{^-■r^'f FOREST FINANCE Guide to Lectures Delivered at the Biltmore Forest School By C. A. SCHENCK, Ph. D. FORESTER TO THE BILTMORE ESTATE ■^ ^ \^<^ ^5*. 1909 THE INLAND PRESS ASHEVILLE, N. C. c^ FOREST FINANCE Guide to Lectures Delivered at the Biltmore Forest School By C. A. SCHENCK, Ph. D. FORESTER TO THE BILTMORE ESTATE 1909 THE INLAND PRESS ASHEVILLE, 5. C. Digitized by the Internet Archive in 2009 with funding from NCSU Libraries http://www.archive.org/details/forestfinanceguiOOsche Biltmore, N. C, January 1, 1909. In usum Delphini: The Biltmore lectures on Forest Finance appear in print since it is nec- essary to place in the hands of the Biltmore students some basal findings con- cerning the financial side of forestry, which findings it is not easy for them to obtain elsewhere. In America, forest finance is and will be the most important branch of forestry; the very difficulty of the financial problems involved in American forestry is enticing; and I am interested, personally, more deeply in the scien- tific and practical development of forest finance than in that of any other branch of American forestry. Special students desirous to attend the Biltmore lectures on forest finance, and otherwise excluded from the Biltmore School, will be welcomed at Bilt- more hereafter. This arrangement is made for the reason that the lecturer is anxious to study forest finance through and with the students — the regulars as well as the specials. Co-operation between teacher and pupil is essential to the development of American forest finance. The interest tables attached to this book are obtained, by extraction and addition, from those published by the Mutual Life Insurance Company of New York. C. A. SCEENCE. FOREST FINANCE SYNOPSIS OF PARAGRAPHS Par. I. Introduction; Par. II. Mathematical principles of finance; Par. III. Increasing or decreasing prices; Par. IV. Receipts and expenses in forestry; Par. V. Taxes; Par. VI. Protective expenses; Par. VII. Capital and money; Par. VIII. Interest; Par. IX. Expectation values; Par. X. Sale values; Par. XI. Gauging the merits of an investment; Par. XII. Maturity of trees. FOREST FINANCE PARAGRAPH 1.— INTRODUCTSON. I. Definition. Forest Finance deals with forestry as an investment. Treated as a branch of science in European literature, it consists of two parts: First Part: Forest Valuation which ascertains the values of forest in- vestments and the values of their components. Second Part: Forest Statics which compares the investments with the returns obtained. Forestry, from the standpoint of a commonweal (federation, state, county, town, city) deals, to a large extent, in abstract or ideal values, — values which are not expressible easily in dollars and cents. It neglects, usually, financial considerations entirely or partially. With the private owner of forests, the financial outcome of his invest- ments is the first and last consideration. The priva!e owner cannot be ex- pected to supply this country with forest products u:iless forestry is as remun- erative an investment as agriculture is found to be, or as manufacture is sup- posed to be, — industries which supply this country v/ith food products and with manufactured products. The mathematical principles involved in Forest Finance arc identical with those confronting the bankers, the insurance companies, — in fact, corironting all business men and all business enterprises that lock ahead into the future. Forest statistics, deficient unfortunately in the United Stares (as in any ether country of rapid development), are important as a basis for financial calculations. Forestal forecasfs in the countries famous for conservative forestry are made easily and with a high degree of certainty. In Canada, in Russia, and generally in the United States, such is not the case. II. History. Forest Finance is one of the most modern branches of forestry. Abroad, i\ was unknown, or unheeded by the practitioners, previous to Max Pressler (about 1860). Pressler's theories were developed and enlarged upon by Gus- tav Heyer. Dr. Wm. Schlich's, and Prof. Charles Vv^immenauer's writings are entirely in line with Heyer's teachings. Financial considerations were despised generally by European foresters until recently. The government cf Saxony was first to adopt financial suc- cess as the goal of its forest policy. sf-^ ^ FOREST FINANCE. - ^. — III. Literafure. The only book on forest finance written ki English is SGiilich''s Vof. IIT, Part II. The interest tables of the various insurance companies may be used to solve forestal equations, in preference to tables of logarithms, PARAGRAFH IL— MATHEMATICAL PRINCIPLES OF FINANCE. The ratio existing between principal invested (V) and atnount obtained" (N), or the ratio between "pre- value" and "aft-value" of an investment is expressed by the following equations [in which (p) represents the rate of in- terest and (n) the number of years covered by the investments}: — N = VXL Op°' (A) N V - ^ = y-^- (B) 1. Op'' <^ .. ^ ^ ^ "// ' N ^ I. Op« = (C) V By payments (a) regularly occurring at given intervals of time a "geom- etrical progression" is formed after the pattern a + ar + ar^ + ar' + ar* + ar(n - 1) The summary of this geometrical progression is r"— 1 a — (Dl r — 1 If the last term of the progression is expressed as "I" (with the view to the elimination of "n"), the summary is / r I — a 4. r — 1 might be designated as "the term beyond the last", or as the terns "before whicTi the progression stops". Similarly, the sum total of periodical payments (R) due at intervals of (m) years, for the first time due after (a) yep.rs and altogether (n) times is, considered as a pre-value, 1. Op™°— 1 1. Op"'a R X (E) 1. 0pm — 1 1. Opmn On the other hand, for the aft-value of such periodical payments (R), the sum total is 1. Op«« — 1 R XI. Opni-a (F) 1. Op°J — 1 In the case of an annuity, (m) and (a) are equal to 1. Consequently, the summary of such annuities considered as a pre-value is FOREST FINANCE 7 1. Op" — 1 R (G) 1. Op°XO. Op The aft-value of such annuities is 1. Opn — 1 (H) 0. Op The aft-value of sixigle payments, annuities and periodical payments at the end of an indefinite period is itself indefinite ( C^ ). The pre-value of a single payment due after an indefinite period of years is equal to zero. The pre-value (V) of annuities or periodical payments running for an indefinite number of years is, however, something very definite, namely, dis- counted backwards to the present day, in the case of an annuity: R V = (I) 0. Op or 0 R 100 V It appears at a glance that this pre-value (V) derived from never-failing annuities — is merely the capital from which a perpetual revenue of p% is expected. Unknowingly, the investor usually figures at indefinitely long per- iods of never failing returns when capitalizing such returns at a given rate of interest. It is only too well known, however, that all investments, except- ing pure real estate investments, have a merely temporary lease of life. As an illustration, we might mind the fact, that the majority of all insurance policies are surrendered, — the insured being unable to pay his dues when he meets with financial reverses : Business investments, in the majority of cases, seem to end unluckily for the investor. The pre-value (V) of periodical payments (R) hereafter due at the end of every 'mth" year until infinity is R V = . (J) 1. Op™ — 1 The influence on present values exercised by payments (receipts or ex- penses), expected after 100 and more years, is very small. For the financial prospects of an enterprise, the current expenses and receipts of the first (n) years are (1. op° — 1) times as influential as the current expenses and receipts of any and all years following after the nth year. The above factor of influence, viz. (1. op° — 1), equals 10 within 50 years, in case of 5% investments ; 63 years, in case of 4% investments; 83 years, in case of 3% investments. 8 FOREST FINANCE "PROVIDED THAT THE RATE OF INTEREST IS HIGH, THE HAP- PENINGS OF A MORE DISTANT FUTURE ARE IMMATERIAL TO THE INVESTOR." The following is a synopsis of the preceding formulae, wherein: — p equals rate of interest. n " number of payments. m " duration of periodical intervals between two payments. a " years after which a periodical rental is due for the first time. R " rentals or payment. V " pre-value. N " aft-value. i At the end (aft-value) At the beginning (pre-value) A sum of money equals V X l.Opn N l.Op" [ Periodical Siunmary | Payments RCl.Op"'"— 1) 1.0pm_l R(1.0pnm_i)l.0pm-a (l.Opni — Dl.Opnni Temporary ) Rentals Annual Payments RCl.Op"— 1) O.Op Rd.Opn— 1) O.Op X l.Opn ( Periodical Summary \ Payments of J OO R X l.Opm-a 1.0pm— 1 Rentals / Annudl V payments OO R O.Op No capitalist and no forester is forced to adopt a financial formula or equation when determining the merits of an investment. THE EQUATION MERELY ILLUSTRATES A LOGICAL MANNER OF FINANCIAL THINK- ING, WHICH IS GENERALLY ADOPTED BY THE INSURANCE COMPAN- IES, BANKERS, AND FAR-SIGHTED BUSINESS MEN. PARAGRAPH III.— INCREASING OR DECREASING PRICES. Stumpage prices are rising in America, — possibly at the rate at which the population increases, possibly faster, — promising to reach the present European level within a few decades of years. Consequently, stumpage now worth "S" dollars per thousand feet will be worth at "x%" rise, after "n" years, Sxl. Ox^. The present value of such stumpage, to be harvested after "n" years, ia discounted backwards at "y" per cent, and amounts to SXl. Ox° 1. Oyo FOREST FINANCE In place of this terra, it is permissible to write: S 1. 0(y — x)° provided that "x" and "y" do not exceed, say, 8% and provided that the per- iod of calculation does not exceed 100 years. Mathematically, the substitution is incorrect; for practical purposes, however, it is permissible within certain limits. If X equals 4.7% and y " 3% and n " 100 years, the mistake made by the "short cut" equals 5.2%. The mistake increases: (1) With the increase of the price percentage (x) and discount per- centage (y). (2) With increasing discrepancy between price percentage (x) and dis- count percentage (y) ; (3) With the increasing number of years (n). Generally, the mistake does not exceed 5%. An advantage of the "short cut" is the larger scope it offers to financial imagination or to differences of opinion relative to the rise of stumpage prices or relative to the proper rate S SXl. OS-^ of discount. Thus, might be interpreted as or as 1. 03° 1. 08° SXl. 04° SXl. 03° or as 1. 07° 1. 06° "THE BASAL RATE OF INTEREST IN AN EQUATION MAY NOT REP- RESENT THE DIVIDEND WHICH THE OWNER EXPECTS TO DERIVE FROM HIS INVESTMENTS." In the cases just given, the investor will realize 8% if stumpage prices rise at 5% ; 7%, if they rise at 4% ; 6%, if they rise at 3% ; or only 3%, if the stumpage prices do not rise at all. If the prices are increasing at the SAME rate at which the values are discounted backward, the summary of the pre-values is (for annuities as well as for intermittent rentals), nXR. l.op°» mth year: l.op^ 2mth year: R Summary = nXR. Obviously, the summary of prevalues, in this case, is C30 for indefinite rentals. It is unreasonable to suppose, that prices will ALWAYS rise and continue to rise. 10 FOREST FINANCE The growth of trees expressed in dollars and cents is composed of the following factors: A. — Increase of volume, due to the annual formation of a new ring or, better, of a new coat all over the old body. B. — Increase of value, the larger diameter fetching a higher price per thousand feet board measure than the smaller diameter (difference in value of different sized logs at the same time). C. — Increase of price (difference in price of the same sized logs at dif- ferent times), due to an increase of population, to increased logging facilities and to waning supplies. The forester speaks of the volume increment, the value increment and the price increment of a tree; and of the volume increment percentage "a.%", the value increment percentage "b%", and the price increment percentage "c%" of a tree or of a forest. Thus, a tree now worth "S" dollars is worth after "n" years SXl.Oa° Xl.Ob'iXl.Oc^; which term is almost equal to SXl.O (a+b+c)^ In the case of young and sound timber all percentages can be assumed to range between 1% and 4%. In the case of primeval timber of large diameter, volume and value in- crement is insignificantly small. On the other hand, primeval timber is getting scarce so rapidly (walnut, cherry, white pine, yellow poplar, white oak) that a large price increment percentage can be depended upon. Learn to differentiate between the merits of investments in first growth and of investments in second growth!! An interesting case of a declining VALUE increment may be found in hickory poles at a time at which they begin to form heartwood; or in poplar poles at a similar time, when they begin to be less fit for match stock or for fibre. An interesting case of declining PRICE increment (aside of panics, aban- doned use of given woods, replacement of one species by another, change of tariff, export prohibition, Panama canal) may be found in small trees left by conservative lumbering. These trees had a better value BEFORE than AFTER the breaking up of the means of transportation. PARAGRAPH IV.— RECEIPTS AND EXPENSES IN FORESTRY. I. — The revenue in forestry may consist of: — A. — Yields derived from sale or lease of forest pasture; from hunting privileges; from water privileges (power or reservoir); from mines, quarries, peat bogs, etc.; from turpentine and maple sugar orchards; from tan bark, cork, mosses, grasses, pharmaceutical herbs, litter, nuts, seeds and so on. B. — Increasing volume of growing stock; increasing value of growing stock and of soil without any lumbering (so-called latent yields). C. — Usually, during and after the installation period, yields obtained from sale of wood products, notably, FOREST FINANCE 11 (a) Stumpage (French system) ; (b) Log yards (German system) ; (c) Manufactured products like lumber, staves, shingles, telephone posts, ties, blocks for carriages, pulp wood, tannin, fence posts, etc. (American system). II. — Timber yields are ascertained by : — A. — Cruising or valuation surveys. B. — Yield tables (applicable only to even aged and pure forests, fairly well stocked). C. — Volume tables (applicable only to sound trees). D. — The increment percentage. In the United States, reliable statistics relative to the growth of the forests — especially of second growth — and of the trees are badly lacking. ni. — Present timber values. The present values of timber (stumpage values) depend, for a given species, on the expense now required for its utilization, — notably on the charges for transportation which are governed by: A. — Distance from the market. B. — Availability of water, ice, snow, railroads and public roads as means of transportation. C. — Volume of stumpage per acre and volume on the entire tract. D. — Quality of the logs (percentage of firsts and seconds, common, cull, mill cull, etc.). £. — Climatic conditions (malarial climates, long and cold winters, short logging seasons). F. — Specific gravity of timber. In the far backwoods, stumpage even of the best trees frequently has a negative value. Near the market, even utterly poor trees assume a positive value. IV.— Future Timber Values. The study of future timber values is of paramount importance with the forestal investor. Similarly *^he capitalist is interested in the advancing value of real estate, the coming J .idends of railroad stock, etc. He must consider A. — For a country : The probability of a general change of timber prices due to: a. Competition of metals and stone (building stone). b. Waning virgin supplies. c. Importations from Canada, the tropics and Europe. d. Increasing population. e. Coming prosperity or coming depression of all industries. f. New uses of timber, especially in the spinning and weaving in- dustries, in the food industries, in the production of alcohol. g. Wages rising or dropping. h. Gold standard. i. Automobile traction. 12 FOREST FINANCE B. — For a species: The possibility of price alterations in favor of or to the detriment of a species locally prevailing (chestnut in Pisgah For- est; spruce in the Adirondacks; cottonwood in Arkansas; remember laws causing the price of wood-alcohol to drop from 67c to 39c per gallon in 1907.) C. — For a locality : The chances for improved access to a special market by improved railroads, improved navigation (Panama canal), and improved public roads; the chances for the opening of new local markets, or for enlarged foreign markets. Opinions relative to future developments necessarily differ in forestry as well as in agriculture, railroading and industrial establishments. On ex- change, such fluctuations and such diversity of opinion are particularly pro- nounced. V. — The expenses in forestry are : A. — Ordinary or running expenses, viz., 1. Outlay for logging and milling; 2. Administrative expenses; 3. Taxes; 4. Protective expenses; 5. Maintenance of boundaries and land marks; 6. Natural or artificial reforestation (this expense equals, in Ger- many, from 10% — 20% of the net stumpage values annually disposed of); 7. Forest pedagogy; 8. Up-keep of investments, notably of the means of transportation (this expense equals, in Germany, from 5% to 15% of the net stumpage values annually disposed of). Many of these ordinary running expenses must be considered, during the installation period, as extraordinary investments. B. — Extraordinary Investments. 1. Soil and, usually, trees. 2. Permanent means of transportation. 3. Wood working establishments. 4. Buildings, farms, pastures, ochards. 5. Surveys and working plans. 6. Fire lanes. 7. Fences for pastures, game, etc. 8. Afforestation. Al! over the world, but especially so in the United States, the capital now invested in a forest is not that which promises to yield the highest rate of int- erest for the next period of years. The principal investment requires addi- tions here and reductions there. The time at which alterations should be made depends upon local factors as well as upon personal opinion. The components of the final investment in conservative forestry are those enumerated under B.— Naturally, there is no need for all of them to be at hand in every case. The share which each component takes or should take FOREST FINANCE 13 in ths aggregate investment, again depends upon local conditions and upon personal opinions. Forest investments, in this connection, do not play any exceptional part. In agriculture, e. g., the final investments are composed of soil, improvements, roads, clearings, live stock, machinery, buildings, etc. Likewise, mining in- vestments do not consist of mineral soil merely; but, in addition to soil, of machinery, buildings, railroads, shafts, etc. A forest must be considered "normal" when the investment which it rep- resents has reached, for the time being, in the owner's opinion, the highest stage of relative remunerativeness, with all of its (the investment's), components balancing in proper equilibrium. Naturally, the owner alone can decide whether this stage is act'ially reached or not. PARAGRAPH V.— TAXES. In America taxes usually depend upon the market value of a taxable object and amount, in the wooded states, to about 19c ad valorem of the same. If the market value '"V" of a given forest grows at the annual rate of "x%" during 'n'' years, the taxes (theoretically at least) increase likewise at the rate of ''x%'\ They accumulate at the rate of "p%" in such a manner as to amount, at the year "n", to the sum total V 1.0x° — 1.0p« X Xl.Ox (M) 100 l.Ox — l.Op Case I: x equals p Then the aft-value of every single tax payment equals, V (1.0x1) 100 The summary of the aft-values equals n \ [l.Ox° /lOO \ or n% of the forest aft-value (which is VXl.Ox°). Thus, if "n" equals 25, the taxes consume }i of the aft-value; if "n" equals 100, the taxes consume the entire aft-value. Case II: x is smaller than p Then 1.0x° is much smaller than 1.0p° ; the summary is much larger than V (1.0x°) or much larger than 100 n the part of the forest aft-value. 100 Thus, if "n" equals 25, the taxes consume more than }:{ of the aft-value; and if '"n" equals 100, the taxes consume more than the entire aft- value. 14 FOREST FINANCE Case III : x is larger than p n Here the taxes consume less than the part of the aft-value, e. g., 100 ' ^' if "n" equals 25, the taxes consume less than 3^ of the aft-value; and if "n" equals 100, the taxes consume less than the entire aft-value. Deductions from the above: — RULE I. Destructive forestry is indicated where a long number of years is expected to elapse before a second cut can be obtained; where taxation ad valorem is high; where the value of the forest grows slowly (x being smaller than p). RULE n. The forester, bent on forest conservation, must endeavor to shorten the period of waiting between cuts by leaving sufficient stumpage and sufficient means of transportation to allow of frequent cuttings within the same forest. RULE m. The damaging effect of taxation depends pre-eminently on the period of waiting; the rate of interest being more irrelevant, "x" being usually equal to or close to "p". After the wholesale removal of the primeval forest, the period of waiting is excessively long. The forester's activity should be called upon before and not after the first inroads of the axe into the primeval woods. PARAGRAPH VI.— PROTECTIVE EXPENSES. The influence exercised on the prospects of conservative lumbering by expenses for forest protection is analogous to the influence of taxes. The decision whether and what protection should be given to a forest, solely rests with the owner. The following may illustrate the influence of the protective expenses on a forest conservatively managed: FIRST. An unprotected forest, "V", may yield an annual net surplus revenue "R" as long as it escapes fires and theft. R y equals or lOOR equals yV V 100 SECOND. Sacrificing annually "D" dollars for protection, the owner retains a revenue, "R — D", and the interest percentage "y" is reduced to "z" per cent., whilst "V" remains much unchanged as long as no fire happens to occur. 100 FOREST FINANCE 16 THIRD. Hence and D y -z R y If D eqtials 8% of R Rs equals lOOD s y — z then and 100 (N) (O) FIFTH. For "y" ranging from 2% to 8% and for "s" ranging from 5% to 30%, the percentage of net revenue "z" is reduced as appears in the table following:— s equals 5% lO^c I 16% ..-, 25% 30% y equals 2 | 19 1.8 j 1.7 | 1.6 1.5 1 14 y - 3 1 2 85 1 2 7 2 55 | 2 4 2 25 i 2 1 y " 4 1 38 ! 3 6 1 3 4 i 3 2 3.0 2 8 y •' 6 1 4.76 1 4.6 ! 4.25 j 4.0 3 75 1 3 6 y " 6 1 5.7 1 8.4 1 5.1 1 4.8 4.6 1 4.2 y •• 7 1 6.66 1 63 j 5 95 | 5 6 5.26 1 4.9 y •• 8 j 7.6 j 7.2 i 6.8 j 6.4 6 0 1 6 6 In the case of a forest which does not yield an annual surplus revenue, the influence of the protective expenses is somewhat different from the above, as is illustrated by the following considerations: — FIRST. Such aforest "V" grows in 'n" years at ■'x%" to a value of VCl.Ox") wherein "V" equals the sale value. SECOND. The same forest "V" protected at an annual expense of "w"% shows a net aft-value, omitting the influence of taxes, etc. w ( 1.0p° — 1 ) V(1.0x°) — V I ]■ (P) 100 ( O.Op ) where "p" equals the per cent, of capitalization selected by the owner. THIRD. The sacrifice brought by the owner for protection's sake is: (1.0p° — 1) (Q) 16 FOURTH. If the ratio equals (l-Op" 4 FOREST FINANCE equals 3^, then the sacrifice If the ratio equals 1/10, then the sacrifice equals P V (1.0p° - 1) 10 Absolutely taken, the sacrifice greatly increases with the length of the period of waiting. Relatively considered, the sacrifice does not increase nec- essarily. p equals 4% x equals 5% n 1.04"-1 Sacrifice w 1 P ~4 Sacrifice w 1 p 10 1.05" to fl w 1 nd z w 1 p ~10 l.Ozn l.Ozn z 10 yr. .48 .12V .05V 1 63 1.51 1.58 4.76 • 20" 1 19 .30V .12V 2 65 2 35 2 S3 4.76 f SO" 2.24 .86V .22 V 4.32 3.72 4 10 4.8 [40" 3.80 6.11 .95V .3SV 7.04 6 09 6 66 4.8 60" 1.63V .61V 11 47 994 10 86 4.86 The produced value, y equals figures in the last and third last columns give the rate of interest in a forest protected at an annual expenditure of w% of its original the rate of interest produced in the unprotected forest as long as all goes well. per cent, of revenue sacrificed for protection, the original sale of the forest. number of years that elapse before the forest is cut. rate at which the forest grows in value, if fires are barred, rate of interest expected by the owner. per cent, of the original value spent annually for protection, rate of interest produced in the protected forest. PARAGRAPH VII.— CAPITAL AND MONEY. A. Any object or thing having earning power is a capital. By "earning power" is understood the power to furnish commodities coveted by man. B. — "Money" is not "capital"; it is merely the "legalized measure of values", and hence frequently the measure of "capital". Different countries legal- FOREST FINANCE 17 ize or use different units of measure, and within the same country, time causes the unit to vary (cattle in the United States; platinum in Russia; silver in some of the Latin countries; glass pearls with the Indians; courie shells with the Siamese). Money, in other words, is nothing but a unit of measuring, having func- tions like those of the yard, the bushel, the pound (all being subject to fluc- tuations) to wit, the functions of measuring. C— All production originates with nature, and all capital consists, in part, of natural creations or natural objects, namely: 1. Natural gifts (soil and soil products) ; 2. Natural forces (wind, water, fire, gravity, electricity, heat, rainfall). D.— Accumulated human labor forms, usually, a part of a capital actuaUy producing (field, wind mills or water mills). E.— Merely natural capitals to which no human labor (accumulated) is at- tached, are usually unproductive; although their earning power might be at hand (most of our waterfalls; the prairies a century ago). Mines and fields, without the addition of accumulated labor, cannot prove their earning power. The forest and the pasture— under certain conditions at least and for limited periods— may create new commodities without requir- ing labor to be previously performed. < . ,, F —As long as the population increases, the individual's share in the "gifts and in the "forces" of nature— especially in the gifts— DECREASES and the units of such gifts and forces increase in value. On the other hand, capital consisting largely of accumulated human labor depreciates under the same circumstances. The more a capital consists of- {^^^^::^ade}-'=°"'P°'''"*'' ^^' ^'"" are its chances to gradually- |">®jj } —in (exchange) value. Rule a. As long as capital, labor, population and money in circulation re- main the same, values remain the same. Rule b. If capital alone decreases (population, labor and money stagnating) less products are available and $1.00 can buy less products or less capital than heretofore. (This rule holds good, especiaUy, in the case of the necessities of life.) Rule c. If population alone grows (capital and money stagnating), $1.00 can buy less natural products or capital than heretofore and can buy more man-made capital or products than heretofore (since labor is cheapened). Rule d. If money alone increases (population and capital stagnating), $1.00 can buy less products, labor or capital than heretofore. As a matter of fact, population and circulating money are on the increase in the United States, whilst capital consisting of natural gifts is decreasing and whilst capital consisting of natural forces remains the same. H.— All economic factors combine as a consequence to continuously lessen the purchasing power of the dollar in the United States. The legalized 18 FOREST FINANCE measure of value getting shorter in its effect, the number of units of value (or dollars) equalling a capital or a product increase necessarily. I.— Gold. The world's production of gold (the money of the leading nations) has increased and continues to increase at an alarming rate. This increase has had the tendency, unavoidably, of cheapening gold, or of reducing its power to purchase other goods. If man were actually to realize the enormous increase of the production of gold, the decline of its purchasing power would be more patent — it would become acute. A commodity (gold is a commodity like silver or iron or wheat, after all) drops in value at a time when it is known (or supposed) to be produced in excess of the demand; — not at a time when it actually happens to be excessively produced. In the case of gold, in the author's opinion, mankind has not begun to realize the enormous increase of the supply; and it is far from anticipating a still more gigantic increase of the supply in the near future at a time when new technical and chemical methods of "gold making" come into play. A demoralizing "slump" in our entire monetary system is unavoidable as soon as gold can be produced at a greatly reduced expense of labor. The knowledge of a slight over-production causes the price of cereals and cotton and lumber to decline perceptibly; similarly, the knowledge of a slight excess production of gold must cause its depreciation. In the past decades, this depreciation has been prevented by a number of countries rapidly adopting the gold standard and accumulating gold in their treasuries. In the future, this depreciation must be marked. If the purchasing power of gold decreases at the rate of 2% per annum (and the author anticipates a more rapid decline), the consequences will be: a. for the possessor of bonds, mortgages, life insurance policies, etc., a heavy loss of capital as well as of interests. b. for a "country of bondholders", and therefore pre-emmently for European countries, heavy losses; c. for "countries of stockholders", and countries rich in pastures and forests and farms, a decided superiority over others not so blessed. A man owning 4% bonds rated at par will do well — if he desires to remain equally wealthy — to consume not over 3-^ of the interests obtained and to re- invest the other 3^2 with a view to counterbalancing the tendency of gold to depreciate. Conclusions. A man owning $100,000 cash in 1908 is less wealthy than the man owning the same amount in 1898. A man who has let out, in 1898, $100,000 and who has consumed in the meantime all interest derived therefrom, is getting less wealthy. He should have saved a portion of the interest actually obtained adding it to the original $100,000. FOREST FINANCE IS On the other hand, a man letting out, in 1898, 10,000 acres of land and retaining them in 1908 in equal productiveness, is absolutely as wealthy now as before; relatively wealthier than before, although he was allowed to con- sume all interest or revenue obtained from the lease. PARAGRAPH VIII.— INTEREST. I. — Definitions. A. — Interest (gross) is the price paid for the use of capital. B. — As freight is the price of "site-difference", so is interest the price of "time-difference". C. — Net interest is the difference of a capital's "earning power" at the beginning and at the end of a season plus the value of the product in the meantime produced by capital and not by labor. D. — Interest may mean either the net or the gross product of capital, i. e., of any object having earning power. E. — The price of the use of labor equals the value (of product, or of capital) which the employer hopes to create thereby. The price of the use of capital equals the value (of product, or of new capital) which the employer hopes to create thereby. F. — Interest is the product of capital; its price is the price of the product I In loans of capital, it is usual to loan the "measure of capital" (gold) and to turn over to the owner thereof the "measure of the product" (gold.) The borrower may use a loan to pay WAGES and in that case he ACT- UALLY borrows LABOR, reconvertmg "ACCUMULATED" labor into "RUN- NING" labor. n. — Gross Interest on Money Loans. This is the product of capital employed in another man's production. It consists of the following parts: — a. The true, net, actual, clear yield of capital "{%&)". b. "Risk quota", or remuneration for risk taken, or capital secretly repaid, or capital apt to be consumed in the course of the pro- duction. This quota is meant to rebuild that much of the origina capital as is iiable to incidental destruction "(^b)". c. Remuneration for labor, financial sagacity and discomforts requiredl from the owner in harvesting the yield of capital "(^c)". d. Quota which must be saved and added to the original in order to allow the owner to remain equally wealthy whilst the purchasing power of money declines "(td)". The investing capitalist invariably over-estimates the true or net yields of his investment ("^a) and proceeds to consume Cb) and (*!d). Few families remain equally "wealthy" in the long run excepting those owning entailed real estate. in. — Interest on merely natural investments (farms) consists of "(fa)" and of "(lie)". The risk "(^b)" is little since the soil, at least, is safe. There is no "iW"- 20 FOREST FINANCE IV. — Interest on capital consisting of accumulated labor has a very large "(^b)". This is proven by the following: — 1. It can be outranked and reduced in value by other and better labor- accumulations (e. g., sulphite fiber process superseding soda fiber process; Southern cotton factories outranking Northern cotton fac- tories; steamships superseding sailing craft). 2. The real necessities of life are more a soil product than a labor pro- duct. In the case of unnecessary articles, fashions and inventions cause continuous fluctuations of the remunerativeness of the in- vestments producing such unnecessary articles. 3. If a production, basing largely on accumulated labor, is found to be remunerative, it is at once overdone; and competition kills the yields (e. g., bicycle manufacturing). 4. Labor-made capital (machinery) is usually consumed in the course of the production. V. — It may be said that no man who wishes to be on the safe side, on an aver- age, should annually consume over 2% on his investment; or that no man should rate the true earning power of his investment at a figure exceed- ing 2%. The financial genius, of course, can do better and can credit himself with a large "(lie)"; he foresees the development of the future correctly; at an outlay of $1,000, for instance, he creates or acquires a capital producing $100 of true net "{%&)", which is worth $5,000. Thus, he owns five times as much as before at the end of the production. * Theoretically, the genius obtains wealth by buying productive capital actually under-rated by the majority of the owners, and by selling productive capital actually over-rated by others. The blunderers foresee the coming events wrongly; they sell on a rising market, and they buy on a falling market. During the year, the investors change their opinion frequently, relative to the outlook of the future; hence continuous fluctuations on exchange. The ratings placed by two men on the same investment coincide in rare cases only; hence few transactions on exchange, a trade being made only when two men happen to agree. VI. — Additional factors influencing the rate of interest: — 1. Unhandy credit systems; 2. Partial or slow courts; 3. Danger of foolish legislation; 4. Amount of indestructible assets. The factors 1, 2 and 3 increase, and the factor 4 decreases the rate of interest. The rate of interest charged for loans and bonds increases whenever the industries prosper. The available money is then withdrawn from loans and put into industrial engagements. VII. — Limits of Interest. 1. The lowest limit is the figure at which the owner prefers to hide or consume his belongings. FOREST FINANCE 21 2. The upper limit is the actual effect of the investment for which means and bounds do not exist. If the investment cannot be duplicated (Standard Oil), the rate of interest becomes a personal matter being governed by the capitalization which the owners choose to adopt. Vin. — The net or true interest 1. has the tendency of equalization A. in loans, because interest is merely the price of such loans re- sembling the price of any other commodity; B. in investments, because universally remunerative investments are soon over-crowded by competition where duplication is pos- sible. Where this is not possible, there abnormal revenue is at once capitalized, the new capital value being added to the ori- ginal ("watered investments"); 2. has the tendency of sinking because the wealth of the nations is rising at a faster rate than the chances at remunerative employment of wealth. IX. — Justification of Interest. 1. The Church, since 325 A. D., has condemned interest after Luke VI : 35. In the early Christian era, loans for consumption only were known, not loans for production. 2. After Adam Smith, the capitalist would not care to take any risk, temporarily parting with the full control of his property, if he did not see any inducements. 3. After Senior, interests are payments due to the owner for abstaining from the immediate consumption of his property. 4. After Marx and La Salle, interest is cut-off from the wages properly belonging to the wage earner. 5. Merely natural capitals (deer, buffalo, trees, grass lands) produce annually. Thus, interest on capital is natural, — is part of the econ- omy of nature. X. — Rate of Interest in Forestry. 1. Conservative Forestry. a. There is no "(Hb)" or "(Hd)" to be deducted from the gross rate of interest, since there is no risk and no influence on the investment due to the declining purchasing power of money. b. The rate of interest compares favorably with agricultural interest because the products of the forest can be stored free of cost, and are exposed but little to drought, inundation, boll weevil, etc. If the products are killed by storm, fire and insects, forestry can bring them to the market, usually, at a scarcely reduced price (see American Lumberman, September 19, 1908). The rate of true interest in conservative forestry is about 23.^% (in Sax- ony, on an average for the year 1905, 2 Vlo% ; see Thar. Forst Jahrbuch, 1907, 1st issue.) and compares very favorably with 4% on bonds and 6% on industrial investments. 22 FOREST FINANCE 2. Destructive Forestry. The net revenue cannot be separated easily from the capital gradually withdrawn from the forest. If only soil (S) remains after complete exhaus- tion, within (n) years, of a forest of the original value (Q) whilst surplus re- ceipts, Ri, R2, R3, etc., are obtained during the (n) years of destructive lum- bering, then the rate of interest, (x), is illustrated by the following equation : — QXl.Ox>i=Rl (1.0x°-l)+R2 (1.0x'i-2)+R3 (1.0x'>-3)+ . . . Rn + S. XI. — Saxon Statistics show: — 1. That the State forests have paid, since 1816, 2% net on the annual average. 2. That the money value of the forest, since 1816, has risen by 3% on the annual average, a rise largely due to the declining purchasing power of gold and partly due to improvements and additional in- vestments. Xn. — The decision in the problem confronting the owner: "Shall I practice conservative forestry or destructive forestry?" must be based on the true rate of net interest obtainable from the one and from the other. It re- mains for the forester to demonstrate the difference between net interest and gross interest. The chances for conservatism in forestry to be superior to radicalism are, on the whole, extremely good and especially so in the United States, since 1. The American lumber market is almost continuously overstocked beyond its digestive capacity. The virgin supplies are being ex- hausted, and are apt to be entirely exhausted by 1950. In the mean- time the stumpage prices of all good timber must increase steadily. 2. It must be remembered that the now wealthy lumbermen have made their wealth by buying stumpage when and where it was under- valued and by holding it for a number of years. Fortunes have never been made by any particular skill in lumbering, milling or sale of lumber. Strange as it may sound: Inactivity has paid better in the case of in- vestments in American forestry than hard work spent in lumbering and milling. There is no reason to anticipate that the future will materially differ from the past. XIII. — Interpretation of the rate of interest on which a calculation is based: X 1) The sum may mean l.op° a) that the calculator expects with a faith in his forecasts expressed by p% receipts or expenses (X) to occur (n) years from date of calculation, or b) that the calculator expects, with a faith in his forecasts approx- imated by (p+y), receipts or expenses X or XXl.oyo l.oy° to occur n years from date of calculation. FOREST FINANCE 28 This possibility of interpretation allows of the expression of widely dif- ferent forecasts by a mere change of the rate of interest underlyiag the cal- culation. The basal rate underlying an equation does not or need not design- ate the actual dividend expected by the calculator. It is the mathematical outcome of his fears and his hopes, of gloomy and of rosy anticipations. PARAGRAPH IX.— EXPECTATION VALUE. The actual value of any object to its owner, or to anybody else (cow, house, railroad bonds, mining stock) equals the pre-value of the expected ser- vices or yields, duninished by the pre-value of the expected expense required to obtain such services or yields. Obviously, the rate of discount is of para- moimt importance relative to the result of the calculation. 'Individual opin- ion" governs the rate of discount as well as the anticipations^of future events. Values rise with the expectation of rising yields, of sinkmg expenses and or reduced rates of interest, and vice versa. Obviously, the selection of the rate of interest, and the forecasts of future yields and expenses, depend, above all, on personal opinions which may be pessimistic or optimistic, bearish or bullish. Applied to forestry, we find the following expectation values: 1. Value of a regular second growth forest (m) years old: thna thnb thuc f.c. i-s.v. +V + + + V 1.0p«-™ l.Opb-m l.Op'^-™ l.Op'^-™ wherein thna, thnb, thnc stands for thinnings in the year a, b, and c of the forest; f.c, for value of final cut; s.v., for soil value after final cut, and V for a perpetual rental defraying taxes and admini- strative expenses reduced by annual receipts for leases, etc. 2. The value of bare, absolute forest soil, planted up at an expense of "pig" and weeded at an expense of "weed" equals thna X LOp*"-* + thnb X l.Op'^b + f .c— pig —weed X l.Op'"™ V— pig (l.Op^-1) 3. The value of an ideal forest in which all age classes are present, which is conservatively managed, close to a ready market (so that in every year of the future there may be obtained a yield from a thinning in a woodlot "a", ''b", "c" years old and also a final yield diminished by reforestation expenses, whilst the expense of administration is an- nually "v" for the entire forest) amounts to thna +thnb +thnc + (f.c— pltg) — v in which O.Op thn equals thinnings p " rate per cent. f.c. " final cut pltg " planting. 24 FOREST FINANCE PARAGRAPH X.— SALE VALUE OF WOODLANDS IN U. S. It is customary to buy timberland merely at the price of the stumpage standing thereon. The purchaser neglects: C / 1) that he can not cut all of the timber at once; and such parts, as ■5 \ he cuts only after some years, should not be assessed at full value ; *" j 2) that taxes, etc., accrue, whilst the timber is cut gradually; > \ 3) that an expense for legal and timber investigations must be covered; g, / 4) that timber values might be destroyed by fire; K I 6) that there is danger of fool-legislation against alien corporationg. a) that soil has value; b) that stumpage prices (and merchantability, hence volume) will increase ; c) that there is a second growth already at hand; d) that local means of transportation increase; e) that taxes might be decreased, and that protective legislation will come; f) that freight rates decrease; g) that population increases, also demand; h) that new uses are found for wood ; i) that investments in forestry are remarkably safe, compared with stocks, bonds, etc. j) that the agricultural value of the soil increases, absolute forest soil becoming absolute farm soil, as the years go by; k) that forest pasture, chase, minerals (rock, clay), waters and water- powers promise an increasing revenue. PARAGRAPH XI.— GAUGING THE MERITS OF AN INVESTMENT. The Success of a business (in farms, mines, forestry) is evidenced by its net gains. Expenses and yields can be compared either by forming their difference which comparison shows an "entrepreneur's" gain or loss; or by forming theu- ratio which method shows the actual dividend obtained from the business. I. — Entrepreneur's gain and loss. Influencing factors are: — a. Lapse of time. b. Constellation of economic conditions. c. Personal foresight. d. Rate of interest introduced into the calculation. An undertaker's gain may be figured out retrospectively or prospectively. An undertaker's gain is fictitious until, the property changing hands, it can be demonstrated to be a fact. FOREST FINANCE 28 The undertaker's gain or loss disappears when the financier introduces a rate of interest at which the discounted expense equals the discounted yields. n. — The forest dividends show what actual rate of interest the owner has made in the past or may earn in the future on his investments. The actual rate of interest introduced in the financial equation causes any undertaker's gain to vanish. The forest dividend is deeply influenced by the price increment of trees (improved means of transportation; enlarged markets, etc.) In the forest, it is difficult to distinguish between actual revenue drawn from the forest and capital withdrawn, since the trees are capital as well as product. In conservative forestry, careful stock taking is required period- ically, so as to show the actual status of the investment. PARAGRAPH XII.— MATURITY OF TREES. I. — In the botanical sense, wood fiber is mature almost after the conception of the cell. A tree 3 inches in diameter is physiologically just as mature as a tree 3 feet in diameter. The highest stage of botanical maturity is the so-called heartwood. II. — From the people's standpoint, timber must be considered mature at a time at which it is best adapted to general usage in the wood consuming industries. The older the tree gets, the larger is, on the whole, its diver- sity of utility. The rotation best adapted to supply the industries of a country is called the "technical rotation". in. — The sylviculturist regenerating the forest from self-sown seed cannot select a rotation which does not allow the trees to profusely propagate their kind. In coppice woods, since the sprouting capacity decreases with increasing diameter, the rotation must be so low as to allow of luxuriant production (sylvicultural rotation). rV. — From the financial standpoint, trees or forests must be considered mature when the net true interest obtained from them ceases to bear a sufficient ratio to the sale value of such trees or forests. Wherever the woods are stocked with even aged and even sized trees, all of the trees reach maturity at or about at the same time. The primeval woods of America do not exhibit, usually, such even aged conditions. The American forester had better speak of the maturity of trees than of the maturity of forests. Factors influencing the maturity of trees in America are, pre-eminently : — a. The price increment, which, in the case of large trees, far exceeds the volume increment and value increment. Stem analyses and volume tables are of little value, consequently, for the financial diagnosis of primeval trees. 26 FOREST FINANCE b. Means or arteries of transportation and the permanency of their char- acter. Where the means of transportation are considered as a permanent investment and not as a temporary expense to be re- imbursed by current operations, a higher age of maturity results naturally. c. In many cases the taxes per acre are not or are scarcely influenced by the severity of the cut. Here it is irrelevant, from the tax payer's standpoint, whether he proceed to log certain sizes or kinds of trees or not. Where, on the other hand, taxes are changed ac- cording to the stumpage found per acre, the standing tree must be charged with that much of the tax per acre as corresponds with its individual contents. Take, e. g., a forest of white pine contain- ing 5,000 ft. per acre consisting of 12 trees averaging 400 ft. b. m., taxed at 30 cts. per acre. The soil has little value. A tree con- .30 X 400 taining 400 ft.b.m. must annually defray =.024, which 6000 expense of .024 must be charged against the tree and must be de- frayed from the annual increase, if any, of the value of the tree. d. Trees acting as mother trees propagating their kind should be credited with the prospective value of the progeny produced by them, on an average. On the other hand, trees acting like weeds and re- tarding the growth of a younger progeny of seedlings and saplings beneath them must be charged with the loss of prospective incre- ment incurred by such second growth. e. Since protective and administrative expenses are governed more by area than by the density of the stands, it is necessary in rare cases only to charge a pro rata of the protective and administrative ex- penses against the individual tree. These expenses incumber the soil like prescriptive rights. f. The question of maturity is a question to be answered in the first and last instance by the owner who is governed by his personal attitude regarding the rate of interest obtainable from his invest- ment; by the prospects of price increment as they appear to him and by personal moments like the lack of cash to defray running expenses, mortgages, etc.; chance of remunerative investment elsewhere; desire to distribute risks; tastes and predilections. Trees of defective character infested by insects or fungi have reached maturity, generally speaking, since the spread of the disease checks their financial increment, and may cause the increment to be negative. V. In Europe the following number of years denote, on an average, the ma- turity of timber: pine 100 yrs.; spruce 90 yrs.; fir 120 yrs.; beech 120 yrs.; oak 160 yrs.; oak coppice 18 yrs.; willows 1 and 2 yrs. In America, naturally, fixed rotations have not been adopted, since the cutting takes place, usually, in the primeval woods. In Virginia, a second and third growth of pine is cut under a rotation of about 60 years. Catalpa FOREST FINANCE 2T is coppiced under a rotation of about 10 years. The very prime trees, notably hardwoods, of a primeval wood are immature from a financial standpoint, if the owner believes that the greatest advance in prices will come to them, such giants getting rare and more rare, year by year. In many cases, the price of inferior stumpage does not promise to rise as much as the price of prime stumpage. On the other hand, in many a case, the indicating percentage of trees promising a large percentage of "cull lum- ber" is manifestly superior to that of trees containing a large percentage of "fas lumber". In Europe, the question of maturity is largely a question of age or (which is almost the same) of diameter. In America, on the other hand, the question is one of conditions — condition of transportation, danger from fire, condition of health, the chances for their improvement or deterioration. Thus, a diam- eter limit or age limit can scarcely denote maturity. The American forester in charge of large districts is confronted many a time with the necessity of treating individual trees according to their financial merits, whilst his Euro- pean colleague in charge of small ranges has to deal with even aged aggre- gates resulting from second growths. VI. — The term "indicating percentage" denotes the current dividend obtain- able from a tree or woodlot. This percentage indicates the maturity of a tree or of a woodlot. A tree or woodlot is mature and should be removed when it ceases to yield (latently, of course) the dividend desired by the owner. The owner or investor discards an investment in forestry as well as in stock when the dividend seems to fall below the limit obtainable by him in other enterprises of similar safety. If he discards at the right time, he will make money; and otherwise not. In the following remarks, the indicating percentage is called "x"; the forest percentage denoting the "limit" just mentioned is called "p". Previous to maturity, "x" is larger than "p"; at maturity, "x" equals "p"; after maturity "x" is smaller than "p". The indicating percentage of a woodlot, for a period of 10 years, is as follows, if the stumpage is now worth "S.S." dollars; if it is worth, after ten years, "S-S^g"; if the cleared soil is worth "C" dollars; if administration and taxes are "v" dollars per annum, forming an administrative capital "V": — (SS + C + V) 1.0x10 - SSio + C + V or (1.0x10—1) (SS + C) 1.0x10 +v -C+SSio O.Ox According to Krafft, the indicating percentage had better be considered as a dividend on stumpage merely v/hilst the soil and the administrative cap- ital should yield the forest dividend required by the owner. Krafft's "x" is more sensitive than the "x" commonly applied since it bears a ratio to part of the investment only. Krafft's "x" is found asfollows: — SS X 1.0x10 + (C+V) 1.0plO= SSio + C+V as FOREST FINANCE In conservative logging when a portion only of the trees are removed from •very acre, the indicating percentage had best be considered as a tree dividend. Whether and how much of the taxes and administrative expense (e) should be charged to the tree, depends upon the local circumstances. Trees occupying soil and preventing, by their presence, a second growth from de- veloping, must be charged with the interest on the value of the soil thus oc- cupied. On the other hand, trees acting as mother trees must be credited with the value of the progeny resulting from their presence. The tree indicating percentage might be expressed, adopting Kraflft's method, as follows : (l.Opn— 1) To X 1.0x°+e + (soil) 1.0p°=Tn + soil + value of progeny O.Op in which "Tq" equals the tree value now. Where the forest stocks on agricul- tural soil, all trees unable to defray the interest on such valuable soil, appear to be mature, or hypermature. VII. — The forester making a working plan for pine and spruce woods is usually confronted by the question of the best diameter limit. The plan advises the owner as to the limit yielding the highest entrepreneur's gain or the highest forest dividend. The heavier the present cut, the smaller is the investment left, whilst the protecting expenses remain the same. On the face of it, it seems unwise to cut clear without considering the financial prospects of trees which might be left on the ground, having 10", 12", 14", etc. in diameter. Obviously, the logging expenses per M feet b. m., are smaller in the case of heavy cutting, than in the case of light cutting, particularly so when the logger must avoid any damage to the trees left standing. Again, obviously, the longer the period of waiting for a second cut, the less are the chances for a good return from conservative logging. The diameter limit might be tested either with the help of the indicating percentage or by the method of the entrepreneur's gain. INTEREST TABLES (EXPLANATORY) Column I indicates the number of years. Column II gives the present value of $1.00 due at the end of the number of years indicated in column I. Column III gives the present value of $1.00 per annum due every year during the period of years indicated in colimm I. Column IV gives the aft-value of $1.00 left invested for the number of years indicated in column I. Column V gives the aft-value of SI. 00 payable annually and left invested for the number of years indicated in column I. 80 ^ PER CENT. I II III iiii V 1 .9950 .9950 1.0050 1.0000 2 .9901 1.9851 1.0100 2.0050 3 .9851 2.9702 1.0151 3.0150 4 .9802 3.9505 1.0202 4.0301 5 .9754 4.9259 1.0253 5.0503 6 .9705 5.8964 1.0304 6.0755 7 .9657 6.8621 1.0355 7.1059 8 .9609 7.8230 1.0407 8.1414 9 .9561 8.7791 1.0459 9.1821 10- ....9513.. 9.7304-. 1.0511.. 10.2280 11 .9466 10.6770 1.0564 11.2792 12 .9419 11.6189 1.0617 12.3356 13 .9372 12.5562 1.0670 13.3972 14 .9326 13.4887 1.0723 14.4642 15 .9279 14.4166 1.0777 15.5365 16 .9233 15.3399 1.0831 16.6142 17 .9187 16.2586 1.0885 17.6973 18 .9141 17.1728 1.0939 18.7858 19 .9096 18.0824 1.0994 19.8797 20 .9051 18 9874 - __1.1049. 20.9791 21 .9006 19.8880 1.1104 22.0840 22 .8961 20.7841 1.1160 23.1944 23 .8916 ' 21 . 6756 1.1216 24.3104 24 .8872 22.5629 1 . 1272 25.4320 25 .8828 23.4456 1 . 1328 26.5591 26 .8784 124.3240 1 . 1385 27.6919 27 .8740 ■^ 25 . 1980 1.1442 28.8304 28 .8697 ^26.0677 1 . 1499 29.9745 29 .8653 iT 26. 9330 1 . 1556 31.1244 30 8610 ___27.7941-- - 1 1614 32.2800 3l' .8567 28.6508 1 . 1672 33.4414 32 .8525 29.5033 1 . 1730 34.6086 33 .8482 30.3515 1.1789 35.7817 34 .8440 30.1955 1 . 1848 36.9606 35 .8398 32.0354 1 . 1907 38.1454 36 .8356 32.8710 1 . 1967 39.3361 37 .8315 33.7025 1.2027 40.5328 38 .8274 34.5299 1.2087 41.7354 39 .8232 35.3531 1.2147 42.9441 40 8191 36 1722 1 2208 .44.1588 41 .8151 36.9873 1.2269 45.3796 42 .8110 37.7983 1.2330 46.6065 43 .8070 38.6053 1.2392 47.8306 44 .8030 39.4082 1.2454 49.0788 45 .7990 40.2072 1.2516 50.3242 46 .7950 41.0022 1.2579 51.5758 47 .7910 41.7932 1.2642 52.8337 48 .7871 42.5803 1.2705 54.0978 49 .7832 43.3635 1.2768 55.3683 60 ....7793_. ...44.1428.. ..._1.2832._ .....56.6452 55 .7601 47.9782 1.3156 63.1200 60 .7414 51.7020 1.3488 69.7600 65 .7231 55.2764 1.3829 76.5800 70 .7053 58.9364 1.4178 83.5600 75 .6879 62.4745 1.4536 90.7200 80 .6710 65.7988 1.4903 98.0600 85 .6545 69.1099 1.5280 105.6000 90 .6383 72.3268 1.5665 113.3000 95 .6226 75.4747 1.6061 121.2200 100.. ..-.6073.- ...78.5449.. ....1.6467.. 129.3400 105 .5923 81.5306 1.6882 137.6400 110 .5777 84.4531 1.7309 146.1800 115 .5635 87.2985 1.7746 154.9200 120 .5496 90.0736 1.8194 163.8800 1 PER CI :nt. I n 1 mi V 1 .9901 .9901 1.0100 1.0000 2 .9803 1.9704 1.0201 2.0100 3 .9706 2.9410 1.0303 3.0301 4 .9610 3.9020 1.0406 4.0604 5 .9515 4.8534 1.0510 5.1010 6 .9420 5.7955 1.0615 6.1520 7 .9327 6.7282 1.0721 7.2135 8 .9235 7.6517 1.0829 8.2857 9 .9143 8.5660 1.0937 9.3685 10 .9053__ 9.4713.. 1.1046.. 10.4622 11 .8963 10.3676 1.1157 11.5668 12 .8874 11.2551 1.1268 12.6825 13 .8787 12.1337 1.1381 13.8093 14 .8700 13.0037 1 . 1495 14.9474 15 .8613 13.8651 1 1.1610 16.0969 16 .8528 14.7179 i 1 . 1726 17.2579 17 .8444 15.5622 1 . 1843 18.4304 18 .8360 16.3983 1.1961 19.6147 19 .8277 17.2260 1.2081 20.8109 20 .8195.. .8114 .18.0456.. 18.8570 1.2202 .22.0190 21" 1.2324 23.2392 22 .8034 19.6604 1.2447 24.4716 23 .7954 20.4558 1.2572 25.7163 24 .7876 21.2434 1.2697 26.9735 25 .7798 22.0232 1.2824 28.2432 26 .7720 22.7952 1.2953 29.5256 27 .7644 23.5596 1.3082 30.8209 28 .7568 24.3164 1.3213 32.1291 29 7493 25.0658 1.3345 33.4504 30 7419 .25.8077.. 1.3478.. 1.3613 .34.7849 31 7346 ■ 26.5423 36.1327 32 7273 27.2696 1.3749 37.4941 33 .7201 27.9897 1.3887 38.8690 34 7130 28.7027 1.4026 40.2577 35 7059 29.4086 1.4166 41.6603 36 6989 30.1075 1.4308 43.0769 37 6920 30.7995 1.4451 44.5076 38 6852 31.4847 1.4595 45.9527 39 6784 32.1630 1.4741 47.4123 40 6717 "■ 6650 32. 8347.. "'33.4997 1.4889 .48.8864 41" 1.5038 50.3752 42 6584 34.1581 1.5188 51.8790 43 6519 34.8100 1.5340 53.3978 44 6454 1 35.4554 1.5493 54.9318 45 6391 36.0945 1.5648 56.4811 46 6327 i 36.7272 1.5805 58.0459 47 6265 i 37.3537 1.5963 59.6263 48 6203 1 37.9740 : 1.6122 61.2226 49 .6141 1 38.5881 1 1.6283 j 62.8348 60 6080 ! 39.1961__ !.... 1.6446.. 1 64.4632 55 "".5786 42.1430 1.7284 1 72.8400 60 .5505 44.9521 1.8166 81.6600 65 .5238 47.6247 1.9093 90.9300 70 4983 50.1644 2.0066 ! 100.6600 75 .4742 52.5841 2.1090 110.9000 80 .4500 54.8858 2.2166 121.6600 85 .4292 57.0742 2.3296 132.9600 90 .4084 59 . 1750 2.4485 144.8500 95 .3886 61 . 1394 2.5733 157.3300 100_. 3697- ._.63.0259.- ....2.7046.. 170.4600 105 .3518 64.8197 2.8425 184.2500 110 .3347 66.5272 2.9875 198.7500 115 .3185 68.1518 3 . 1399 213.9900 120 .3030 1 69.6979 3.3001 230.0100 31 32 1}4 PER CENT. I 1 II III iiii V 1 .9852 .9852 1.0150 1.0000 2 .9707 1.9559 1.0302 1.0150 3 .9563 2.9122 1.0457 3.0452 4 .9422 3.8544 1.0614 4.0909 6 .9283 4.7826 1.0773 5.1523 6 .9145 5.6972 1.0934 6.2290 7 .9010 6.5982 1 . 1098 7.3230 8 .8877 7.4859 1 . 1265 8.4328 9 .8746 8.3605 1.1434 9.5593 10.. ....8617__ 9.2222.. 1.1605.. 10.9027 11 .8489 10.0711 1 . 1779 11.8633 12 .8364 10.9075 1 . 1959 13.0412 13 .8240 11.7315 1.2130 14.2368 14 .8118 12.5434 1.2318 15.4504 15 .7999 13.3432 1.2502 16.6821 16 .7880 14.1313 1.2690 17.9324 17 .7764 14.9076 1.2880 19.2014 18 .7649 15.6726 1.3073 20.4894 19 .7536 16.4262 1.3270 21.7967 20 7425.. .7315 ...17.1686.. 17.9001 1.3469 . 23.1237 21 1.3671 24.4705 22 .7207 18.6208 1 . 3876 25.8376 23 .7100 19.3309 1.4084 27.2251 24 .6995 20.0304 1.4295 28.6335 25 .6892 20.7196 1.4509 30.0630 26 .6790 21.3986 1.4727 31.5140 27 .6690 22.0676 1.4948 32.9867 28 .6591 22.7267 1.5172 34.4815 29 .6494 23.3761 1.5400 35.9987 30 6398.- .6303 ...24.0158.. 24.6461 1.5631 . 37.5387 31 1.5865 39.1018 32 .6210 25.2671 1.6103 40.6883 33 .6118 25.8790 1.6345 42.2986 34 .6028 26.4817 1.6590 43.9331 35 .5939 27.0756 1.6839 45.5921 36 .5851 27.6607 1.7091 47.2760 37 .5764 28.2371 1.7348 48.9851 38 .5679 28.8051 1.7608 50.7199 39 .5595 29.3646 1.7872 52.4807 40 ....5513.. .5431 ...29.9158.. 30.4590 1.8140.. 54.2679 41 1.8412 56.0819 42 .5351 30.9940 1.8688 57.9231 43 .5272 31.5212 1.8969 59.7920 44 .5194 32.0406 1.9253 61.6889 45 .5117 32.5523 1.9542 63.6142 46 .5042 33.0565 1.9835 65.5684 47 .4967 33.5532 2.0133 67.5519 48 .4894 34.0426 2.0435 69.5652 49 .4821 34.5247 2.0741 71.6087 50 4750.. .4409 34.9997 . .. 2.1052.. 73.6828 65 37.2715 2.2679 84.5296 60 .4093 39.3803 2.4432 96.2147 65 .3799 41.3373 2.6320 108.8000 70 .3527 43 . 1549 2.8355 122.3640 75 .3274 44.8409 3.0546 136.9670 80 .3039 46.4073 3.2907 152.7110 85 .2821 47.8603 3.5450 169.6600 90 .2618 49.2099 3.8189 187.9300 95 .2431 50.4618 4.1141 207.6000 100.. 2256.. ...51.6247.. ....4.4320_. 228.8030 105 .2094 52.7036 4.7746 251.6330 110 .1944 53.7055 5.1436 276.2380 115 .1805 54.6351 5.5411 302.7330 120 .1675 55.4985 5.9693 331.2880 2 PER CENT. 33 I II III iiii V 1 .9804 .9804 1.0200 1.0000 2 .9612 1.9416 1.0404 2.0200 3 .9423 2.8839 1.0612 3.0604 4 .9238 3.8077 1.0824 4.1216 5 .9057 4.7135 1.1041 5.2040 6 .8880 5.6014 1 . 1262 6.3081 7 .8706 6.4720 1.1487 7.4343 8 .8535 7.3255 1.1717 8.5830 9 .8368 8.1622 1.1951 9.7546 10__ ..-.8203.. .8043 8. 9826.. 9.7868 . 1.2190 10 9497 11 1.2434 12.1687 12 .7885 10.5753 1.2682 13.4121 13 .7730 11.3484 1.2936 14.6803 14 .7579 12.1062 1.3195 15.9739 16 .7430 12.8493 1.3459 17.2934 16 .7284 13.5777 1 . 3728 18.6393 17 .7142 14.2919 1.4002 20.0121 18 .7002 14.9920 1.4282 21.4123 19 .6864 15.6785 1.4568 22.8406 20._ __-.6730.. .6598 __.16.3514.. 17.0112 ..1.4859 24 2974 21 1.5157 25.7833 22 .6468 17.6580 1.5460 27.2990 23 .6342 18.2922 1.5769 28.8450 24 .6217 18.9139 1.6084 30.4219 26 .6095 19.5235 1.6406 32.0303 26 .5976 20.1210 1.6734 33.6709 27 .5859 20.7069 1.7069 35.3443 28 .5744 21.2813 1.7410 37.0512 29 .5631 21.8444 1.7758 38.7922 30. _ __-.5521.. .5412 - .22.3965. 22.9377 .-.-1.8114__ 40.5681 31 1.8476 42.3794 32 .5306 23.4683 1.8845 44.2270 33 .5202 23.9886 1.9222 46.1116 34 .5100 24.4986 1.9607 48.0338 36 .5000 24.9986 1.9999 49.9945 36 .4902 25.4888 2.0399 51.9944 37 .4806 25.9695 2.0807 54.0343 38 .4712 26.4406 2.1223 56.1149 39 .4619 26.9026 2.1647 58.2372 40.. 4529.. .4440 -.27.3555 ....2.2080.. .60.4020 41 27.7995 2.2522 62.6100 42 .4353 28.2348 2.2972 64.8622 43 .4268 28.6616 2.3432 67.1595 44 .4184 29.0800 2.3901 69.5027 46 .4102 29.4902 2.4379 71.8927 46 .4022 29.8923 2.4866 74.3306 47 .3943 30.2866 2.5363 76.8172 48 .3865 30.6731 2.5871 79.3535 49 .3790 31.0521 2.6388 81.9406 60.. 3715.. .3365 ...31.4236.. 33.1748 ....2.6916.. _ .84.5794 66 2.9717 98.5865 60 .3048 34.7609 3.2810 114.0520 66 .2760 36.1973 3.6225 131 .1250 70 .2500 37.4986 3.9995 149.9780 75 .2265 38.6763 4.4158 170.7900 80 .2051 39.7445 4.8754 193.7720 85 .1858 40.7111 5.3828 219.1400 90 .1683 41.5869 5.9431 247.1570 95 .1524 42.3800 6.5617 278.0850 100.. ....1380.. ...43.0984.. ....7.2446.. 312.2320 105 .1250 43.7489 7.9987 349.9300 110 .1132 44.3382 8.8312 391.5590 116 .1026 44.8719 9.7503 437.5150 120 .0929 45.3554 10.7652 488.2580 34 21^ PER CENT. I ir III iiii V 1 .9756 .9756 1.0250 1.0000 2 .9518 1.9274 1.0506 2.0250 3 .9286 2.8560 1.0769 3.0756 4 .9060 3.7620 1 . 1038 4.1525 6 .8839 4.6458 1.1314 5.2563 6 .8623 5.5081 1 . 1597 6.3877 7 .8413 6.3494 1 . 1887 7.5474 8 .8207 7.1701 1.2184 8.7361 9 .8007 7.9709 1.2489 9.9545 10 .7812 ..8.7521._ 1.2801.. 11.2034 11 .7621 9.5142 1.3121 12.4835 12 .7436 10.2578 1.3449 13.7956 13 .7254 10.9832 1.3785 15.1404 14 .7077 11.6909 1.4130 16.5190 15 .6905 12.3814 1.4483 17,9319 16 .6736 13.0550 1.4845 19.3802 17 .6572 13.7122 1.5216 20.8647 18 .6412 14 .3534 1.5597 22.3863 19 .6255 14.9789 1.5987 23.9460 20 ._..6103.. .5954 15.5892_. 16.1845 ..1.6386.. 25.5447 21 1.6796 27.1833 22 .5809 16.7654 1.7216 28.8629 23 .5667 17.3321 1.7646 30.5844 24 .5529 17.8850 1.80S7 32.3490 26 .5394 18.4244 1.8539 34.1578 28 .5262 18.9506 1.9003 36.0117 27 .5134 19.4640 1.9478 37.9120 28 .5009 19.9649 1.9965 39.8598 29 .4887 20.4535 2.0464 41.8563 30 .4767 . 20.9303.. 21.3954 ..2.0976.. 43.9027 31 .4651 2 . 1500 46.0003 32 .4538 21.8492 2.2038 48.1503 33 .4427 22.2919 2.2589 50.3540 34 .4319 22.7238 2.3153 52.6129 35 .4214 23.1452 2.3732 54.9282 36 .4111 23.5563 2.4325 57.3014 37 .4011 23.9573 2.4933 59.7339 38 .3913 24.3486 2.5557 62.2273 39 .3817 24.7303 2.6196 64.7830 40 ._..3724__ .3633 25.1028.. 25.4661 2.6851 67 . 4026 4l" 2.7522 70.0876 42 .3545 25.8206 2.8210 72.8398 43 .3458 26.1664 2.8915 75.6608 44 .3374 26.5038 2.9638 78.5523 45 .3292 26.8330 3.0379 81.5161 46 .3211 27.1542 3.1139 84.5540 47 .3133 27.4675 3.1917 87.6679 48 .3057 27.7732 3.2715 90.8596 49 .2982 28.0714 3.3533 94.1311 50 .2909.. .28.3623.. 3.4371.. 97.4843 66 .2571 29.7140 3.8888 115.551 60 .2273 30.9087 4.3998 135.992 66 .2009 31.963 4.9780 159 . 120 70 .1775 32.898 5.6321 185.284 75 .1569 33.645 6.3722 214.888 80 .1387 34.452 7.2096 248.383 85 .1226 35.096 8.1570 286.280 90 .1084 35.666 9.2289 329 . 154 95 .0958 36.171. 10.4416 377.664 100. _ ....0846.. ...36. 614... ...11.8137.. -...432.549 105 .0748 37.007 13.3661 494.644 110 .0661 37.355 15.1226 564.902 115 .0584 37.664 17 . 1098 644.392 120 .0517 37.934 19.3581 734.326 3 PER CENT. 86 I II III IV V 1 .9709 .9709 1.0300 1.0000 2 .9426 1.9135 1.0609 2.0300 3 .9151 2.8286 1.0927 3.0909 4 .8885 3.7171 1.1255 4 . 1836 6 .8626 4.5797 1 . 1593 5.3091 6 .8375 5.4172 1.1941 6.4684 7 .8131 6.2303 1.2299 7.6625 8 .7894 7.0197 1.2668 8.8923 9 .7664 7.7861 1 . 3048 10.1591 10 7441.. 8 5302 ' -1 3439 11 .4639 11 .7224 9^2526 1.3842 12 '8075 12 .7014 9.9540 1.4258 14.1920 13 .6810 10.6350 1.4685 15.6178 14 .6611 11.2961 1.5126 17.0863 15 .6419 11.9379 1.5580 18.5989 16 .6232 12.5611 1.6047 20.1569 17 .6050 13.1661 1.6528 21.7616 18 .5874 13.7535 1.7024 23.4144 19 .5703 14.3238 1.7535 25.1169 20-- 5537__ 14.S775-- 1 8061 26 8704 21 .5375 15^4150 1^8603 28^6765 22 .5219 15.9369 1.9161 30.5368 23 .5067 16.4436 1.9736 32.4529 24 .4919 16.9325 2.0328 34.4265 25 .4776 17.4131 2.0938 36.4593 26 .4637 17.8768 2.1566 38.5530 27 .4502 18.3270 2.2213 40.7096 28 .4371 18.7641 2.2879 42.9309 29 .4243 19.1885 2.3566 45.2189 30— 4120-- ---19 6004-- 2.4273- 47.5754 31 .4000 20.0004 2.5001 50.0027 32 .3883 20.3888 2.5751 52.5028 S3 .3770 20.7658 2.6523 55. 0778 34 .3660 21.1318 2.7319 57.7302 So ,3554 21.4872 2.8139 60.4621 36 .3450 21.8323 2.8983 63.2759 37 .3350 22.1672 2.9852 66 . 1742 38 .3252 22.4925 3.0748 69 . 1594 39 .3158 22.8082 3.1670 72.2342 40- ---.3066- ---23.1148- --3. 2620- 75.4013 41 .2976 23.4124 3.3599 78.6633 42 .2890 23.7014 3.4607 82.0232 43 .2805 23.9819 3.5645 85.4839 44 .2724 24.2543 3.6715 89.0484 45 .2644 24.5187 3.7816 92.7199 46 .2567 24. 7754 3.8950 96.5015 47 .2493 25.0247 4.0119 100.3965 48 .2420 25.2667 4.1323 104.4084 49 .2350 25.5017 4.2562 108.5406 50- — .2281- -.25.7298- --4.3839- 112.7969 55 .1968 26.7744 5.0821 136.072 60 .1697 27.6756 5.8916 163.053 65 .1464 28.452 6.8300 194.333 70 .1263 29.123 7.9178 230.594 75 .1089 29.702 9 . 1789 272.630 80 .0940 30.201 10 .6409 321.363 85 .0811 30.701 12 .3357 377.857 90 .0699 31.002 14.3005 443.349 95 .0603 31.323 16.5782 519.273 100-- 0520- --31. 599— -.-19.2186- --607.288 105 .0449 31.838 22.2797 709.323 110 .0387 32.043 25.8282 827.608 115 .0334 32.220 29.9420 964.733 120 .0288 32.373 34.7110 1,123.70 3H PER CENT. I II III IV V 1 .9662 .9662 1.0350 1.0000 2 .9335 1.8997 1.0712 2.0350 3 .9019 2.8016 1.1087 3.1062 4 .8714 3.6731 1.1475 4.2149 6 .8420 4.5151 1 . 1877 5.3625 6 .8135 5 . 3286 1.2293 6.5502 7 .7860 6.1145 1.2723 7.7794 8 .7594 6.8740 1.3168 9.0517 9 .7337 7.6077 1.3629 10.3685 10_- 7089.. 8 3166 1.4106.. - 11 7314 11 .6849 9.0016 1.4600 13.1420 12 .6618 9.6633 1.5111 14.6020 13 .6394 10.3027 1.5640 16.1130 14 .6178 10.9205 1.6187 17.6770 15 .5969 11.5174 1.6753 19.2957 16 .5767 12.0941 1.7340 20.9710 17 .5572 12.6513 1.7947 22.7050 18 .5384 13.1897 1.8575 24.4997 19 .5202 13.7098 1.9225 26.3572 20 5026 14 2124 1 9898 - 28 2797 21 .4856 14.6980 2.0594 30.2695 22 .4692 15.1671 2.1315 32.3289 23 .4533 15.6204 2.2061 34.4604 24 .4380 16.0574 2.2833 36.6665 26 .4231 16.4815 2.3632 38.9499 26 .4088 16.8904 2.4460 41.3131 27 .3950 17.2854 2.5316 43.7591 28 .3817 17.6670 2.6202 46.2906 29 .3687 18.0358 2.7119 48.9108 30.. 3563.. ...18.3920.- 2.8068.. 51.6227 31 .3442 18.7363 2.9050 54.4295 32 .3326 19.0689 3.0067 57.3345 33 .3213 19.3902 3.1119 60.3412 34 .3105 19.7007 3.2209 63.4532 35 .3000 20.0007 3.3336 66.6740 36 .2898 20.2905 3.4503 70.0076 37 .2800 20.5705 3.5710 73.4579 38 .2706 20.8411 3.6960 77.0289 39 .2614 21 . 1025 3.8254 80.7249 40.. ....2526.. .2440 ...21.3551.. 21.5991 3.9593- 84.5503 41 4.0978 88.5095 42 .2358 21.8349 4.2413 92.6074 43 .2278 22.0627 4.3897 96.8487 44 .2201 22.2828 4.5433 101.2383 45 .2127 22.4955 4.7024 105.7817 46 .2055 22.7009 4.8669 110.4840 47 .1985 22.8994 5.0373 115.3510 48 .1918 23.0912 5.2136 120. 3883 49 .1853 23.2766 5.3961 125.6018 50.. — .1791.. -.23.4556.- 5.5849__ 130.9979 55 .1508 24.2641 6.6331 160.947 60 .1269 24.9447 7.8781 196.517 65 .1069 25.5168 9.3567 238.763 70 0900 26.0004 11.1128 288.938 75 .0758 26.4067 13.1986 348.531 80 .0638 26.7488 15.6757 419.307 85 .0537 27.0368 18.6179 503.368 90 .0452 27.2793 22.1122 603.205 95 .0381 27.4798 26.2623 721.780 100 _. -.-.0321.. -.-27.6554.. -. .31. 1914- ....862.612 105 .0270 27.8002 37.0456 1,029.874 110 .0227 27.9221 43.9986 1,228. 53 115 .0191 28.0247 52.2565 1,464.471 120 .0161 28.1111 62.0643 1,744.69 4 PER CENT. 87 I 11 HI iin V 1 .9615 .9615 1.0400 1.0000 2 .9246 1.8861 1.0861 2.0400 3 .8890 2.7751 1 . 1249 3.1216 4 .8548 3.6299 1 . 1699 4.2465 6 .8219 4.4518 1.2167 5.4163 6 .7903 5.2421 1.6253 6.6330 7 .7599 6.0021 1.3159 7.8983 8 .7307 6.7327 1.3686 9.2142 9 .7026 7,4353 1.4233 10.5828 10 6756-- 8 1109-- 1 .4802-- 12.0061 11 .6496 8.7605 1.5395 13,4864 12 .6246 9.3851 1.6010 15.0258 13 .6006 9.9856 1.6651 16.6268 14 .5775 10.5631 1.7315 18.2919 15 .5553 11.1184 1.8009 20.0236 16 .5339 11.6523 1.8730 21.8245 17 .5134 12.1657 1.9479 23.6975 18 .4936 12.6593 2,0258 25.6454 19 .4746 13.1339 2 , 1068 27.6712 20 -4564 1 3 ^903 2 1911-- 29.7781 21 .4388 14.0292 2^2788 31 '9692 22 .4220 14.4511 2,3699 34.2480 23 .4057 14.8568 2,4647 36.6179 24 .3901 15.2470 2,5633 39.0826 25 ■ 3751 15.6221 2,6658 41.6459 26 .3607 15.9828 2,7725 44.3117 27 .3468 16.3296 2,8834 47.0842 28 .3335 16.6631 2.9987 49.9676 29 .3207 16.9837 3.1187 52.9663 30- 31 --.3083- .2965 --17.2920-- 17.5885 3.2434-- 56 0849 3^3731 59^3283 32 .2851 17,8736 3.5081 62.7015 S3 .2741 18.1476 3.6484 66.2095 34 2636 18.4112 3.7943 69.8579 36 . 2534 18.6646 3.9461 73.6522 36 .2437 18.9083 4.1039 77.5983 37 .2343 19.1426 4.2681 81.7022 38 .2253 19.3679 4.4388 85.7903 39 .2166 19.5845 4.6164 90.4091 40 2083 19 7928 4.8010-- 95.0255 41 .2003 19^9931 4.9931 99.8265 42 .1926 20 .1856 5 . 1928 104.8200 43 .1852 20.3708 5.4005 110.0124 44 .1780 20.5488 5.6165 115.4129 45 .1712 20.7200 5.8412 121,0294 46 .1646 20.8847 6.0748 126,8706 47 .1583 21.0429 6.3178 132,9454 48 .1522 21.1951 6.5705 139.2632 49 .1463 21.3415 6.8333 145.8337 50 - 1407— -21.4822-- 7.1067- ..-152.6671 55 .1157 22 . 1086 8.6464 191.159 60 .0951 22.6235 10,5196 237.991 65 .0781 23.0466 12,7987 294.967 70 .0642 23.3945 15,5716 364.290 75 .0528 23.6281 18,9453 448.642 80 .0434 23.9154 23,0498 551 . 245 85 .0357 24 . 1085 28,0436 676.090 90 .0293 24 . 2673 34,1193 827.983 95 .0241 24.3977 41,5114 1,012.785 100.. _...0198_. __ -24.5050. - ___50,5049-- ..1,237.622 105 .0163 24.5931 61,4470 1,511.175 110 .0134 24 . 6656 74.7597 1,843.992 115 .0110 24.7251 90.9566 2,248.915 120 .0090 24.7741 110.663 2,741.558 38 4H PER CENT. I II in nil V 1 .9569 .9569 1.0450 1.0000 2 .9157 1.8727 1.0920 2.0450 3 .8765 2.7490 1.1412 3.1370 4 .8386 3.5875 1 . 1925 4.2782 6 .8022 4.3900 1.2462 5.4707 6 .7679 5.1579 1.3023 6.7169 7 .7348 5.8927 1.3609 8.0192 8 .7032 6.5959 1.4221 9.3800 9 .6729 7.2688 1.4861 10.8021 10 6439 7 9125 1 5530 12 2882 ll" .6162 8.5289 1.6229 13.8412 12 .4897 9.1186 1.6959 15.4640 13 .5643 9.6829 1.7722 17.1599 14 .5400 10.2229 1.8519 18.9321 15 .5167 10.7395 1.9353 20.7841 16 .4945 11.2340 2.0224 22.7193 17 .4732 11.7072 2.1134 24.7417 18 .4528 12.1600 2.2085 26.8551 19 .4333 12.5933 2.3079 29.0634 20 4146 13 0079 2.4117.. 31 3716 2l" .3968 13^4047 2.5202 33.7831 22 .3797 13.7844 2.6337 36.3034 23 .3634 14.1478 2.7522 38.9370 24 .3477 14.4955 2.8760 41.6892 25 .3327 14.8282 3.0054 44.5652 26 .3184 15.1466 3.1407 47.5706 27 .3047 15.4513 3.2820 50.7113 28 .2916 15.7429 3.4279 53.9933 29 .2790 16.0219 3.5840 57.4230 30._ 2670-. --16.2889- 3.7453.. 61.0071 31 .2555 16.5444 3.9139 64.7524 32 .2445 16.7889 4.0900 68.6602 33 .2340 17.0229 4.2740 72.7562 34 .2239 17.2468 4.4664 77.0303 35 .2143 17.4610 4.6673 81.4966 36 .2050 17.6660 4.8774 86.1640 37 .1962 17.8622 5.0969 91.0413 38 .1878 18.0500 5.3262 96.1382 39 .1797 18.2297 5.5659 101.4644 40__ .._.1719_- -.18.4016- 5.8164.. ....107.0303 41 .1645 18.5661 6.0781 112.8467 42 .1574 18.7235 6.3516 118.9248 43 .1507 18.8742 6.6374 125.2764 44 .1442 19.0184 6.9361 131.9138 45 .1380 19.1563 7.2482 138.8500 46 .1320 19.2884 7.5744 146.0982 47 .1263 19.4147 7.9153 153.6726 48 .1209 19.5356 8.2715 161.5879 49 .1157 19.6513 8.6437 169.8594 50 .. .1107._ .0888 19.7620 — 9.0326.. 178.5030 55 20.2480 11.2563 227.9180 60 .0713 20.6380 14.0274 289.4980 65 .0572 20.9509 17.4807 366.2380 70 .0459 21.2021 21.7841 461.8700 75 .0368 21.4118 27.1470 581.2670 80 .0296 21.5653 33.8301 729.5580 85 .0237 21.6951 42.1585 914.6330 90 .0190 21.7992 52.5371 1145.2700 95 .0153 21.8828 65.4708 1432.6840 100 __ _...0123__ -.21.9499- .. .81.5885.. ...1790.8600 105 .0098 22.0036 101.674 2237.2000 110 .0079 22.0468 126.704 2793.4300 115 .0063 22.0815 157.897 3486.6000 120 .0051 22.1093 196.768 4350.4000 5 PER CENT. 39 I II III nil V 1 .9524 .9524 1.0500 1.0000 2 .9070 1.8594 1.1025 2.0500 3 .S63S 2.7232 1.1576 3.1525 4 . S227 3.5460 1.2155 4.3101 5 . 7835 4.3295 1.2763 5.5256 6 .7462 5.0757 1.3401 6.8019 7 .7107 5.7864 1.4071 8.1420 8 .6768 6.4632 1.4775 9.5491 9 .6446 7.1078 1.5513 11.0266 10 6139 7.7217-- 1 6289 12.5779 ll" """;5847" 8 '3064 1.7103 14.2068 12 .5568 8.8623 1.7959 15.9171 13 .5303 9.3936 1.8856 17.7130 14 .5051 9.8986 1.9799 19.5986 15 .4810 10.3797 2.0789 21.5786 16 .4581 10.8378 2.1829 23.6575 17 .4363 11.2741 2.2920 25.8404 18 .4155 11.6896 2.4066 28.1324 19 .3957 12.0853 2.5270 30.5390 20 _ .3769-_ 12 4622 .-2.6533-- 33.0660 2l'" '"';35S9" """l2;8212 ' 2.7860 35.7193 22 .3418 13.1630 2.9253 38.5052 23 .3256 13.4886 3.0715 41.4305 24 .3101 13.7986 3.2251 44.5020 25 .2953 14.0939 3.3864 47.7271 26 .2812 14.3752 3.5557 51.1135 27 .2678 14.6430 3.7335 54.6691 28 .2551 14.8981 3.9201 58.4026 29 .2429 15.1411 4.1161 62 . 3227 30 2314 15.3725__ 4 3219 66.4388 31 ' "'^2204' ""'15.5928 4.5380 70.7608 32 .2099 15.8027 4.7649 75.2988 33 .1999 16.0025 5.0032 80.0638 34 .1904 16.1929 5.2533 85.0670 35 .1813 16.3742 5.5160 90.3203 36 .1727 16.5469 5.7918 95.8363 37 .1644 16.7113 6.0814 101.6281 38 .1566 16.8679 6.3855 107.7095 39 .1491 17.0170 6.7048 114.0950 40_. -...1420-_ .._17.1591.- 7.0400-. 120.7998 41 .1353 17.2944 7.3920 127.8398 42 .1288 17.4232 7.7616 135.2318 43 . 1227 17.5459 8.1497 142.9933 44 .1169 17.6628 8.5572 151.1430 45 .1113 17.7741 8.9850 139.7002 46 .1060 17.8801 9.4343 168.6852 47 . 1009 17.9810 9.9060 178.1194 48 .0961 18.0772 10.4013 188.0254 49 .0916 18.1687 10.9213 198.4267 50_. ..-.0872-_ _. .18. 2559- ..-11.4674.. 209.3480 55 .0683 18.6335 14.6356 272.7130 60 .0535 18.9293 18.6792 353.5840 65 .0419 19.1191 23.8399 456.7980 70 .0329 19.3427 30.4264 588.5290 75 .0257 19.4849 38.8327 756.6540 80 .0202 19.5965 49.5614 971.2290 85 .0158 19.6838 63.2544 1,245.0880 90 .0124 19.7523 80.7304 1,594.6100 95 .0097 19.8058 103.035 2,040.7000 100 0076 19 . 8479 . . ..131.501... 167.833 ..2,610.0300 105 .0060 19.8808 3,336.6600 110 .0047 19.9066 214.202 4,264.0300 115 .0037 19.9268 273.382 5,447.6400 120 .0029 19.9427 348.912 6.958.2400 40 6M PSR CENT. I u 1 nx iiii V 1 .9479 .9479 1.0550 1.0000 2 .8985 1.8463 1.1130 2.0550 3 .8516 2.6979 1.1742 3.1680 4 .8072 3.5052 1.2388 4.3423 5 .7651 4.2703 1.3070 5.5811 6 .7252 4.9955 1.37S8 6.SSS1 7 .6854 5.6830 1.4547 8.2689 8 .6516 6.3346 1.5347 9,7216 9 .6176 6.9522 1.6191 11,2563 10- 5854 — 7.5376— 1.7081-- 12,8754 11 .5549 8.0925 1,8021 14,5835 12 .5260 8.6185 1,9012 16.3856 13 .4986 9.1171 2,0058 18.2868 14 .4726 9.5896 2.1161 20.2928 15 .4479 10.0376 2,2325 22.4087 16 .4246 10.4622 2,3553 • 24.6411 17 .4024 10.8648 2.4848 26.9964 18 .3815 11.2461 2.6215 29.4812 19 .3616 11.6077 2.7656 32.1027 20- --3427- -_11.9501- 2.9178- 34.8683 21 .3249 12.2752 3.0782 37.7881 22 ,3079 12.5S32 3.4275 40.8643 23 .2919 12.8750 3.4262 44.1118 24 .2767 13.1517 3.6146 47.53S0 25 .2622 13.4139 3.8134 51.1526 26 .2486 13.6625 4.0231 5f.9660 27 .2356 13.8981 4.2444 58.9891 23 .2233 14.1214 4.4778 03.2335 29 .2117 14.3331 4.7241 67.7114 30- --2008- .1902 --14.5337- 14.7239 -- 4.9840 71.1355 31 5.2581 77.4194 32 . 1803 14.9042 5.5473 82.6775 33 .1709 15.0751 5.8524 88.2248 34 .1620 15.2370 6.1742 94.0771 35 . 1535 15,3908 6.5138 100.2514 38 .1455 15,5361 6.8721 106.7652 37 .1379 15.6740 7.2501 113.6373 38 .1307 15.8047 7.6488 120.8873 39 .1239 15.9287 8.0695 128.5381 40- 1175- -.16.0461- --8. 5133- 136,6056 41 .1113 16.1575 8.9815 145,1189 42 .1055 16.2630 9.4755 154,1005 43 .1000 16.3630 9.9967 163,5760 44 .0948 16.4579 10,5465 173,5727 45 .0899 16.5477 11,1266 184,1192 46 .0852 16.6329 11,7385 195,2457 47 .0807 16.7137 12,3841 206,9842 48 .0765 16.7902 13,0653 219,3684 49 .0725 16.8628 13,7838 232,4336 50- --.0688- -.16.9315- --14,5420- 246.2175 55 .0526 17.2251 19,0046 327.3563 60 .0403 17.4498 24,8381 433.4200 65 .0308 17.6216 32,4623 572.0384 70 .0230 17.7630 43,4150 771.1818 75 .0176 17.8614 56.7414 1,013.4800 80 .0138 17.9309 72,4703 1,299.4600 85 .0106 17.9898 94,7152 1,703.9127 90 .0081 18.0349 123,7883 2,232.5145 95 .0062 18.0694 161,7855 2,923.3727 100- 0047- - .18.0958- - -211.4463- -3.826.2963 105 .0036 18.1160 276.3503 5,008.3691 110 .0028 18.1315 361.2768 6,550.4873 115 .0021 18.1433 472.0413 8,564.3873 120 .0016 18.1523 616.9357 11,198.8309 6 PER CENT. I II Ill nil 1 ^ 1 .9434 .9434 1.0600 1 , 0000 2 .8900 1.8334 1 . 1236 2 , 0600 3 .8396 2.6730 1.1910 3,1836 4 .7921 3.4651 1.2625 1 4.3746 6 .7473 4.2124 1.3382 1 5.6371 6 .7050 4.9173 1.4185 1 6,9753 7 .6651 5.5824 1.5036 j 8.3938 8 .6274 6.2098 1.5938 1 9.8975 9 .5919 6.8017 1 1.6895 11.4913 10-. ....5584.. 7.3601.. :.... 1.7908.. 13.1808 11 .5268 7.8869 1.8983 14.9716 12 .4970 8.3838 2.0122 16.8699 13 .4688 8.8527 2.1329 18.8821 14 .4423 9.2950 2.2609 21.0151 15 .4173 9.7122 2.3966 23 . 2760 16 .3936 10.1059 2.5404 25.6725 17 .3714 10.4772 2.6928 28.2129 18 .3503 10.8276 2.8543 30,9057 19 .3305 11.1581 3.0256 33 . 7600 20„ ....3118.. .2942 __.l 1.4699.. 11.7641 ....3.2071.. 36.7856 21 3.3996 39.9927 22 .2775 12.0416 3.6035 43.3923 23 .2618 12.3034 3.8197 46.9958 24 .2470 12.5504 4.0489 50.8156 26 .2330 12.7834 4.2919 54.8645 26 .2198 13.0032 4.5494 59.1564 27 .2074 13.2105 4.8223 63 . 7058 28 .1956 13.4062 5.1117 68.5281 29 .1846 13.5907 5.4184 73.6398 30._ . ..1741.. .1643 ...13.7648.. 5.7435 79,0582 84.8017 31 13.9291 6.0881' 32 .1550 14.0840 6.4534 90.8S98 33 .1462 14.2302 6.8406 97.3432 34 .1379 14.3681 7.2510 104.1838 35 .1301 14.4982 7.6861 111.4348 36 .1227 14.6210 8.1473 119.1209 37 .1158 14.7368 8.6361 127.2681 38 .1092 14.8460 9.1543 135.9042 39 .1031 14.9491 9.7035 ' 145.0585 40.. ....0972.. ...15.0463__ ...10.2857.. 154.7620 41 .0917 15.1380 10.9029 165.0477 42 .0865 15.2245 11.5570 : 175.9505 43 .0816 15.3062 12.2505 1 187.5076 44 .0770 15.3832 12.9855 j 199 . 7580 46 .0727 15.4558 13.7646 i 212.7435 46 .0685 15.5244 14.5905 226,5081 47 .0647 15.5890 15.4659 241.0985 48 .0610 15.6500 16.3939 256.5645 49 .0575 15.7076 17.3775 272.9584 60.. ....0543.. ...15.7619.. ...18.4202.. 290.3359 66 .0406 15.9905 24.6507 394.1783 60 .0303 16.1611 32.9883 533.1383 65 .0226 16.2891 14.1458 719.0966 70 .0169 16.3845 159.0772 967.9533 75 .0126 16.4558 1 79.0587 1,300.9783 80 .0095 16.5091 105.7985 1,746.6416 85 .0071 16.5489 141.5827 2,343.0450 90 .0053 16.5787 189.4698 3,141.1633 96 .0039 16.6009 ' 253.5538 , 4,209.2300 100.. ....0029..' ...16.6175..' .-339.3125... -5,638.5416 106 .0022 16.6299 1 454.0770 ' 7,551.2833 110 .0016 16.6392 1 607.6591 10,110,9850 115 .0012 16.6461 i 813.1867 13,536.4450 120 .0009 ' 16.6513 ! 1,088,2280 18,120.4667 41 42 7 PER CENT. I II III iiii V 1 .9346 .9328 1.0700 1.0000 2 .8736 1.8043 1 . 1449 2.0700 3 .8163 2.6228 1.2250 3.2142 4 .7629 3.3857 1.3108 4.4400 6 .7130 4.0986 1.4026 5.7514 6 .6663 4.7657 1.5007 7.3529 7 .6227 5.3886 1.6058 8.6542 8 .5820 5.9700 1.7182 10.2600 9 .6439 6.5143 1.8385 11.9786 10- 11 5083-- 7.0228— -- 1 9671 13 8159 .4751 7.4971 2.1049 15.7843 12 .4440 7.9414 2.2522 17.8886 13 .4150 8.3557 2.4098 20.1400 14 .3878 8.7442 2.5785 22.5500 16 .3624 9.1071 2.7590 25.1286 16 .3387 9.4457 2.9522 27.8886 17 .3161 9.7686 3.1588 30.8400 18 .2959 10.0571 3.3800 34.0000 19 .2765 10.3343 3.6165 37.3786 20- 21 2584 — -..10.5928-- 3.8697-- 40 9528 .2415 10.8343 4.1406 44.8657 22 .2257 11.0600 4.4304 49.0057 23 .2109 11.2714 4.7405 63.4343 24 .1971 11.4685 5.0724 55.3200 25 .1842 11.6528 5.4275 63.2500 26 .1722 11.8242 5.8075 68.6786 27 .1609 11.9857 6.2140 74.4857 28 .1504 12.1357 6.6490 80.7000 29 .1406 12.2757 7.1144 87 . 3346 30- 31 .1314-- 12 4071 7 6124 94.4628 ""!l228 12.5300 8.1452 102.0742 32 .1147 12.6457 8.7154 110.2700 33 .1072 12.7528 9.3255 118.9500 34 .1002 12.8528 9.9783 128.2618 36 .0937 12.9457 10.6768 138.2400 36 .0875 13.0343 11.4241 148.9157 37 .0818 13.1157 12.2239 160.3414 38 .0765 13.1914 13.0795 172.5642 39 .0715 13.2628 13.9960 185.6428 40- -..0668- ...13.3300.. ...14.9747.. -- 199. 6386 41 .0624 13.3928 16.0230 214.6143 42 .0583 13.4514 17.1446 230.6371 43 .0545 13.5057 18.3448 247.7828 44 .0509 13.5571 19.6290 266.1428 46 .0476 13.6043 21.0030 285.7571 46 .0445 13.6485 22.4332 306.1886 47 .0416 13.6900 24.0463 329.2328 48 .0387 13.7314 26.7888 364.1257 49 .0363 13.7657 27.5306 379.0086 80- -..0339- ...13.8000.. ...29.4577- - -406. 5386 66 .0242 13.9385 41.3162 576.9458 60 .0173 14.0371 57.9482 813.6468 66 .0123 14.1085 81.2755 1146.7928 70 .0088 14.1585 113.9929 1614.1844 75 .0062 14.1959 159.8823 2141.1767 80 .0045 14.2200 224.2440 2269.7471 86 .0032 14.?385 314.5138 3160.6286 90 .0023 14.2514 441 . 1230 4478.7682 95 .0016 14.2614 618.7000 6287.4714 100. 0011.. ...14.2685.. ..867.7600- ...8824.2867 106 .0008 14.2728 1217.0812 12382.2855 110 .0006 14.2757 1707.0235 17372.6886 116 .0004. 14.2785 2394.1978 24371.7642 120 .0003 14.2800 3357.9923 34188.5400 8 PER CENT. 4S I 11 in nil V 1 .9259 .9250 1.0800 1.0000 2 .8573 1.7825 1.1664 2.0800 3 .7938 2.5762 1.2597 3.2463 4 .7350 3.3112 1.3605 4.5062 6 .6806 3.9912 1.4693 6.8366 6 .6302 4.6212 1.5869 7.3362 7 .5840 5.1987 1.7138 8.9225 8 .5403 5.7450 1.8509 10.6363 9 .5002 6.2462 1.9990 12.4875 10- 4632- 6.7087 2 1589 14 4862 11 .4289 7.1375 2.3317 ""'l6;6463 12 .3971 7.5350 2.5182 18.9775 13 .3676 7.9037 2.7196 21.4950 14 .3405 8.2425 2.9372 24.2150 15 .3152 8.5587 3.1722 27.1525 16 .2919 8.85-13 3.4260 30.3250 17 .2703 9.1200 3.7000 33.7500 18 .2502 9.3712 3.9960 37.4500 19 .2317 9.6025 4.3157 41.4463 20- 2145-- 9.8175-- 4 6610 45.7625 21 .1987 10.0150 5.0339 50.4237 22 .1839 10.2000 5.4366 55.4575 23 .1703 10.3700 5.8716 60.8950 24 .1577 10.5275 6.3413 66.7663 25 .1460 10.6737 6.8486 73.1075 26 .1352 10,8087 7.3964 79.9800 27 .1252 10.9337 7.9882 87.3525 28 .1159 11.0500 8.6272 95.3400 29 .1073 11.1575 9.3174 103.9675 30- --.0994- .0920 -.11.2562- 11.3487 10 0629 113 2862 31 10.8678 123.3475 32 .0852 11.4337 11.7371 134.2138 33 .0789 11.5125 12.6763 145.9537 34 .0730 11.5862 13.6904 158.6300 36 .0676 11.6537 14.7853 172.3163 36 .0626 11.7162 15.9684 187.1050 37 .0580 11.7737 17.2460 203.0750 38 .0537 11.8275 18.6249 220.3113 39 .0497 11.8775 20.1159 238.9488 40- -..0460- .0426 -.11.9237- 11.9662 ...21. 7250.. -259.0625 41 23.4630 280.7876 42 .0395 12.0050 25.3400 304.2500 43 .0365 12.0425 27.3672 329.5900 44 .0338 12.0762 29.5567 356.9588 45 .0313 12.1075 31.9213 386.5163 46 .0290 12.1362 34.4750 418.4376 47 .0269 12.1625 37.2330 452.9125 48 .0249 12.1875 40.2117 490.1463 49 .0230 12.2112 43.4207 530.2588 50- 0213- .0145 -.12.2325- 12.3175 46 9029 - 573.7863 66 68.9160 848.9500 60 .0099 12.3750 101.2605 1253.2563 66 .0067 12.4150 148.7849 1847.3113 70 .0046 12.4412 218.6150 2720.1875 76 .0031 12.4600 321.2177 4002.7213 80 .0021 12.4725 471.9761 5887.2013 85 .0014 12.4812 693.4888 8656.1100 90 .0010 12.4862 1018.9649 12724.5613 96 .0007 12.4900 1497.1993 18702.4913 100- -..0005- . — 12.4925- -2199.8838.. ,.27486.0476 105 .0003 12.4950 3232.3656 40392.0700 110 .0002 12.4962 4749.4130 59355.1625 115 .0001 12.4975 6978.4677 87218.3463 120 .0001 12.4975 10253.6792 128158.4900 44 10 PER CENT. I II Ill iiii V 1 .9091 0.908 1 . 1000 1.0000 2 .8264 1.735 1.2100 2.1000 3 .7513 2.486 1.3310 3.3100 4 .6830 3.169 1.4641 4.6410 6 .6209 3.790 1.6105 6.1050 6 .5645 4.354 1.7716 7.7160 7 .5132 4.867 1.9487 9.4870 8 .4665 5.334 2.1436 11.4360 9 .4241 5.758 2.3580 13.5800 10- 3855_. 6.144.— 2.5938- 15.9380 11 .3505 6.494 2.8531 18.5310 12 .3186 6.813 3.1385 21.3850 13 .2897 7.102 3.4523 24.5230 14 .2633 7.366 3.7976 27.9760 15 .2394 7.605 4.1773 31.7730 16 .2176 7.823 4.5950 35.9500 17 .1978 8.021 5.0545 40.5450 18 .1799 8.200 5.5600 45.6000 19 .1635 8.364 6.1160 51 . 1600 20- 1486— 8 513 --. 6.7276 57.2760 21 .1351 8.648 7.4004 64.0040 22 .1228 8.771 8.1404 71.4040 23 .1117 8.882 8.9545 79.5450 24 .1015 8.984 9.8500 88.6000 25 .0923 9.076 10.8349 98.3490 26 .0839 9.160 11.9184 109 . 1840 27 .0763 9.236 13.1103 121.1030 28 .0693 9.306 14.4213 134.2130 29 .0630 9.369 15.8634 148.G340 30- -_.0573- --9.426-. .--17.4498.- -..164.4980 31 .0521 9.478 19.1948 181.9480 32 .0474 9.525 21.1143 201 . 1430 33 .0431 9.568 23.2257 222.2570 34 .0391 9.608 25.5483 245.4830 35 .0356 9.643 28.1032 271.0320 36 .0324 9.675 30.9135 299.1350 37 .0294 9.705 34.0049 330.0490 38 .0273 9.726 37.4054 364.0540 39 .0243 9.756 41 . 1460 401.4600 40-. -..0221- . 9.778-. ...45.2605- 442.6050 41 .0201 9.798 49.7866 487.8660 42 .0183 9.816 54.7655 537.6550 43 .0166 9.833 60.2420 592.4200 44 .0151 9.848 66.2662 652.6620 45 .0137 9.862 72.8928 718.9280 46 .0125 9.874 80.1822 791.8220 47 .0113 9.886 88.2004 872.0040 48 .0103 9.896 97.0207 960.2070 49 .0094 9.905 106.7228 1057.2280 50- — 0085- ....9.914... -117.3926- ..-1163.9260 55 .0053 9.946 189.0668 1880.6680 60 .0033 9.966 304.4944 3034.9440 65 .0020 9.979 490.3932 4893.9320 70 .0013 9.986 789.7876 7887.8760 75 .0008 9.991 1271.9648 12709.6480 80 .0005 9.994 2048.5188 20475.1880 85 .0003 9.996 3299 . 1742 32981.7420 90 .0002 9.997 5313.3659 53123.6590 95 .0001 9.998 8557.2549 85562.5490 100- .00007a 9.9992.- 9.9994 13781.6139- 22195.5102 137806.1390 105 .00005 221945.1020 110 .00003 9.9996 35746.1983 357451.9830 115 .00002 9.9997 57569.8666 575688.6660 120 .00001 9.9998 92717.0213 927160.2130