
.9066256
.0933744
35
.9955223
.0044777
87
.8941963
•1058037
36
.9953929
.0046071
88
.8921906
.1078094
37
.9952599
.0047401
89
.8946097
•1053903
38
.9951231
.t)048769
90
.8689010
.1310990
39
.9948110
.0051890
91
.8538720
.1461280
40
.9943150
.0056850
92
.8573325
•1426675
41
.9939759
.0060241
93
.8696662
.1303338
42
.9937129
.0062871
94
.8750613
.1249387
43
.9936204
.0063796
95
.8846065
.1153935
44
•9935254 «
.0064746
96
.8935447
.1064553
45
,9935206
.0064794
97
.8908555
.1091445
46
.9935172
.0064828
98
.8952647
.1047353
47
.9936111
.0063889
99
.9128498
.0871502
48
.9939056
.0060944
100
.8908555
.1091445
49
.9940164
.0059836
101
\8538720
.1461280
50
.9941330
,0058670
102
.7781513
.2218487
51
.9937482
•0062518
103
.5228787
.4771213
652
TABLB XXVI.
Showing the Probabilitiet of Sumvorahip between every Two Liret whereof the
Diffexenoe of Age it either Ten Years or any multiple of Ten^ according to the
Carlisle Table of Mortality.
Difference Ten Ycaw.
Age of
Pfobabllity
Protaability
Affttof
Probability
Probability
of Adyiutf
before b;
of R dying
bofure A.
or A dying
before B?
of B dying
beforQ A.
A.
fi.
A.
B.
0
10
.5834
.4166
48
58
.3174
.68*26
1
11
.5103
.4897
49
59
.3156
.6844
2
12
•4699
.5301
50
60
.3152
.6848
3
13
•4354
.5646
51
61
•3167
.6a33
4
14
.4154
.5846
52
62
.3185
•6815
5
15
.4004
.5996
53
63
.3202
.6798
6
16
.3920
.6080
54
64
.3217
.6783
7
17
.3871
,61*29
55
65
.3232
.6768
8
18
.3844
.6156
56
65
.3246
.6754
9
19
.3830
.6170
57
67
.3258
.6742
10
20
.3825
.6175
58
68
.3264
.6736
11
21
.3825
.6175
59
69
.3253
.6747
12
22
.3821
.6179
60
70
.3222
.6778
13
23
.3317
.6183
61
71
.3160
.6840
14
24
.3812
.6188
62
72
.3099
.6901
15
25
.3805
.6195
63
73
.3052
.6948
16
26
.3794
.6206
64
74
.3028
.6972
17
27
.3780
.6220
65
75
.3031
.6969
18
28
.3767
.6233
66
76
.3044
.6956
19
29
.3756
.6244
67
77
.3074
.6926
20
30
.3749
.6251
68
7B
.3112
.6888
21
31
.3743
.6257
69
79
.3145
.6855
22
32
.3737
.6263
70
80
.3201
•6799
23
33
.3732
.6268
71
81
.3261
.6739
24
34
.3725
.6275
72
82
.3326
.6674
25
35
• 3718
.6282
73
83
.3363
.6637
26
36
.3710
.6290
74
84
.3373
.6627
27
37
.3703
.6297
75
85
.3323
.6677
28
38
.3694
.6306
76
86
.3286
•6714
29
39
.3681
.6319
77
87
.3256
.6744
30
40
• 3662
.6338
78
88
,3285
.6715
31
41
.3645
.6355
79
89
.3331
.6669
32
42
.3630
.6370
80
90
.3289
.6711
33
43
.3618
.6382
81
91
.3434
.6566
34
44
.3607
.6393
82
92
•3697
.6303
35
45
.3595
•6405
83
93
.4020
.5980
36
46
.3582
.6418
84
94
.4304
.5696
37
47
.3568
.6432
85
95
.4619
,5381
38
48
.3550
.6450
86
96
.4357
.5143
39
49
.3527
.6473
87
97
.4963
.5037
40
50
.3498
.6502
88
98
.4989
.5011
41
51
.3459
.6541
89
99
.4937
.5063
42
52
.3418
.6582
90
100
.4640
.5360
43
53
.3374
.6626
91
101
.4041
.5959
44
54
.3331
.6669
92
102
.3120
.6880
45
55
.3288
.6712
93
103
.2037
.7963
46
56
.3246
.6754
94
104
.1250
.8750
47
57
.3207
.6793
TABLK XXVr.
^3
Showing the Probahilities of Saryivortbip betwMn every Tiro Litres whereof the
Difference of Age is either Ten Yean or any multiple of TeD> According to tha
Carlisle Table of Mortolity.
Difference Twenty Yeaw.
Age of
Probiibltlty
Probability
Age of
Probability
Probability
of A dying
before B.
of B dying
before A.
of A dying
before B.
of B dviug
before A.
A.
B.
A.
43
B.
0
20
.5182
.4818
63
.2019
.7981
1
21
•4343
.5657
44
64
.1979
.8021
2
22
•3877
.6123
45
65
• 1939
.8061
3
23
.3479
.6521
46
66
.1899
.8101
4
24
.3246
.6754
47
67
.1859
.8141
5
25
.3069
.6931
48
68
.1823
,8177
6
26
.2966
,7034
49
69
.1794
.8206
7
27
.2900
.7100
50
70
.1770
.8230
8
28
.2B60
.7140
51
71
.1752
.8248
9
29
.2837
.7163
52
72
.1739
.8261
10
30
.2829
.7171
53
73
.1735
.8265
11
31
.2825
• 7175
54
74
,1742
.8258
12
32
.2819
.7181
55
75
.1767
.8233
13
33
.2812
.7188
55
76
.1797
.8203
14
34
.2803
.7197
57
77
.1838
.8162
15
35
.2792
.7208
58
78
.1877
.8123
16
36
.2776
.7224
59
79
.1895
.8105
17
37
.2756
.7244
60
80
.1901
.8099
18
38
.2736
.7264
61
81
.1869
.8131
19
39
.2716
.7284
62
82
.1838
.8162
20
40
.2697
.7303
63
83
.1802
.8198
21
41
.26S0
.7320
64
84
.1774
.8226
22
42
.2666
.7334
65
85
.1742
.8258
23
43
.2653
•7347
66
86
.1729
.8271
24
44
.2640
.7360
67
87
.1742
.8258
25
45
.2627
.7373
68
88
• 1797
.8203
26
46
.2612
• 7388
69
89
.1860
•8140
27
47
.2596
.7404
70
90
.1906
•8094
28
48
.2576
.7424
71
91
.2078
.7922
29
49
.2547
.7453
72
92
•2340
.7660
30
50
.2508
.7492
73
93
.2615
.7385
31
51
.2465
.7535
74
94
.2834
.7166
32
52
.2423
.7577
75
95
.2997
.7003
33
53
.2383
.7617
76
96
.3105
.6895
34
54
.2344
.7656
77
97
.3115
.6885
35
55
.2305
.7695
78
98
.3043
.6957
36
56
.2267
.7733
79
99
.2958
.7042
37
57
.2228
.7772
80
100
.2609
.7391
38
58
.2190
• 7810
81
101
.2236
.7764
39
59
.2155
.7845
82
102
.1760
.8240
40
60
.2122
.7878
83
103
.1231
.8769
41
61
•2091
.7909
84
104
.0794
•9206
42
62
• 2056
.7944
Digitized by LjOOQ IC
554
TABLE ZXVI.
filhowing the Probabilltiet of Survivorship between every Two Lives whereof tiie
Diflference of Age ii either Ten Years or any multiple of Ten ; according to the
Carlisle TaUe of Mortality.
Diflference Thirty Yeara.
Age of
PfobaWlUy
of A dying
beforaB.
PfobabiUty
of B dying
before A.
Age of
PfobabQtty
of A dying
beforoB.
PtobabiUty
olBdyieg
befiinA.
A.
B.
A.
B.
0
30
.4672
.5328
38
68
• 1335
.8665
I
31
.3750
.6250
39
69
• 1300
.8700
2
32
.3239
.6761
t
70
.1260
.8740
3
33
.2802
.7198
71
.1211
.8789
4
34
.2546
.7454
42
72
.1161
.8839
5
35
.2351
.7649
43
73
.1112
.8883
6
36
.2236
.7764
44
74
.1070
.6930
7
37
.2163
.7837
46
75
.1036
.8964
8
38
.2117
.7883
46
76
• 1005
.8995
9
30
.2088
• 7912
4P
77
•0978
.9022
10
40
.2073
• 7927
48
7S
•0955
.9045
11
41
. .2064
.7936
4P
79
.0936
.9064
12
42
.2054
. .7946
50
80
. .0929
.9071
13
43
.2044
.7956
51
81
•0927
.9073
14
44
.2033
.7967
52
82
.0929
.9071
15
45
.2019
.7981
53
83
.0931
.9069
16
46
.1999
.8001
54
84
.0936
.9064
17
47
,1975
.8025
56
85
.0943
.9057
18
48
.1948
.6052
56
86
.0963
.9037
19
49
. .1919
.8081
57
87
.1000
.9000
20
50
.1888
.8112
58
88
[ .1060
.8940
21
51
• .1855
.8145
58
89
• 1110
.8890
22
52
.1825
.8175
60
90
.1125
.8875
23
53
.1795
.8205
61
91
.1166
.8834
24
54
.1766
.8234
62
92
. .1248
.8752
25
55
.1737
.8263
m
93
.1336
.8664
26
56
. .1708
.8292
64
94
.1408
.8592
87
bl
. .1679
.8321
66
95
.1472
.8523
28
58
.1649
.8351
66
96
.1509
.8491
29
59
.1616
.8384
67
97
.1508
.8492
30
60
. .1579
.8421
6»
98
.1498
.8502
31
61
.1546
.8454
69
99
• 1445
.8555
32
62
.1515
.8485
70
100
• 1281
.8716
33
63
.1486
.8514
71
101
.1119
.8881
34
64
.1457
.8543
72
102
.0914
.9086
35
65
.1428
.8572
73
103
.0659
.9341
36
66
. .1399
.8601
74
104
•0431
.9549
37
67
. .1368
.8632
Digitized by LjOOQ iC
TABLE XXVI.
5^
SbowiD^ the Probabilii'iei of Survifotship between every Two Lifos whereof tho
DifTereqce of Age is either Ten Years or any Multiple qf Te% according to the
Carlisle Table of Mortality.
Difference Forty Ye«T9.
A8»or
Age of
Probability
ofAdyinf
Probability
or H dying
Probability
df A dying
before If.
FrobabOity
ofB dying
A.
B.
b«fore II.
bofjro A.
4.
B.
before A.
e
40
.4258
.5742
33
73
.0853
.9147
1
41
.8268
.6732
ai
74
• .0829
.9171
2
42
.2721
.7279
35
75
• .0813
.9187
3
43
.2253
.7747
35
76
.0799
.9201
4
44
.1980
• .8020
37
77
.0788
.9212
5
45
.1771
.8-Z29
38
78
.0776
.9224 •
6
46
.1648
• .83J2
39
79
.0761
.9239
^
47
• 1563
.8432
40
80
.0745
.9255
8
48
.1516
.8484
41
81
.0719
.9281
9
49
.1481
.8519
42
82
.0691
.9309
10.
50
.1457
.8543
48
83
.0658
.9342
11
&1
.1438
.8562
44
84
.0625
.9375
12
52
.1418
.^5S2
45
85
.0590
.9410
13
53
.1396
.8604
46
86
.0560
.9440
14
54
.1374
.8626
47
87
.0536
.9464
15
55
.1349
.8651
48
88
.0526
.9474
16
56
.1320
• .^680
49
89
.0522
.9478
17
57
• .1286
.8714
50
90
.0517
.9-*83
18
58
.1252
.8748
51
91
.0549
.9451
19
59
.1221
.8779
52
92
.0605
.9395
20
60
.1194
.8806
53
93
.0669
.9331
21
61
.1172
.8828
54
94
.0726
.9274
22
62
.1153
.8847
55
95
.0784
.9216
23
63
.1134
.8866
56
96
.0831
.9169
24
64
.1115
.8S85
57
97
.0862
.9133
25
65
.1097
.8903
.8923
58
98
.0888
.9112
26
66
.1077
.1057
59
99
• .0876
.9124
27
67
.9943
60
106
.0778
.9222
28
68
.^035
•9965
61
101
.0640
.9360
29
69
.1005
.8995
62
102
.9483
.9517
30
70
.0965
.9035
63
103
.0319
.9681
31
71
.0924
.9076
64
104
.0199
•9801
32
72
.0885
.9115
Digitized by VjOOQ IC
»ft6
TABLB XXVI.
ShowiDg the Probabilitiet of SumTonhip between every Two Livei wbereof the
Difference of Age ii either Ten Tean or any Multiple of Ten, according to the
Carlisle Table of Mortality.
Difiereace Fifty Years.
Age of
Age of
PPoUbillty
of A dying
Probability
of B dying
Piobability
ofAdykif
Probalilily
of B dyiuff
A.
B.
50
before B.
before A.
A.
B.
78
beroro B.
before aT
0
.3921
.6079
.0596
.9404
1
51
.2866
.7134
29
79
.0532
.9418
2
52
.2260
.7720
3D
80
.0560
.9440
3
53
.1963
.8037
31
81
•0535
.9455
4
54
.1479
.8521
38
82
.0513
.9487
5
55
.1250
.8750
38
63
•0493
.9507
C
56
.1113
.8887
34
84
.0476
.9524
7
57
.1023
.8977
35
85
.0459
.9541
8
58
.0965
.9035
36
86
.0448
.9552
9
59
.0928
.9072
37
87
.0442
.9558
10
60
.0903
.9092
38
88
.0445
.9555
11
61
.0898
•9102
39
89
.0448
.9552
12
62
.0887
.9113
40
90
.0441
.9559
13
63
.0875
.9125
41
91
.0449
.9551
14
64
.0861
.9139
42
92
.0470
.9530
15
65
.0845
.9155
43
93
•0488
.9518
16
66
.0823
.9177
44
94
.0495
.9505
17
67
.0796
.9204
45
95
.0494
.9506
18
68
•0768
.9232
46
96
.0482
.9518
19
69
.0739
.9261
47
97
.0453
.9547
20
70
.0710
.9290
48
98
.0422
.9578
21
71
.0691
.9319
49
99
.0384
•9616
22
72
.0657
.9343
50
100
.0322
•9678
23
73
.0637
.9363
51
101
.0264
.9736
24
74
.0622
.9378
52
102
.0202
•9798
25
75
.0613
.9387
58
103
.0135
.9865
26
76
.0605
• 9395
54
104
.0084
•9916
27
77
•0601
.9399
Digitized by VjOOQ IC
TABUS XXVL
&&J
Showing the Probabilitiei of Survivorahip between erery Two Livei, whereof the
Difference of Age it either Ten Years or any Multiple of Ten, according to the
Carlisle Table of Mortality.
Difference Sixty Years.
Difference Seventy Years.
Agtof
Age of
Probability
ofAdylug
ProUbOity
of B dying
ProbabUUy
of A dying
Probability
of B dying
A.
B.
60
tefore B.
before A.
A.
B.
before B.
before A.
0
.3521
.6479
0
70
.3198
.6802
1
61
.2456
.7544
1
71
.2117
.7883
2
62
.1877
.8123
2
72
.1543
.8457
3
63
.1378
.8622
3
73
.1051
.8949
4
64
.1087
.8913
4
74
.0774
•9226
5
6
7
8
9
65
06
67
68
69
.0864
.0732
.0647
.0592
.0557
.9136
.9268
.9353
.9408
.9443
5
6
7
8
9
75
76
77
78
79
.0565
.0445
.0371
.0325
.0297
.9435
.9555
.9629
.9675
.9703
10
70
.0536
.9464
11
71
.0522
.9478
10
80
.0284
.9716
12
72
.0507
.9493
11
81
.0277
.9723
13
73
.0495
.9505
12
82
.0269
.9731
14
74
.0485
.9515
13
83
.0260
.9740
15
75
.0478
.9522
14
84
.0252
.9748
16
17
18
19
76
77
78
79
.0466
.0452
.0436
.0418
.9534
.9548
.9561
.9582
15
16
17
18
65
86
87
88
.0240
.0224
.0204
.0182
.9760
.9776
.9796
.9818
20
80
.0403
.9597
19
89
.0156
.9844
21
81
.0386
.9614
22
82
.0373
.9627
20
90
.0119
.9881
23
83
.0361
.9639
21
91
.0079
.9921
24
84
.0351
.9649
22
92
.0027
.9973
25
26
85
86
.0342
.0336
.9658
.9664
23
24
93
94
.0265
.0277
.9735
.9723
27
28
29
87
88
89
.0337
.0344
.0345
.9663
.9656
.9655
25
26
27
95
96
97
.0288
.0294
.0294
.9712
.9706
.9706
30
90
.0331
.9669
28
98
.0291
.9709
31
91
.0333
.9667
29
99
.0274
.9726
32
92
.0347
.9653
33
93
.0364
.9636
30
100
.0228
.9772
34
94
.0378
.9622
31
101
.0180
.9820
35
36
37
95
96
97
.0389
.0393
.0386
.9611
.9607
.9614
32
33
34
102
103
104
.0131
.0084
.0051
.9869
.9916
.9949
38
98
.0377
.9623
39
99
.0356
.9644
40
100
.0307
.9693
41
101
.0250
.9750
42
102
.0187
.9813
43
103
.0121
.9879
44
104
.0074
.9926
Digitized by LjOOQ IC
538
TABLE XXVI.
Showing^ the Probabilities of Sumvorshlp between eveiy Two Lives, whereof the
Diflbrence of A^ is either Ten Years or any Multiple of Tea, according to the
Carlisle Table of Mortalitj.
Difference Eighty Years.
Difference Ninety Yean.
Age of
Age or
Piobabilily
of A dying
Pfobabilily
of B dying
ProbabaUy
or A dying
Probability
of B dying
A.
B.
before B.
before A.
A.
0
B.
90
bofore B.
bcfoceA.
0
80
.2758
• 7242
.2192
.7808
1
81
• 1767
.8233
1
91
.1365
.8635
2
82
.1274
.8726
2
92
.1027
.8973
3
83
.0835
.9165
3
93
.0695
•9305
4
84
.0592
• 9408
4
94
.0512
.9468
5
85
.0402
.9598
5
95
.0358
.9642
6
86
.0295
.9705
6
96
.0267
.9733
7
87
• 0231
.9769
7
97
.0204
.9796
8
88
.0197
.9803
8
98
.0164
.9836
9
89
.0178
.9822
9
99
• 0134
.9866
10
90
.0170
.9830
10
100
.0108
• 9892
11
91
.0178
.9822
11
101
.0088
.9912
12
92
.0193
.9807
12
102
.0066
•9934
13
93
.0209
.9791
13
103
.0044
•9956
14
94
.0223
•9777
14
104
«0028
.9972
15
95
.0234
•9766
16
96
.0235
.9765
17
97
.0226
.9774
18
98
.0212
.9788
19
99
.0192
.9808
20
100
.0158
.9842
21
101
.0124
.9876
22
102
.0091
.9909
23
103
•0059
.9941
24
104
.0035
•9965
Difference One Hundred Years.
Age of
ProbabiHty
ofAdyiBg
before B.
Pnb»biHty
A.
B.
100
101
102
103
104
ofBdyiDg
before A.
0
1
2
3
4
.2120
.1142
.0687
.0299
.0144'
.7880
.8858
.9313
.9701
.9856
f^
/ '^ "digitized by Google
Digitized by LjOOQ iC
Digitized by VjOOQ iC
Digitized by VjOOQ IC
Digitized by VjOOQ iC
/
4
1 05) tG*>
m S790
V.I
zed by ^
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■*>
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