GIFT or 
 
 A.llen Knipht 
 

INDEMNITY BONDS FOR 15 OR 20 YEARS 
 
 (including insurance), for from 
 
 $1,000 to $100,000, 
 
 ARE ISSUED BY THE 
 
 EQUITABLE LIFE ASSURANCE SOCIETY 
 
 OF THE UNITED STATES, 
 Payable at the death of the assured, if previous to their maturity. 
 
 PAYABLE FOR IN ANNUAL, SEMI-ANNUAL OR QUARTERLY INSTALMENTS. 
 
 BONDS PAID UP IN 10 YEARS. 
 
 ANNUAL INSTALMENTS PER $1,000. 
 
 20-YEAR BOND 20 ANNUAL INSTALMENTS. 
 
 IS-YEAR BOND 10 ANNUAL INSTALMENTS. 
 
 Age at issue. 
 20 
 
 $50" 
 50 
 50 
 60 
 80 
 
 Cash return on 
 maturity of bond 
 at end of 20 years 
 (on basis explain- 
 ed below), $1,700. 
 
 Age at issue. 
 20 
 
 $100 
 IOO 
 IOO 
 IOO 
 
 1 20. 
 
 Cash return on 
 maturity of bond 
 at end of 15 years 
 (on basis explain- 
 ed below), between 
 $1,300 and $1,400. 
 
 30. . 
 
 "\O. . 
 
 40 .... 
 
 40. . 
 
 SO. . 
 
 SO. . 
 
 60 
 
 60 
 
 
 
 The exact amount of profits which will be earned and distributed among the 
 holders of such Indemnity Bonds as become fully paid-up and then mature, cannot be 
 stated in advance, as they depend in a measure upon varying quantities, such as the 
 rate of interest, mortality and expense ; but careful calculations, based on the experi- 
 ence of the Society up to the present time, show the surplus profits which would be 
 payable with such bonds if they had been issued by the Society 15 or 20 years ago 
 and matured to-day. While such figures can give only an approximate idea of the 
 results of the future, they furnish the best attainable data upon which to judge of the 
 value of these Bonds. 
 
 \ 
 
THE THIRTIETH ANNUAL STATEMENT OF 
 
 The Equitable Life Assurance Society 
 
 OF THE UNITED STATES, 
 
 For the Year Ending December 31, 1889. 
 
 AMOUNT OF LEDGER ASSETS, JANUARY i, 1889 .. $89,427,026.92 
 
 Less Contingent Sinking Fund 600,000.00 
 
 $88,827,026.92 
 Incotne. 
 
 Premiums $25i357i522-75 
 
 Interest, Rents, etc Si35. 765-53 $30,393,288.28 
 
 $119,220,315.20 
 Disbu rsements. 
 
 Claims by Death and Matured Endowments $7,878,499.53 
 
 Dividends, Surrender Values, Annuities and Discounted Endowments.... 3,964,358.36 
 
 Total Paid Policy-holders $11,842,857.89 
 
 Dividend on Capital 7,000.00 
 
 Commissions, Advertising, Postage and Exchange 3,176,239.09 
 
 General Expenses, State, County, City Taxes 2,820,855.91 $17,846,952.89 
 
 Net Ledger Assets, December 31, 1889 $101, 373,362.31 
 
 Assets. 
 
 Bonds and Mortgages $23,637,873.52 
 
 Real Estate, including the Equitable Buildings and purchases under fore- 
 closure of mortgages 16,536,541.33 
 
 United States Stocks, State Stocks, City Stocks, in Trust Companies and 
 
 other Investments 451645,395.63 
 
 Loans secured by Bonds and Stocks (Market Value, $3,404,859) 2,705,000.00 
 
 Real Estate outside the State of New York, including purchases under 
 
 foreclosure of mortgages 8,116,755.06 
 
 Cash in Banks and in transit (since received and invested) 3,960,630.63 
 
 Due from Agents on account of Premiums 771,166.14 $101,373,362.31 
 
 Market value of Stocks and Bonds over book value 2,697,138.55 
 
 Interest and Rents due and accrued 829,895.26 
 
 Premiums deferred and in transit 2,249,913.00 
 
 Total Assets, December 31, 1889 $107,150,309.12 
 
 I hereby certify, that after a personal examination of the securities and accounts 
 described in this statement, I find the same to be true and correct as stated. 
 
 JOHN A. McCALL, Comptroller. 
 
 Total Liabilities, including legal reserve on all existing Policies (4% Standard) $84.329,234.9a 
 
 Total Undivided Surplus over 1$ Reserve #22,821,074.20 
 
 Of which the proportion contributed (as computed) by Policies in general 
 
 class, is $6,848,611.20 
 
 Of which the proportion contributed (as computed) by Policies in Tontine 
 
 class, is . 15,972,463.00 
 
 We certify to the correctness of the above calculation of the reserve 
 
 and surplus. From this surplus the usual dividends will be made. GEO. W. PHILLIPS, \ A ftua -; f . 
 
 J.G.VANCISE, fAt****** 
 
 New Assurance written in 1889 $1751264,100 
 
 Total Outstanding Assurance $631.016,666 
 
 We, the undersigned, have, in person, carefully examined the" accounts, and counted and examined in 
 detail the assets of the Society, and certify that the foregoing statement thereof is correct. 
 
 BENNINGTON F. RANDOLPH, ) Special Committee of the Board of Directors, 
 
 THOS. S. YOUNG, HENRY S. TERBELL, V appointed to examine the accounts and as- 
 
 GEORGK W. CARLETON, E. BOUDINOT COLT, ) sets at the close of the year 1889. 
 
 BOARD OF DIRECTORS. 
 
 HENRY B. HYDE, PRESIDENT. 
 JAMES W. ALEXANDER, VICE-PRESIDENT. 
 
 Louis FITZGERALD, 
 HENRY A. HURLBUT, 
 HENRY G. MARQUAND, 
 WM. A. WHEELOCK, 
 HENRY DAY, 
 M. HARTLEY, 
 H. M. ALEXANDER, 
 CHAUNCBY M. DEPEW, 
 CHARLES G. LANDON, 
 CORNELIUS N. BLISS, 
 ALANSON TRASK, 
 E. BOUDINOT COLT 
 EUGENE KELLY, 
 
 JOHN D. JONES, 
 JOHN SLOANE, 
 S. BORROWE, 
 B. WILLIAMSON, 
 G. W. CARLETON, 
 E. W. LAMBERT, 
 H. S. TERBELL, 
 THOMAS S. YOUNG, 
 WILLIAM M. BLISS, 
 JOHN J. McCooK, 
 B. F. RANDOLPH, 
 JOHN A. STEWART, 
 LEVI P. MORTON, 
 
 GEO. C. MAGOUN, 
 WM. B. KENDALL, 
 DANIEL D. LORD, 
 H. J. FAIRCHILD, 
 WM. ALEXANDER, 
 HORACE PORTER, 
 C. B. ALEXANDER, 
 GEO. DE F. L. DAY, 
 J. F. DE NAVARRO, 
 JOSEPH T. Low, 
 EDWARD W. SCOTT, 
 CHARLES S. SMITH, 
 GEORGE H. STUART, \ 
 
 A. VAN BERGEN, 
 T. DE WITT CUYLER 
 OLIVER AMES, 
 EUSTACE C. FITZ, 
 S. H. PHILLIPS, 
 HENRY R. WOLCOTT, 
 GUSTAV G. POHL, 
 JOHN A. MCCALL, 
 JAMES H. DUNHAM, 
 DANIEL R. NOYES, 
 WALDO ADAMS. 
 
FIRST EDITION. 
 
 How TO VALUE BONDS. 
 
 PUBLISHED UNDER THE AUSPICES OF 
 
 THE EQUITABLE LIFE ASSURANCE SOCIETY 
 
 OF NEW YORK. 
 
 
 HORATIO J. CROAD, 
 
 ACTUARY, ETC., 16 AND 18 EXCHANGE PLACE, NEW YORK. 
 
 ALL RIGHTS^ RESERVED. 
 
 NEW YORK: 
 BURR PRINTING HOUSE, 
 
 18 JACOB STREET. 
 

 
 Entered according to Act of Congress in the year 1889, by Horatio J. Croad, in the Office 
 of the Librarian of Congress in Washington. 
 
 A 
 
 
THE publication of this little treatise was suggested by the fact that there have 
 been so many doubts and so much mystery as to the mode of valuing bonds mathe- 
 matically, and also as to the real meaning of a person being able to pay a certain 
 price for a bond of a particular denomination in order to realize either a lower or 
 higher rate of interest on the investment than the bond calls for. 
 
 For instance. An 8$ $1,000 bond having 5 years to run, interest payable semi- 
 annually and costing $1,284.14 (market price, 128.41), is said to realize, at the rate of 
 2$ annually or i$ semi-annually on the investment. 
 
 The following will explain its meaning : 
 
 First. The investor receives the semi-annual interest on the bond $ 40.00 
 
 ifi on the investment of $1.284.14 is 12.84 
 
 Difference $ 27.16 
 
 If $27.16 is set aside every half year and invested at 2$ annually (or 
 
 i$ semi-annually), it would in 5 years amount to $ 284. 14 
 
 To which add the face value of the bond 1,000.00 
 
 The original amount invested $1284. 14 
 
 Second. The bond at maturity is worth $1,000, and the semi-annual 
 interest is $ 40.00 
 
 By the payment of $30.00 at the end of every half year (interest computed at \<jb 
 semi-annually), the investor can borrow at the time the bond is purchased $284.14, and 
 at the end of 5 years the debt would be liquidated. 
 
 So that the investor of $ 1,000 gets semi-annually $ 40.00 
 
 Pays out for the $284.14 30.00 
 
 \% on $i,ooo is the difference , $ 10.00 
 
 Third. A 4$ $1,000 bond having 5 years to run, interest payable semi-annually 
 to realize 4^^ on the investment, is said to be worth $977.83 (market value, 97.78). 
 That is, on the investment of $977.83 the investor receives semi-annually. $ 20.00 
 An investment of $22.17 ($1,000 minus $977.83) would yield every six 
 
 months at 4^$ annually, and then the fund would be exhausted $ 2. 50 
 
 Total amount received semi-annually ......................... $ 22 . 50 
 
 $22.50 is 2 1 X% on $1.000 semi-annually, or 4,^$ annually on the investment. 
 
 Fourth. Or 2^% on the investment of $977.8313 .................... $ 22.00 
 
 Actual semi-annual interest ..................... . .................. 20.00 
 
 Difference f $ 2 . oo 
 
 If the investor spend $22.00 semi-annually instead of $20.00 there will be a defi- 
 ciency of $2.00 every six months, which, had it been invested at ^%% annually (2%'fa 
 semi-annually), it would in 5 years have amounted to $22. 17, which is balanced by the 
 difference between $1,000 received at the maturity of the bond and the $977.83, the 
 amount paid for it. 
 
 Note. The reinvestments are made at the rate of interest to be realized. The 
 U. S. Treasury Department, Price, and others have adopted this method as per letter 
 in possession of the author of this work from the late Actuary Elliott of the U. S. 
 Treasury, and the tables in this work are intended for the valuation of bonds according 
 to it. 
 
 380357 
 
Example I. What is the value of an 8$ bond for $1,000, having 5 years to run, 
 interest payable semi-annually so as to realize 2$ (\% semi-annually on the invest- 
 ment) ? 
 
 Semi-annual interest on bond $40.00 
 
 $40.00 every half year for 5 years, at 2% per annum, amounts to $ 418 . 18 
 
 Add.. . 1,000.00 
 
 $1,418.18 
 
 $1,418.18 due in 5 years, discounted at 2$ per annum (\% semi-annually), 
 
 is $1,284.14 
 
 51,284.14 is the present value of the bond that is, $1.00 in 5 years, at 
 zfo per annum (interest semi-annual), amounts to $ 1.10462 
 
 [,418.18 divided by 1.10462 $1,284.14 
 
 Example II. What is the value of a \% bond for $1,000, having 5 years to run, 
 interest payable semi-annually, so as to realize 4X$ ( 2 X$ semi-annually) on the in- 
 vestment ? 
 
 Semi-annual interest on bond $20.00 
 
 $20.00 every half year for 5 years, at 4%% per annum, amounts to $ 221 . 51 
 
 Add.. 1,000.00 
 
 $1,221 .51 
 
 Amount of $1.00 in 5 years at 4%%, interest payable semi-annually $ i .2492 
 
 $1,221.51 divided by 1.2492 $ 977.83 
 
 $977.83 is the present value of the bond. 
 
 ANOTHER METHOD. 
 
 
 
 A much more simple method is the following . 
 
 Example I. (See above.) Semi-annual interest on bond $ 40.00 
 
 " to be realized. . 10.00 
 
 Difference $ 3 - 00 
 
 So that a price is to be paid for it now which will cause a loss to the investor of 
 $30.00 every six months out of the $40.00 received. 
 
 The present value, then, of future losses will be the premium to be paid on the bond. 
 Referring to Table I., page 10. The present value of $1.00 for every half 
 year for 5 years, at 2% per annum, is $9.4713. This, multiplied by 30, 
 
 gives the premium on the bond $ 284. 14 
 
 Add.. 1,000.00 
 
 The value of the bond $1,284. 14 
 
PRC 
 The following is the proof, and shows t 
 PresentValue, $1,284.14, 5 yrs. to maturity. 
 Add i % f or 6 mos 1 2.84 
 
 )OF. 
 
 he values every six months to maturity : 
 $1,145.61 
 Add i% 11.46 
 
 Deduct 
 
 i 296.98 
 40.00 
 
 Deduct 
 Add \% 
 Deduct 
 Add \% 
 Deduct 
 Add \% 
 Deduct 
 Add \% 
 Deduct 
 
 1,157.07 
 40.00 
 
 Add \% 
 
 1,256.98, 4^ " " 
 12.57 
 
 1,1 17.07, 2 yrs.to maturity. 
 11.17 
 
 Deduct 
 
 1,269.55 
 40.00 
 
 1,128.24 
 40.00 
 
 Add \<f 
 
 1,229.55,4 " 
 12.30 
 
 1,088.24, i X " 
 10.88 
 
 Deduct 
 
 1,241.85 
 40.00 
 
 1,099.12 
 40.00 
 
 Add \% 
 
 1,201.85, 3#" 
 
 1 2. 02 
 
 1,059.12, i year " 
 10.59 
 
 Deduct 
 
 1,213.87 
 4O.OO 
 
 1,069.71 
 40.00 
 
 Add i% 
 
 11.74 
 
 1,029.71, YL " " 
 
 10.29 
 
 Deduct 
 
 1,185.61 
 40.00 
 
 1,040.00 
 40.00 
 
 Forward 
 
 I,I45.6l, 2^" " 
 
 1,000.00 at maturity. 
 
 ANOTHE 
 $1.00 every six months for five years at 
 Dividing the premium, $284.14 by io.4< 
 $27.16 is the semi-annual Sinking Func 
 1% per annum, and will at the matur 
 $40.00 less $27.16 is $12.84. 
 $12.84 is the net interest realized on the 
 annually on the investment, or 2% annually 
 PROOF BY Si 
 $27.16 end of *4 year. 
 Add \% .27 
 27.16 
 
 R PROOF. 
 z% per annum 
 
 )22I 
 
 amounts to $10.46221 
 
 27.16 
 
 to be set asid 
 ty of the bond 
 
 investment se 
 NKING FUND. 
 Add \% 
 
 Add \% 
 
 M 
 
 Add \% 
 Add i* 
 Add i% 
 
 e and improved at 
 amount to ....284.14 
 
 ni-annually, and is \% semi- 
 
 $138.53 
 1.38 
 27.16 
 
 Add \% 
 Add \% 
 
 Add \% 
 Forward 
 
 54.59 " I 
 
 54 
 27.16 
 
 167.07 end of 3 years. 
 1.67 
 27.16 
 
 82.29 " " * ^ y rs - 
 .82 
 27.16 
 
 . 
 
 195.90 " 3X " 
 1.96 
 27.16 
 
 110.27 " " 2 " 
 I.IO 
 27.16 
 
 225.02 " " 4 " 
 2.25 
 27.16 
 
 138.53 " " 2^ " 
 
 254.43 " " 4^ " 
 2.55 
 27.16 
 
 284.14 " " 5 " 
 
 
Subtracting these respective amounts from $1,284.14 and the results will be the 
 values as arrived at by the former proof : 
 
 $1,284.141688 * * $1,284.14, 5 years to maturity. 
 
 1,284.14 " $27.16 1,256.98 \V 2 " " 
 
 1,284.14 " 54.59 1,229.55 4 
 
 1,284.14 " 82.29 1,201.85 3/ " " 
 
 1,284.14 " 110.27 i,i73-87 3 
 
 1,284.14 " 138.53 1,145.61 2% " " 
 
 1,284.14 " 167.07 1,117.07 2 " " 
 
 1,284.14 " 195.90 1,088.24 l % " " 
 
 1,284.14 " 225.02 1,059.12 I year " 
 
 1,284.14 " 254.43 1,029.71 X 
 1,284.14 " 284.14 1,000.00 maturity. 
 Being the same results as by the former proof. 
 
 PROOF BY THESE TABLES. 
 
 Referring to Table I., page 10. 
 
 The present values of $1.00 every six months for 5 years, at 2% per annum, are as 
 follows : 
 
 5 years $94713 
 
 4X " 8.56602 
 
 4 " 7.65168 
 
 3^ " 6.72819 
 
 3 " 579548 
 
 2^ " 4.85343 
 
 2 " 3-90I97 
 
 i% " 2.94099 
 
 I year 1 .97040 
 
 j " 99010 
 
 Multiplying these respectively by $40.00 less $10.00 ($30.00) will give the premiums, 
 and then adding $1,000 will give the values, as follows : 
 
 5 years, $284.14; add $1,000 $1,284.14 
 
 4X " 256.98 " " 1,256.98 
 
 4 " 229.55 " 1,229.55 
 
 3X " 201.84 " " 1,201.84 
 
 3 " I73-87 " " 1,173-87 
 
 2% " I45.6I " " I,I45.6l 
 
 2 " 117.06 " " I,II7.06 
 
 \y z " 88.24 " " 1,088.24 
 
 I year 59-J2 " " 1,059.12 
 
 X " ** 29.71 " " 1,029.71 
 
 " * * " " 1,000.00 
 
 NOTE. There is a variation of i cent occasionally on account of fractions. 
 
 Treating each of these values as those of an independent bond each half year, the 
 results would be the same, but the Sinking Funds would be different, and as 
 follows : 
 
 Present value of a bond having 5 years to run $1,284.14 
 
 " " " " 4 " " 1,229.55 
 
 ' ' " 3 " " 1,173.87 
 
 " " " " " 2 " " I,II7.O7 
 
 " " " " " I year " 1,059.12 
 
The sinking funds for these are as follows : 
 5 year bond,. $40.00 less $12.84 $27.16 
 4 " " " " 12.30 27.70 
 3 " " " " 11.74 28.26 
 2 " " " " 11.17 28.83 
 I " " " " 10.59 29.41 
 
 The amounts $12.84, $12.30, etc., are obtained by taking 1% of the values of the 
 bonds that is, 
 \% on $1,284.14 $12.84 
 1,229.55 12.30 
 1,173.87 11.74 
 " 1,117.07 11.17 
 " 1,059.12 IO -59 
 
 
 THE MODE OF PROVING TABLES I., II., III., IV., V., VI., VII., VIII., IX., AND X. 
 
 
 For instance. The present value of $i 
 annum (\<fa semi-annually), is $9.47130 (set 
 $9.47130, 5 yrs. 
 Add \% 9472 
 
 .00 each half year for 5 years, at 1% per 
 : Table I., page lo). 
 
 $4.85343 
 Add i% 4854 
 
 9.56602 
 Deduct 1 .00 
 
 4.90197 
 Deduct i.oo 
 
 8.56602, \y z " 
 
 Add \% 8566 
 
 3.901 97, 2 yrs. 
 Add i$ 3902 
 
 8.65168 
 Deduct i.oo 
 
 3-94099 
 Deduct i.oo 
 
 7.65168, 4 
 Add i% 7651 
 
 2.94099, \y z " 
 
 Add i% 2941 
 
 7.72819 
 Deduct i.oo 
 
 2.97040 
 Deduct i .00 
 
 6.72819, 3X " 
 Add i$ 6729 
 
 1.97040, i year 
 Add \% 1970 
 
 6.79548 
 Deduct i.oo 
 
 i .99010 
 Deduct i.oo 
 
 5-79548, 3 " 
 Add \% 5795 
 
 .99010, j " 
 Add \% 990 
 
 5-85343 
 Deduct i.oo 
 
 I.OOOOO 
 
 Deduct i.oo 
 
 Forward 4.85343 2j " 
 
 * * 
 
 RULE FOR VALUING BONDS. 
 
 Find the difference between the semi-annual interest on the bond and 
 the interest to be realized. Multiply it by the present value of $1.00 for 
 every half year during the term of the bond at the rate to be realized. If 
 the rate to be realized is greater than that of the bond, subtract the result 
 from $1,000, and if the rate to be realized is less than that of the bond, 
 add it to $1,000. The amounts thus obtained will be the values required. 
 NOTE. Where time and price are given, the rate of interest realized can only 
 be approximately ascertained. 
 
Example III. What is the value of a 4$ bond for $1,000, having 50 years to run, 
 so as to realize ^%% on the investment, interest payable semi-annually ? 
 
 Semi-annual interest on bond .......................................... $20.00 
 
 " " to be realized on the bond ......................... 22.50 
 
 Difference $2.50 
 
 Present value of $1.00 for every half year for fifty years at the rate to be 
 
 realized (4)4% per annum). See Table VI $39.64174 
 
 $39.64174 multiplied by 2.50 $99.10 
 
 As the rate to be realized is greater than that of the bond, this amount has to be 
 subtracted from $1,000. 
 
 $1,000 minus $99.10 $ 900.90 
 
 $900.90 is the value of the bond, or market value, 90.09. 
 
 Example IV. What is the value of the bond in the last example so as to realize 
 on the investment ? 
 
 Semi-annual interest on bond $20 . oo 
 
 " " to be realized JO 
 
 Difference $ 2.50 
 
 Present value of $1.00 for every half year for fifty years at the rate to be 
 
 realized (3%% per annum). See Table IV $47.06147 
 
 $47.06147 multiplied by 2.50 $ 117.65 
 
 As the rate to be realized is less than that of the bond, this amount has to be 
 added to $ 1,000. 
 
 $1,000 plus $117.65 $1,117.65 
 
 $1,117.65 is the value of the bond, or market value, 111.77. 
 
 NOTE. Of course bonds of any amount would be dealt with as in the foregoing examples. 
 
 Example V. What are the values of an 8$ $1,000 bond, having 50 years to run, 
 so as to realize 2, 2^, 2#, 2#, 3, 3#, $#, &, 4, 4#, 4#. 4#. 5. S%> S J A, Stf, 6, 
 6/, 6^, 6% and 7$ interest payable semi-annually ? 
 
 Referring to Tables, the present values of $1.00 every six months for 50 years, at 
 the rates required to be realized, are as follows : 
 

 
 
 
 Difference in 
 
 
 
 Difference in 
 
 At 
 
 Present Value of 
 $1.00 every half 
 year for 50 years. 
 
 semi-annual 
 interest real- 
 ized and that 
 to be real- 
 
 At 
 
 Present Value of 
 $1.00 every half 
 year for 50 years. 
 
 semi-annual 
 interest real-, 
 ized and that 
 to be real- 
 
 
 
 ized. 
 
 
 
 ized. 
 
 2_ % 
 
 $63.02888 
 
 $30.00 
 
 4#* 
 
 $38.07860 
 
 $16.25 
 
 
 59.84906 
 
 28.75 
 
 5 
 
 36.61410 
 
 15.00 
 
 2>2 
 
 56.90134 
 
 27.50 
 
 
 35.24058 
 
 13-75 
 
 2^ 
 
 54.16588 
 
 26.25 
 
 \y z 
 
 33-95I04 
 
 12.50 
 
 3 
 
 51.62470 
 
 25.00 
 
 5\ 
 
 32.73910 
 
 11.25 
 
 3* 
 
 49.26150 
 
 23-75 
 
 6 
 
 31.59891 
 
 IO.OO 
 
 
 47.06147 
 
 22.50 
 
 6X 
 
 30.52513 
 
 8.75 
 
 3K 
 
 45.01117 
 
 21.25 
 
 
 29.51288 
 
 7.50 
 
 4 
 
 43-09835 
 
 2O.OO 
 
 6^ 
 
 28.55768 
 
 6.25 
 
 
 41.31192 
 
 18.75 
 
 7 
 
 27.65543 
 
 5.00 
 
 4/5 
 
 39.64174 
 
 17.50 
 
 
 
 
 Multiplying these respective amounts, and then adding $ 1,000 to each result, will 
 
 give the respective values. 
 
 For instance At 2$ 6302888x30 ... $1890.87 
 
 Add i .000.00 
 
 
 
 $2890.87 
 
 $2890.87 is the value of the bond, or market value, 289.09. 
 
 Completing the operations in a similar manner, and the following are the results 
 
 obtained : 
 
 
 Value of $1,000 
 
 Market 
 
 A i 
 
 Value of $i,ooo 
 
 Market 
 
 At 
 
 bond. 
 
 quotation. 
 
 At 
 
 bond. 
 
 quotation. 
 
 2 % 
 
 $2,890.87 
 
 289.09 
 
 M% 
 
 $1,618.78 
 
 161.88 
 
 ** 
 
 2,720.66 
 2,564.79 
 
 272.07 
 256.48 
 
 $ 
 
 1,549.21 
 1,484.56 
 
 154.92 
 148.46 
 
 2|2 
 
 2,421.85 
 
 242.19 
 
 S% 
 
 1,424-39 
 
 142.44 
 
 3 
 
 2,290.62 
 
 229.06 
 
 5% 
 
 1,368.31 
 
 136^3 
 
 3X 
 
 2,169.96 
 2,058.88 
 
 217.00 
 205.89 
 
 6 
 6X 
 
 1,267.10 
 
 131.60 
 126.71 
 
 4 
 
 1,956.49 
 1,861.97 
 
 195.65 
 186.20 
 
 6# 
 
 1,221.35 
 1,178.49 
 
 122.14 
 117.85 
 
 
 1,774.60 
 
 177.46 
 
 7 
 
 1,138.28 
 
 113.83 
 
 4/4 
 
 1,693.73 
 
 169.37 
 
 
 
 
 
 
FIXED RATES FOR SINKING FUNDS, ETC. 
 
 There are many advocates in this country and in Europe of a fixed rate 
 of interest for all sinking funds (annuities to provide for difference 
 between par value and cost of bonds). Without an arbitrary rate no 
 comparative values can be made. Many Railroad, Banking, Insurance 
 and other corporations have a regular Sinking Fund account on their 
 ledgers, to which is charged or credited the Sinking Fund, which has to 
 be set aside at regular periods, and credited with interest, so that at the 
 bond's maturity there will not only be realized the amount which the 
 bond calls for, but there will also be a fund to be added to it which will 
 make it up to its original cost. Also from this fund can be used in 
 the same way at regular periods an amount which, with compounding 
 interest, would have amounted to, at the bond's maturity, the difference 
 between cost and face value. 
 
 When the Sinking Fund (which is usually at 3^ or 4$) is at a fixed 
 rate, the method of arriving at the bond's value is as follows : 
 
 Example VI. What is the value of a $%'/<> $1,000 bond, having 50 
 years to run, so as to realize 3$ annually on the investment, interest 
 payable semi-annually, and the Sinking Fund to be at 4$ per annum ? 
 
 Difference between semi-annual interest realized on bond 
 
 and that to be realized ................................ $2.50 
 
 Amount of $1.00 per every 6 months for 50 years at 4% per 
 
 annum ............................................... $312.2323 
 
 $312.2323 X 2.50 X ioo ................................ $78,058.08 
 
 See Table XI. 
 $100 -f i^ ($312.2323) .................................. $568.34845 
 
 $78,058.08 divided by 568.34845 $137. 34 
 
 Add TOOO.OO 
 
 $1137.34 is the value of the bond. 
 
 PROOF. 
 
 Semi-annual Sinking Fund is $ .44 
 
 312.2323 
 
 Net semi-annual interest, $17.50 less 44 cents 17.06 
 
 $17.06 is T.Yz'fo semi-annually on $1137.34, or 3$ annually. 
 
CAR TRUST, BUILDING LOAN AND INSTALMENT PLAN PROBLEMS. 
 
 By these tables can also be solved problems such as the following : 
 Example VII. A person borrowing (say) $5,000 wishes to pay it back 
 
 (principal and interest) in (say) fifty equal semi-annual instalments. 
 
 What would be the semi-annual payment, interest computed at 3^, 4 
 
 and ^/zfo per annum ? 
 
 Referring to Tables III. aud V., the present values of $1.00 every 
 
 half year for 25 years (50 payments) are 
 
 At 3}^ ................................................ $33.14121 
 
 ' 4$ .................................................. 31.42361 
 
 29.83440 
 
 Dividing $5,000 respectively by these amounts, and the following are 
 the results : 
 
 At 3^$ .................................................. $150.87 
 
 " 4$ .................................................... 159-12 
 
 " 4/^$ .................................................. 167.59 
 
 So that a person borrowing $5,000, by paying half yearly $150.87 for 25 
 years pays off the loan and also interest at 3/^$ per annum, and similarly 
 by paying the other amounts the interest paid is at 4 and 
 
 PROOF. 
 
 $5,000 in 25 years, at $%% per annum (interest semi-annual- 
 
 ly), amounts to $11,903.95 
 
 $5,000 in 25 years, at 4$ per annum (interest semi-annually), 
 
 amounts to i3>457-95 
 
 $5,000 in 25 years, at 4^$ per annum (interest semi-annual- 
 ly), amounts to 15,2 10. 25 
 
 and 
 
 $150.87 every half year for 25 years, at zY^% P er annum, 
 
 amounts to 1 1,903.95 
 
 $159.12 every half year for 25 years, at 4$ per annum, 
 
 amounts to i3>457-95 
 
 $167.59 every half year for 25 years, at 4^2$ per annum, 
 
 amounts to 15,210.25 
 
TABLE I. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 
 nf 
 
 At rates per cent, per annum. 
 
 OI 
 
 years. 
 
 i. 
 
 i%. 
 
 iK- 
 
 *k- 
 
 2. 
 
 a#. 
 
 # 
 
 .99502 
 
 99379 
 
 .99256 
 
 99133 
 
 .99OIO 
 
 .98888 
 
 I 
 
 1.98510 
 
 1.98141 
 
 1.97772 
 
 i .97405 
 
 1 .97040 
 
 1.96675 
 
 -iX 
 
 2.97025 
 
 2.96289 
 
 2.95556 
 
 2.94826 
 
 2.94099 
 
 2-93374 
 
 2 
 
 3.95050 
 
 3-93827 
 
 3.92611 
 
 3.91401 
 
 3.90197 
 
 3.88998 
 
 2^ 
 
 4.92587 
 
 4.90760 
 
 4.88944 
 
 4.87138 
 
 4.85343 
 
 4.83558 
 
 3 
 
 5.89638 
 
 5.87091 
 
 5.84560 
 
 5.82045 
 
 579548 
 
 5.77066 
 
 3/2 
 
 6.86207 
 
 6.82823 
 
 6.79464 
 
 6.76129 
 
 6.72819 
 
 6.69534 
 
 4 
 
 7.82296 
 
 7.77961 
 
 7.73661 
 
 7.69397 
 
 7.65168 
 
 * 7-60973 
 
 4^ 
 
 8.77906 
 
 8.72508 
 
 8.67158 
 
 8.61856 
 
 8.56602 
 
 8.51395 
 
 5 
 
 9.73041 
 
 9.66467 
 
 9.59958 
 
 9-53513 
 
 947130 
 
 9.40811 
 
 5X 
 
 10.67703 
 
 10.59843 
 
 10.52067 
 
 10.44374 
 
 10.36763 
 
 10.29232 
 
 6 
 
 11.61893 
 
 11.52639 
 
 11.43491 
 
 11.34448 
 
 11.25508 
 
 11.16669 
 
 6^ 
 
 12.55615 
 
 12.44859 
 
 12.34235 
 
 12.23740 
 
 12.13374 
 
 12.03134 
 
 7 
 
 13.48871 
 
 13.36506 
 
 13.24302 
 
 13.12258 
 
 13.00370 
 
 12.88637 
 
 7/2 
 
 14.41662 
 
 14.27583 
 
 14.13700 
 
 14.00008 
 
 13.86505 
 
 13-73189 
 
 8 
 
 15-33993 
 
 15.18095 
 
 15.02431 
 
 14.86997 
 
 14.71787 
 
 14.56800 
 
 8^ 
 
 16.25863 
 
 16.08045 
 
 15.90503 
 
 15-73231 
 
 15.56225 
 
 15.39480 
 
 9 
 
 17.17277 
 
 16.97436 
 
 16.77918 
 
 16.58717 
 
 16.39827 
 
 16.21241 
 
 9X 
 
 18.08236 
 
 17.86272 
 
 17.64683 
 
 17.43462 
 
 17.22601 
 
 17.02093 
 
 10 
 
 18.98742 
 
 18.74556 
 
 18.50802 
 
 18.27471 
 
 18.04555 
 
 17.82045 
 
 iotf 
 
 19.88798 
 
 19.62291 
 
 19.36280 
 
 19.10752 
 
 18.85698 
 
 18.61107 
 
 ii 
 
 20.78406 
 
 20.49482 
 
 2O.2I 121 
 
 19-93311 
 
 19.66038 
 
 19.39290 
 
 tf 
 
 21.67568 
 
 21.36131 
 
 21.05331 
 
 20.75153 
 
 20.45582 
 
 20.16604 
 
 12 
 
 22.56287 
 
 22.22242 
 
 21.88915 
 
 21.56286 
 
 21.24339 
 
 20,93057 
 
 12^ 
 
 23.44564 
 
 23.07818 
 
 22.71876 
 
 22.36715 
 
 22.O23I6 
 
 21.68659 
 
 13 
 
 24.32402 
 
 23.92863 
 
 23.54219 
 
 23.16446 
 
 22.79520 
 
 22.43421 
 
 I3# 
 
 25.19803 
 
 24-77379 
 
 24-35949 
 
 23.95485 
 
 23.55961 
 
 23-17351 
 
 H 
 
 26.06769 
 
 25.61371 
 
 25.17071 
 
 24.73839 
 
 24.31644 
 
 23.90458 
 
 HX 
 
 26.93302 
 
 26.44841 
 
 25.97589 
 
 25-51513 
 
 25.06579 
 
 24.62752 
 
 15 
 
 27.79405 
 
 27.27792 
 
 26.77508 
 
 26.28514 
 
 25.80771 
 
 25-34242 
 
 i5X 
 
 28.65080 
 
 28.10228 
 
 27.56832 
 
 27.04847 
 
 26.54229 
 
 26.04936 
 
 16 
 
 29.50328 
 
 28.92152 
 
 28.35565 
 
 27.80517 
 
 27.26959 
 
 26.74844 
 
 i6tf 
 
 30-35I53 
 
 29.73567 
 
 29.13712 
 
 28.55531 
 
 27.98969 
 
 27.43974 
 
 17 
 
 3I-I9555 
 
 30.54477 
 
 29.91278 
 
 29.29895 
 
 28.70267 
 
 28.12336 
 
 I7X 
 
 32.03537 
 
 31.34884 
 
 30.68266 
 
 30.03613 
 
 29.40858 
 
 28.79936 
 
 18 
 
 32.87102 
 
 32.14791 
 
 31.44680 
 
 30.76692 
 
 30.10750 
 
 29.46785 
 
 i8# 
 
 33.70250 
 
 32.94203 
 
 32.20527 
 
 31-49137 
 
 30.79951 
 
 30.12890 
 
 19 
 
 34.52985 
 
 33-73121 
 
 32.95808 
 
 32.20954 
 
 31.48466 
 
 30.78260 
 
 i9# 
 
 35-35309 
 
 34.51548 
 
 33.70529 
 
 32.92147 
 
 32.16303 
 
 31.42902 
 
 20 
 
 36.17223 
 
 35.29489 
 
 34.44694 
 
 33.62723 
 
 32.83469 
 
 32.06825 
 
 20^ 
 
 36.98729 
 
 36.06946 
 
 35.18306 
 
 34.32687 
 
 3349969 
 
 32.70037 
 
 21 
 
 37.79830 
 
 36.83921 
 
 35.9I37I 
 
 35-02045 
 
 34.I58II 
 
 33-32546 
 
 2I# 
 
 38.60527 
 
 37.60419 
 
 36.63892 
 
 35.70800 
 
 34.8IOOI 
 
 33.94360 
 
 22 
 
 39.40823 
 
 38.36441 
 
 37.35873 
 
 36.38959 
 
 35-45545 
 
 34-55485 
 
 22% 
 
 40.20720 
 
 39.11991 
 
 38.07318 
 
 37.06527 
 
 36.09451 
 
 35-15931 
 
 23 
 
 41.00219 
 
 39.87072 
 
 38.78231 
 
 37.73509 
 
 36.72724 
 
 35-75705 
 
 23/4 
 
 41.79322 
 
 40.61686 
 
 39.48617 
 
 38.39910 
 
 37-35370 
 
 36.34813 
 
 24 
 
 42.58032 
 
 4I-35837 
 
 40.18478 
 
 39-05734 
 
 37.97396 
 
 36.93264 
 
 24^ 
 
 43.36350 
 
 42.09528 
 
 40.87820 
 
 39.70988 
 
 38.58808 
 
 37.51064 
 
 25 
 
 44.14279 
 
 42.82760 
 
 41.56645 
 
 40.35676 
 
 39.19612 
 
 38.08222 
 
TABLE II. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 
 r\( 
 
 At rates per cent, per annum. 
 
 OI 
 
 years. 
 
 I. 
 
 I*. 
 
 Ifr 
 
 I*. 
 
 2. 
 
 9*. 
 
 25X 
 
 44.91820 
 
 43-55538 
 
 42.24957 
 
 40.99803 
 
 39.79814 
 
 38.64743 
 
 26 
 
 45.68975 
 
 44.27864 
 
 42.92762 
 
 41-63373 
 
 40.39419 
 
 39.20636 
 
 26/ 2 
 
 46.45746 
 
 44.99741 
 
 43.60061 
 
 42.26392 
 
 40.98435 
 
 39-75907 
 
 27 
 
 47-22135 
 
 457H7I 
 
 44.26860 
 
 42.88865 
 
 41.56866 
 
 40.30563 
 
 *7X 
 
 47.98145 
 
 46.42157 
 
 44.93161 
 
 43-50795 
 
 42.14719 
 
 40.84612 
 
 28 
 
 48.73776 
 
 47.12703 
 
 45.58969 
 
 44.12189 
 
 42.71999 
 
 41.38058 
 
 28/2 
 
 49.49031 
 
 47.82810 
 
 46.24287 
 
 44-73050 
 
 43.28712 
 
 41.90911 
 
 i 2 9 
 
 50.239 I 
 
 48.52482 
 
 46.89118 
 
 45.33382 
 
 43.84863 
 
 42.43175 
 
 ' 29^ 
 
 50.98419 
 
 49.21722 
 
 47.53467 
 
 45.93192 
 
 44.40459 
 
 42.94858 
 
 30 
 
 51.72556 
 
 49.90531 
 
 48.17337 
 
 46.52483 
 
 44.95504 
 
 43.45966 
 
 30/2 
 
 52.46324 
 
 50.58913 
 
 48.80732 
 
 47.11259 
 
 45.50004 
 
 43.96505 
 
 3i 
 
 53.19726 
 
 51.26870 
 
 4943654 
 
 47-69526 
 
 46.03964 
 
 44.46482 
 
 3'X 
 
 53.92762 
 
 51.94405 
 
 50.06109 
 
 48.27287 
 
 46.57390 
 
 44.95903 
 
 32 
 
 54.65435 
 
 52.61 520 
 
 50.68098 
 
 48.84547 
 
 47.10287 
 
 45-44774 
 
 32^ 
 
 55-37746 
 
 53.28219 
 
 51.29626 
 
 49.41311 
 
 47.62661 
 
 45.93102 
 
 33 
 
 56.09698 
 
 53-94503 
 
 51.90695 
 
 49.97582 
 
 48.14516 
 
 46.40892 
 
 33K 
 
 56.81291 
 
 54.60376 
 
 52.51311 
 
 50.53365 
 
 48.65857 
 
 46.88150 
 
 34 
 
 57.52529 
 
 55.25839 
 
 53-H475 
 
 5 1 .08664 
 
 49.16690 
 
 47.34883 
 
 34^ 
 
 58.23411 
 
 55.90896 
 
 53.71191 
 
 51.63484 
 
 49.67020 
 
 47.81096 
 
 35 
 
 58.93942 
 
 56.55549 
 
 54.30462 
 
 52.17828 
 
 50.16851 
 
 48.26794 
 
 35X 
 
 59.64121 
 
 57.19800 
 
 54.89292 
 
 52.71701 
 
 50.66190 
 
 48.71984 
 
 36 
 
 60.33951 
 
 57.83652 
 
 5547685 
 
 53.25106 
 
 51.15039 
 
 49.16672 
 
 36K 
 
 61.03434 
 
 58.47108 
 
 56.05643 
 
 53.78048 
 
 5I-6340S 
 
 49.60862 
 
 37 
 
 61.72571 
 
 59.10169 
 
 56.63169 
 
 54-30531 
 
 52.11292 
 
 50.04561 
 
 37X 
 
 62.41365 
 
 5972839 
 
 57.20267 
 
 54.82558 
 
 52.58705 
 
 50-47773 
 
 38 
 
 63.09815 
 
 60.35120 
 
 57.76940 
 
 55.34I35 
 
 53.05649 
 
 50.90505 
 
 38X 
 
 63.77926 
 
 60.97013 
 
 58.33191 
 
 55.85264 
 
 53.52I27 
 
 51.32762 
 
 39 
 
 64.45697 
 
 61.58523 
 
 58.89023 
 
 56.35949 
 
 53.98146 
 
 51.74548 
 
 39# 
 
 65.13132 
 
 62.19650 
 
 5944440 
 
 56.86195 
 
 54-43709 
 
 52.15869 
 
 40 
 
 68.80231 
 
 62.80397 
 
 59.99444 
 
 57.36005 
 
 54.88821 
 
 52.56731 
 
 40)4 
 
 66.46996 
 
 63.40768 
 
 60.54039 
 
 57.85383 
 
 55.33486' 
 
 52.97138 
 
 4i 
 
 67.13428 
 
 64.00763 
 
 61.08227 
 
 58.34332 
 
 55.77709 
 
 53.37096 
 
 4iX 
 
 67.79531 
 
 64.60385 
 
 61.62012 
 
 58.82857 
 
 56.21494 
 
 53.76609 
 
 42 
 
 68.45304 
 
 65.19638 
 
 62.15396 
 
 59.30961 
 
 56.64845 
 
 54.15683 
 
 42^ 
 
 69.10750 
 
 65.78522 
 
 62.68384 
 
 59.78648 
 
 57.07768 
 
 54-54322 
 
 43 
 
 69.75871 
 
 66.37040 
 
 63.20976 
 
 60.25921 
 
 57.50265 
 
 54.92531 
 
 43X 
 
 70.40668 
 
 66.95195 
 
 6373!77 
 
 60.72785 
 
 57.92342 
 
 55.303I5 
 
 44 
 
 71.05142 
 
 67.52989 
 
 64.24990 
 
 61.19241 
 
 58.34002 
 
 55.67678 
 
 44X 
 
 71.69296 
 
 68.10424 
 
 64.76417 
 
 61.65295 
 
 58.75249 
 
 56.04626 
 
 45 
 
 72.33130 
 
 68.67502 
 
 65.27461 
 
 62.10949. 
 
 59.16088 
 
 56.41163 
 
 45X 
 
 72.96647 
 
 69.24226 
 
 65.78125 
 
 62.56207 
 
 59.56523 
 
 56.77294 
 
 46 
 
 73.59847 
 
 69.80597 
 
 66.28412 
 
 63.01073 
 
 59-96557 
 
 57.13022 
 
 46K 
 
 74-22734 
 
 70.36618 
 
 66.78324 
 
 6345549 
 
 60.36195 
 
 5748353 
 
 47 
 
 74.85307 
 
 70.92291 
 
 67.27865 
 
 63.89640 
 
 60.75441 
 
 57.83291 
 
 47/2 
 
 7547569 
 
 71.47619 
 
 67-77038 
 
 64.33348 
 
 61.14298 
 
 58.17840 
 
 48 
 
 76.09522 
 
 72.02602 
 
 68.25844 
 
 64.76677 
 
 61.52770 
 
 58.52005 
 
 4 8K 
 
 76.71166 
 
 72.57245 
 
 68.74287 
 
 65.19631 
 
 61.90862 
 
 58.85790 
 
 49 
 
 77-32503 
 
 73-11547 
 
 69.22369 
 
 65.62211 
 
 62.28576 
 
 59.19199 
 
 49X 
 
 77.93536 
 
 73.655I3 
 
 69.70093 
 
 66.04423 
 
 62.65917 
 
 59.52237 
 
 50 
 
 78.54264 
 
 74.19143 
 
 70. 1 7462 
 
 66.46268 
 
 63.02888 
 
 59.84906 
 
TABLE TIL 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 
 At rates per cent, per annum. 
 
 years. 
 
 .* 
 
 .*. 
 
 3- 
 
 3*. 
 
 ,*. 
 
 3* 
 
 X 
 
 .98765 
 
 .98644 
 
 .98522 
 
 .98401 
 
 .98280 
 
 .98160 
 
 I 
 
 1.96312 
 
 1.95949 
 
 1.95588 
 
 1.95229 
 
 1 .94870 
 
 1.94512 
 
 u* 
 
 2.92653 
 
 2.91935 
 
 2.91220 
 
 2.90508 
 
 2.89798 
 
 2.89092 
 
 2 
 
 3.87806 
 
 3.86619 
 
 3-85438 
 
 3.84263 
 
 3.83094 
 
 3.81931 
 
 2^ 
 
 4.81783 
 
 4.80019 
 
 4.78265 
 
 4.76520 
 
 4.74786 
 
 4.73061 
 
 3 
 
 5.74601 
 
 5.72152 
 
 5.69719 
 
 5.67301 
 
 5.64900 
 
 5.62514 
 
 
 6.66273 
 
 6.63035 
 
 6.59821 
 
 6.56631 
 
 6.53464 
 
 6.50320 
 
 4 
 
 7.56812 
 
 7.52686 
 
 7-48593 
 
 7.44532 
 
 7.40505 
 
 7.36511 
 
 4% 
 
 8.46234 
 
 8.41120 
 
 8.36052 
 
 8.31028 
 
 8.26049 
 
 8.21115 
 
 5 
 
 9-34553 
 
 9-28355 
 
 9.22219 
 
 9.16141 
 
 9.10122 
 
 9.04162 
 
 5X 
 
 10.21780 
 
 10.14407 
 
 10.07112 
 
 9-99893 
 
 9.92749 
 
 9.85680 
 
 6 
 
 11.07931 
 
 10.99292 
 
 10.90751 
 
 10.82305 
 
 10.73955 
 
 10.65698 
 
 6j 
 
 11.93018 
 
 11.83025 
 
 H.73I53 
 
 1 1 .63400 
 
 11.53764 
 
 11.44244 
 
 7 
 
 12.77055 
 
 12.65623 
 
 12.54338 
 
 12.43198 
 
 12.32201 
 
 12.21344 
 
 7/2 
 
 13.60055 
 
 13.47100 
 
 I3-34323 
 
 13.21720 
 
 . 13.09288 
 
 12.97024 
 
 8 
 
 14.42029 
 
 14.27473 
 
 14.13126 
 
 13.98987 
 
 13.85050 
 
 13.71312 
 
 8jS^ 
 
 15.22992 
 
 15.06755 
 
 14.90765 
 
 14.75018 
 
 14.59508 
 
 14.44233 
 
 9 f 
 
 16.02955 
 
 15.84962 
 
 15.67256 
 
 15-49833 
 
 15.32686 
 
 15.15811 
 
 
 16.81931 
 
 16.62108 
 
 16.42617 
 
 16.23452 
 
 1 6.04606 
 
 15.86073 
 
 10 
 
 17.59932 
 
 17.38207 
 
 17.16864 
 
 16.95893 
 
 16.75288 
 
 16.55041 
 
 I0# 
 
 18.36969 
 
 18.13275 
 
 17.90014 
 
 17.67177 
 
 17-44755 
 
 17.22739 
 
 II 
 
 19.13056 
 
 18.87324 
 
 18.62083 
 
 18.37320 
 
 18.13027 
 
 17.89192 
 
 II> 
 
 19.88204 
 
 19.60369 
 
 19.33086 
 
 19.06342 
 
 18.80125 
 
 18.54422 
 
 12 
 
 '20.62423 
 
 20.32423 
 
 20.03041 
 
 19.74261 
 
 19.46069 
 
 19.18451 
 
 12% 
 
 21.35727 
 
 21.03500 
 
 20.71961 
 
 20.41093 
 
 20.10878 
 
 19.81301 
 
 13 
 
 22.08125 
 
 21.73613 
 
 21.39863 
 
 21.06856 
 
 20.74573 
 
 20.42995 
 
 I 3/ / 2 
 
 22.79630 
 
 22.42775 
 
 22".o6762 
 
 21.71568 
 
 21.37173 
 
 21-03553 
 
 14 
 
 23.50252 
 
 23.10998 
 
 22.72672 
 
 22.35246 
 
 21.98695 
 
 21.62997 
 
 14/4 
 
 24.20002 
 
 23.78297 
 
 23.37608 
 
 22.97905 
 
 22.59160 
 
 22.21347 
 
 15 
 
 24.88891 
 
 24.44683 
 
 24.01584 
 
 23.59562 
 
 23.18585 
 
 22.78623 - 
 
 I5 # 
 
 25.56929 
 
 25.10168 
 
 24.64615 
 
 24.20233 
 
 23.76988 
 
 23.34844 
 
 16 
 
 26.24127 
 
 2574765 
 
 25.26714 
 
 24.79934 
 
 24.34386 
 
 23.90031 
 
 i6j 
 
 26.90496 
 
 26.38486 
 
 25.87896 
 
 25.38680 
 
 24.90797 
 
 24.44203 
 
 17 
 
 27.56046 
 
 27.01342 
 
 26.48173 
 
 25.96488 
 
 25.46238 
 
 24-97377 
 
 ! 7X 
 
 28.20786 
 
 27.63346 
 
 27.07560 
 
 26.53370 
 
 26.00725 
 
 25.49572 
 
 18 
 
 28.84727 
 
 28.24509 
 
 27.66068 
 
 27.09343 
 
 26.54275 
 
 26.00807 
 
 1 8^ 
 
 29.47878 
 
 28.84842 
 
 28.23713 
 
 27.64422 
 
 27.06904 
 
 26.51099 
 
 19 
 
 30.10250 
 
 29.44358 
 
 28.80505 
 
 28.18619 
 
 27.58628 
 
 27.00465 
 
 i /4 
 
 30.71852 
 
 30.03065 
 
 29.36458 
 
 28.71950 
 
 28.09463 
 
 27.48923 
 
 20 
 
 31-32693 
 
 30.60977 
 
 29.91585 
 
 29.24428 
 
 28.59423 
 
 27.96489 
 
 20^ 
 
 31.92784 
 
 31.18103 
 
 30.45896 
 
 29.76067 
 
 29.08524 
 
 28.43179 
 
 21 
 
 32.52132 
 
 31-74454 
 
 30.99405 
 
 30.26880 
 
 29.56780 
 
 28.89010 
 
 21^ 
 
 33- I0 748 
 
 32.30041 
 
 31.52123 
 
 30.76881 
 
 30.04207 
 
 29.33998 
 
 22 
 
 33.68640 
 
 32.84874 
 
 32.04062 
 
 31.26082 
 
 30.50817 
 
 29.78157 
 
 22% 
 
 34.25817 
 
 33-38963 
 
 32.55234 
 
 31.74496 
 
 30.96626 
 
 30.21504 
 
 23 
 
 34.82288 
 
 33-923I9 
 
 33.05649 
 
 32.22137 
 
 31.41647 
 
 30.64053 
 
 23^ 
 
 35.38062 
 
 34-44951 
 
 33.55319 
 
 32.69015 
 
 31.85894 
 
 31.05819 
 
 24 
 
 35-93I48 
 
 34.96869 
 
 34.04255 
 
 33.15144 
 
 32.29380 
 
 31.46816 
 
 2 4X 
 
 36.47554 
 
 35-48083 
 
 34.52468 
 
 33.60535 
 
 32.721 18 
 
 31.87059 
 
 25 
 
 37.01288 
 
 35.98602 
 
 34.99969 
 
 34.05201 
 
 33.14121 
 
 32.26561 
 
 
 
 
 1 
 
 
TABLE IV. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 *t 
 
 At rates per cent, per annum. 
 
 Of 
 
 years. 
 
 **. 
 
 a#, 
 
 3- 
 
 a#< 
 
 3#. 
 
 3*. 
 
 25X 
 
 37.54358 
 
 36.48436 
 
 35.46767 
 
 34.49152 
 
 33-55401 
 
 32-65336 
 
 26 
 
 38.06773 
 
 36.97594 
 
 35.92874 
 
 34.92401 
 
 33.95972 
 
 33-03397 
 
 26^ 
 
 38.58542 
 
 37.46086 
 
 36.38300 
 
 35-34957 
 
 34.35845 
 
 3340758 
 
 27 
 
 39.09671 
 
 37-939I9 
 
 36.83054 
 
 35-76834 
 
 3475032 
 
 33-77431 
 
 27^ 
 
 39.60169 
 
 38.41104 
 
 37.27147 
 
 36.18041 
 
 35-13545 
 
 34-13429 
 
 28 
 
 40.10043 
 
 38.87649 
 
 37.70588 
 
 36.58589 
 
 35-5!395 
 
 34.48765 
 
 28# 
 
 40.59302 
 
 39-33562 
 
 38.13387 
 
 36.98488 
 
 35.88595 
 
 34.83450 
 
 29 
 
 41.07952 
 
 39-78853 
 
 38.55554 
 
 37-37750 
 
 36.25155 
 
 35-17497 
 
 29^ 
 
 41.56002 
 
 40.23530 
 
 38.97097 
 
 37.76384 
 
 36.61086 
 
 35.50918 
 
 30 
 
 42.03459 
 
 40.67600 
 
 39.38027 
 
 38.14400 
 
 36.96399 
 
 35-83723 
 
 30^ 
 
 42.50330 
 
 41.11073 
 
 3978352 
 
 38.51808 
 
 37-31104 
 
 36.15924 
 
 31 
 
 42.96622 
 
 41.53956 
 
 40. 1 8080 
 
 38.88618 
 
 37-65213 
 
 36.47533 
 
 3# 
 
 43.42343 
 
 41.96257 
 
 40.57222 
 
 39-24839 
 
 37-98735 
 
 36.78560 
 
 32 
 
 43.87499 
 
 42.37985 
 
 40.95785 
 
 39.60481 
 
 38.31681 
 
 37.09016 
 
 32X 
 
 44.32098 
 
 42.79147 
 
 41-33779 
 
 39-95553 
 
 38.64060 
 
 37-389" 
 
 33 
 
 44.76146 
 
 43.I975 
 
 41.71211 
 
 40.30065 
 
 38.95882 
 
 37.68256 
 
 33X 
 
 45.19651 
 
 43-59803 
 
 42.08089 
 
 40.64025 
 
 39.27157 
 
 37.97062 
 
 34 
 
 45.62618 
 
 43-99312 
 
 42.44423 
 
 40.97441 
 
 39.57893 
 
 38.25337 
 
 34/2 
 
 46.05055 
 
 44.38286 
 
 42.80220 
 
 41-30323 
 
 39.88102 
 
 38.53091 
 
 35 
 
 46.46968 
 
 44-76731 
 
 43.I5487 
 
 41.62680 
 
 40.17790 
 
 38.80335 
 
 35^ 
 
 46.88363 
 
 45.14654 
 
 43-50234 
 
 41.94519 
 
 40.46968 
 
 39.07077 
 
 36 
 
 47.29247 
 
 45.52064 
 
 43.84467 
 
 42.25849 
 
 40.75645 
 
 39-33327 
 
 36X 
 
 47.69627 
 
 45.88965 
 
 44.18194 
 
 42.56678 
 
 41.03828 
 
 39-59094 
 
 37 
 
 48.09508 
 
 46.25367 
 
 44.51422 
 
 42.87014 
 
 41.31526 
 
 39-84387 
 
 37X 
 
 48.48897 
 
 46.61274 
 
 44.84160 
 
 43.16865 
 
 41.58748 
 
 40.09214 
 
 38 
 
 48.87800 
 
 46.96694 
 
 45.16414 
 
 43.46238 
 
 41.85502 
 
 40.33584 
 
 38X 
 
 49.26222 
 
 47-3 J634 
 
 45.48191 
 
 43-75 J 42 
 
 42.11795 
 
 40.57506 
 
 39 
 
 49.64170 
 
 47.66101 
 
 45-79499 
 
 44.03584 
 
 42.37636 
 
 40.80988 
 
 39^ 
 
 50.01649 
 
 48.00099 
 
 46.10343 
 
 44.3I57I 
 
 42.63033 
 
 41.04037 
 
 40 
 
 50.38666 
 
 48.33637 
 
 46.40732 
 
 44.59111 
 
 42.87994 
 
 41.26662 
 
 40^ 
 
 50.75225 
 
 48.66719 
 
 46.70672 
 
 44.86210 
 
 43.12524 
 
 41.48871 
 
 4i 
 
 51.11334 
 
 48.99353 
 
 47.00170 
 
 45.12875 
 
 43-36633 
 
 41.70671 
 
 4# 
 
 51.46996 
 
 49.3I544 
 
 47.29231 
 
 45.39II5 
 
 43.60328 
 
 41.92069 
 
 42 
 
 51.82219 
 
 49.63299 
 
 47.57863 
 
 45.64935 
 
 43.83614 
 
 42.13074 
 
 42^ 
 
 52.17006 
 
 49-94623 
 
 47.86072 
 
 45.90342 
 
 44.06501 
 
 42-33693 
 
 43 
 
 52.51364 
 
 50.25522 
 
 48.13864 
 
 46.15342 
 
 44.28993 
 
 42.53931 
 
 43X 
 
 52.85298 
 
 50.56002 
 
 48.41246 
 
 46.39943 
 
 44.51099 
 
 42.73798 
 
 44 
 
 53.18813 
 
 50.86069 
 
 48.68222 
 
 46.64151 
 
 44.72824 
 
 42.93298 
 
 44X 
 
 53.51914 
 
 51.15727 
 
 48.94800 
 
 46.87971 
 
 44.94176 
 
 43.12440 
 
 45 
 
 53.84606 
 
 51.44984 
 
 49.20985 
 
 47.11411 
 
 45.15161 
 
 43.31229 
 
 45^ 
 
 54.16895 
 
 5I-73844 
 
 49.46784 
 
 47.34476 
 
 45-35785 
 
 43-49673 
 
 46 
 
 54.48785 
 
 52.02312 
 
 49.72201 
 
 47.57I7I 
 
 45.56054 
 
 43.67777 
 
 46X 
 
 54.80282 
 
 52.30394 
 
 49.97242 
 
 4779505 
 
 45-75974 
 
 43.85548 
 
 47 
 
 55.11389 
 
 52.58095 
 
 50.21913 
 
 48.01480 
 
 45-95552 
 
 44.02992 
 
 47 X 
 
 55.42113 
 
 52.85421 
 
 50.46220 
 
 48.23105 
 
 46.14793 
 
 44.20115 
 
 48 
 
 55-72457 
 
 53-12375 
 
 50.70168 
 
 48.44384 
 
 46-33704 
 
 44-36923 
 
 48^ 
 
 56.02427 
 
 53-38965 
 
 50.93761 
 
 48.65322 
 
 46.52288 
 
 44-53421 
 
 49 
 
 56.32026 
 
 53.65I93 
 
 51.1 7006 
 
 48.85926 
 
 46.70554 
 
 44.69616 
 
 49X 
 
 56.61261 
 
 53.91066 
 
 51.39907 
 
 49.06200 
 
 46.88505 
 
 44.85512 
 
 50 
 
 56.90134 
 
 54.16588 
 
 51.62470 
 
 49.26150 
 
 47.06147 
 
 45.01117 
 
TABLE V. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 ^.f 
 
 At rates per cent, per annum. 
 
 of 
 
 years. 
 
 4- 
 
 4#. 
 
 4#. 
 
 4# 
 
 5- 
 
 5*. 
 
 % 
 
 .98039 
 
 .97919 
 
 .97800 
 
 .97680 
 
 .97561 
 
 97442 
 
 I 
 
 1.94156 
 
 1.93801 
 
 1-93447 
 
 1.93094 
 
 1.92742 
 
 1.92392 
 
 I# 
 
 2.88388 
 
 2.87688 
 
 2.86990 
 
 2.86295 
 
 2.85602 
 
 2.84913 
 
 2 
 
 3-80773 
 
 3.79621 
 
 3-78474 
 
 3-77333 
 
 3.76197 
 
 3.75067 
 
 2^ 
 
 4.71346 
 
 4.69641 
 
 4.67945 
 
 4.66259 
 
 4.64583 
 
 4.62916 
 
 3 
 
 5.60143 
 
 5.57788 
 
 5.55448 
 
 5.53I23 
 
 5.50813 
 
 548517 
 
 & 
 
 6.47199 
 
 6.44101 
 
 6.41025 
 
 6.37971 
 
 6-34939 
 
 6.31929 
 
 4 
 
 7.32548 
 
 7.28618 
 
 7.24718 
 
 7.20851 
 
 7.17014 
 
 7.13207 
 
 4X 
 
 8.16224 
 
 8.11376 
 
 8.06571 
 
 8.01808 
 
 7.97087 
 
 7.92407 
 
 5 
 
 8.98258 
 
 8.92412 
 
 8.86622 
 
 8.80887 
 
 8.75206 
 
 8.69580 
 
 5X 
 
 9.78685 
 
 9.71762 
 
 9.64911 
 
 9-58131 
 
 9.51421 
 
 94478o 
 
 6 
 
 iQ-57534 
 
 10.49461 
 
 10.41478 
 
 10.33583 
 
 10.25776 
 
 10.18056 
 
 6^ 
 
 H.34837 
 
 11-25543 
 
 11.16360 
 
 11.07285 
 
 10.98318 
 
 10.89458 
 
 7 
 
 12.10625 
 
 12.00042 
 
 11.89594 
 
 11.79278 
 
 1 1.69091 
 
 II-59033 
 
 7/2 
 
 12.84926 
 
 12.72991 
 
 12.61217 
 
 12.49600 
 
 12.38138 
 
 12.26829 
 
 8 
 
 I3.5777I 
 
 13.44422 
 
 i3-3 I26 3 
 
 13.18290 
 
 13.05500 
 
 12.92890 
 
 8^ 
 
 14.29187 
 
 14.14367 
 
 13.99768 
 
 13-85387 
 
 13.71220 
 
 13.57262 
 
 9 
 
 14.99203 
 
 14.82856 
 
 14.66766 
 
 14.50928 
 
 14.35336 
 
 14.19988 
 
 9X 
 
 1 5.67846 
 
 15.49920 
 
 15.32290 
 
 15.14948 
 
 14.97889 
 
 14.81108 
 
 10 
 
 I6.35I43 
 
 16.15589 
 
 15.96371 
 
 1577483 
 
 15.58916 
 
 15.40666 
 
 ioX 
 
 17.01121 
 
 16.79892 
 
 16.59043 
 
 16.38567 
 
 16.18455 
 
 15.98700 
 
 ii 
 
 17.65805 
 
 17.42856 
 
 17.20335 
 
 16.98234 
 
 16.76541 
 
 16.55250 
 
 H l /2 
 
 18.29220 
 
 18.04510 
 
 17.80279 
 
 17.56516 
 
 17.33211 
 
 I7-I0353 
 
 12 
 
 J 8.9i393 
 
 18.64881 
 
 18.38904 
 
 18.13447 
 
 17.88499 
 
 17.64047 
 
 12% 
 
 19.52346 
 
 19.23996 
 
 18.96238 
 
 18.69057 
 
 18.42438 
 
 18.16367 
 
 13 
 
 20.12104 
 
 19.81881 
 
 19.52311 
 
 I9.23377 
 
 18.95061 
 
 18.67349 
 
 13* 
 
 20.70690 
 
 20.38562 
 
 20.07150 
 
 19.76436 
 
 19.46401 
 
 19.17027 
 
 14 
 
 21.28127 
 
 20.94063 
 
 20.60783 
 
 20.28265 
 
 1 9.96489 
 
 I9.65435 
 
 I4# 
 
 21.84438 
 
 2 1 .48409 
 
 21.13235 
 
 20.78891 
 
 20.45355 
 
 20. 1 2604 
 
 15 
 
 22.39646 
 
 22.01625 
 
 21.64533 
 
 21.28343 
 
 20.93029 
 
 20.58566 
 
 i5# 
 
 22.93770 
 
 22-53733 
 
 22.14702 
 
 21.76648 
 
 21.39541 
 
 21.03353 
 
 16 
 
 23-46833 
 
 23.04757 
 
 22.63767 
 
 22.23832 
 
 21.84918 
 
 21.46995 
 
 i6tf 
 
 23.98856 
 
 2354719 
 
 23.H753 
 
 22.69921 
 
 22.29188 
 
 21.89520 
 
 I? 
 
 24.49859 
 
 24.03642 
 
 23.58683 
 
 23.14941 
 
 22.72379 
 
 22.30957 
 
 I7# 
 
 24.99862 
 
 24.51546 
 
 24.04580 
 
 23.58917 
 
 23.14516 
 
 22.71335 
 
 18 
 
 25.48884 
 
 24.98454 
 
 24.49467 
 
 24.01872 
 
 23.55625 
 
 23.10679 
 
 i8# 
 
 25.96945 
 
 2544386 
 
 24.93366 
 
 24.43831 
 
 23.95732 
 
 23.49018 
 
 19 
 
 26.44064 
 
 25.89362 
 
 25.36299 
 
 24.84817 
 
 24.34860 
 
 23.86375 
 
 I9# 
 
 26.90259 
 
 26.33402 
 
 25.78288 
 
 25.24852 
 
 24.73034 
 
 24.22777 
 
 20 
 
 27.35548 
 
 26.76526 
 
 26.19352 
 
 25-63958 
 
 25.10277 
 
 24.58248 
 
 20^ 
 
 27-79949 
 
 27.18753 
 
 26.59513 
 
 26.02156 
 
 25.46612 
 
 24.92812 
 
 21 
 
 28.23479 
 
 27.6OIOO 
 
 26.98790 
 
 26.39469 
 
 25.82061 
 
 25.26492 
 
 2lX 
 
 28.66156 
 
 28.00588 
 
 27-37203 
 
 26.75916 
 
 26.16644 
 
 25.59310 
 
 22 
 
 29.07996 
 
 28.40233 
 
 27.74771 
 
 27.11518 
 
 26.50385 
 
 25.91288 
 
 22> 
 
 29.49016 
 
 28.79053 
 
 28.11512 
 
 27.46293 
 
 26.83302 
 
 26.22449 
 
 23 
 
 29.89231 
 
 29.17066 
 
 28.47444 
 
 27.80262 
 
 27.15417 
 
 26.52813 
 
 23K 
 
 30.28658 
 
 29.54287 
 
 28.82586 
 
 ' 28.13443 
 
 27.46748 
 
 26.82400 
 
 24 
 
 30.67312 
 
 29-90734 
 
 29.16955 
 
 28.45854 
 
 27.77315 
 
 27.1 1230 
 
 24X 
 
 31.05208 
 
 30.26422 
 
 29.50567 
 
 28.77513 
 
 28.07137 
 
 27.39323 
 
 25 
 
 31.42361 
 
 30.61368 
 
 29.83440 
 
 29.08437 
 
 28.36231 
 
 27.66697 
 
TABLE VI. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 /->* 
 
 At rates per cent, per annum. 
 
 OI 
 
 years. 
 
 4- 
 
 4* 
 
 4* 
 
 4* 
 
 5- 
 
 5#. 
 
 25^ 
 
 31.78785 
 
 30.95587 
 
 30.15589 
 
 29.38645 
 
 28.64616 
 
 27.93371 
 
 26 
 
 32.14495 
 
 31.29094 
 
 30.47031 
 
 29.68151 
 
 28.92308 
 
 28.19363 
 
 26^ 
 
 32.49505 
 
 31.61903 
 
 30.77781 
 
 29.96973 
 
 29.19325 
 
 28.44690 
 
 27 
 
 32.83828 
 
 31.94030 
 
 31.07854 
 
 30.25126 
 
 29.45683 
 
 28.69369 
 
 27^ 
 
 33-17479 
 
 32-25489 
 
 31.37265 
 
 30.52626 
 
 29.71398 
 
 28.93417 
 
 28 
 
 33-50469 
 
 32.56292 
 
 3 1 .66030 
 
 30.79488 
 
 29.96486 
 
 29.16849 
 
 28^ 
 
 33.82813 
 
 32.86455 
 
 31.94161 
 
 31.05727 
 
 30.20962 
 
 29.39683 
 
 29 
 
 34.14523 
 
 33.I5990 
 
 32.21673 
 
 3I-3I358 
 
 30.44841 
 
 29.61932 
 
 29^ 
 
 34.45610 
 
 33-44911 
 
 32.48580 
 
 3L56393 
 
 30.68137 
 
 29.83612 
 
 30 
 
 34.76089 
 
 33-73230 
 
 32.74895 
 
 31.80848 
 
 30.90866 
 
 30.04738 
 
 3oX 
 
 35.05969 
 
 34.00960 
 
 33.00631 
 
 32.04736 
 
 31.13040 
 
 30.25323 
 
 3i 
 
 35-35264 
 
 34.281 12 
 
 33.25800 
 
 32.28069 
 
 3I-34673 
 
 30.45382 
 
 3'# 
 
 35-63984 
 
 34.54700 
 
 33-50416 
 
 32.50861 
 
 3I-55778 
 
 30.64927 
 
 32 
 
 35.92141 
 
 34.80734 
 
 33.74490 
 
 32.73124 
 
 31.76369 
 
 30.83973 
 
 32X 
 
 36.19747 
 
 35.06227 
 
 33-98034 
 
 32.94871 
 
 31.96458 
 
 31.02532 
 
 33 
 
 36.46810 
 
 35-3II89 
 
 34.21060 
 
 33-16113 
 
 32.16056 
 
 31.20615 
 
 33X 
 
 36-73343 
 
 35-55632 
 
 3443580 
 
 33-36863 
 
 32-35177 
 
 31-38237 
 
 34 
 
 36.99356 
 
 35.79566 
 
 34.65604 
 
 33-57I3I 
 
 32.53831 
 
 3I-55407 
 
 34X 
 
 37.24859 
 
 36.03002 
 
 34.87H3 
 
 33-76929 
 
 32.72030 
 
 31.72139 
 
 35 
 
 37.49862 
 
 36.25951 
 
 35.08208 
 
 33.96268 
 
 32.89786 
 
 31.88442 
 
 35# 
 
 37-74374 
 
 36.48422 
 
 35.28810 
 
 34.15158 
 
 33.07108 
 
 32.04328 
 
 36 
 
 37.98406 
 
 36.70425 
 
 3548959 
 
 34.33609 
 
 33.24008 
 
 32.19808 
 
 36X 
 
 38.21967 
 
 36.91971 
 
 35.68664 
 
 34-51633 
 
 33-40495 
 
 32.34893 
 
 37 
 
 38.45066 
 
 37.13068 
 
 35-87935 
 
 34.69239 
 
 33-5658I 
 
 3249591 
 
 37K 
 
 38.67711 
 
 37.33727 
 
 36.06783 
 
 34.86436 
 
 33.72274 
 
 32-63913 
 
 38 
 
 38.89913 
 
 37-53955 
 
 36.25215 
 
 35.03234 
 
 33-87584 
 
 32.77869 
 
 38X 
 
 39.1 1680 
 
 3773763 
 
 36.43242 
 
 35-I9643 
 
 34.02521 
 
 32.91468 
 
 39 
 
 39.330I9 
 
 37.93158 
 
 36.60873 
 
 35-35670 
 
 34.17094 
 
 33-047I9 
 
 39^ 
 
 39-53940 
 
 38.12150 
 
 36.78115 
 
 35-5I326 
 
 34.31311 
 
 33-17631 
 
 40 
 
 39-74451 
 
 38.30746 
 
 36.94978 
 
 35.66619 
 
 34.45182 
 
 33-302I3 
 
 40^ 
 
 39.94560 
 
 38.48956 
 
 37.11470 
 
 35.81557 
 
 34.587H 
 
 33-42473 
 
 4i 
 
 40.14275 
 
 38.66787 
 
 37-27599 
 
 35-96I49 
 
 34.71916 
 
 33.54420 
 
 <M# 
 
 40.33603 
 
 38.84247 
 
 37-43373 
 
 36.10402 
 
 34.84796 
 
 33.66061 
 
 42 
 
 40.52552 
 
 39-oi343 
 
 37.58800 
 
 36.24324 
 
 34.97362 
 
 33-77404 
 
 42X 
 
 40.7 1 1 29 
 
 39. 1 8084 
 
 37.73888 
 
 36.37923 
 
 35.09621 
 
 33-88457 
 
 43 
 
 40.89342 
 
 39.34476 
 
 37-88643 
 
 36.51207 
 
 35.21582 
 
 33.99227 
 
 43X 
 
 41.07198 
 
 39.50528 
 
 38.03074 
 
 36.64183 
 
 35.33251 
 
 34.09722 
 
 44 
 
 41.24704 
 
 39.66245 
 
 38.17187 
 
 36-76857 
 
 35-44635 
 
 34.19948 
 
 44^ 
 
 41.41867 
 
 39-81635 
 
 38.30990 
 
 36.89238 
 
 35-55741 
 
 34.29913 
 
 45 
 
 41.58693 
 
 39.96705 
 
 38.44489 
 
 37.01331 
 
 35-66577 
 
 34.39623 
 
 45X 
 
 41.75189 
 
 40.11462 
 
 38.57691 
 
 37.I3I44 
 
 35-77I48 
 
 34.49084 
 
 46 
 
 41.91362 
 
 40.25911 
 
 38.70602 
 
 37.24683 
 
 35.87462 
 
 34.58304 
 
 46^ 
 
 42.07218 
 
 40.40060 
 
 38.83230 
 
 37-35954 
 
 35-97523 
 
 34.67288 
 
 47 
 
 42.22762 
 
 40.53914 
 
 38.95579 
 
 37.46964 
 
 36.07340 
 
 34.76042 
 
 47X 
 
 42.38002 
 
 40.67480 
 
 39.07657 
 
 37.577i8 
 
 36.16917 
 
 34.84572 
 
 48 
 
 42.52943 
 
 40.80764 
 
 39.19469 
 
 37.68223 
 
 36.26261 
 
 34-92883 
 
 4 8X 
 
 42-67592 
 
 40.93771 
 
 39.31021 
 
 37.78484 
 
 36.35376 
 
 35-00983 
 
 49 
 
 42.81952 
 
 41.06508 
 
 39-423 1 9 
 
 37-88507 
 
 36.44269 
 
 35.08875 
 
 49X 
 
 42.96032 
 
 41.18980 
 
 39-53368 
 
 37-98297 
 
 36.52946 
 
 35.16565 
 
 50 
 
 43-09835 
 
 4L3"92 
 
 39-64I74 
 
 38.07860 
 
 36.61410 
 
 35.24058 
 
TABLE VII. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 
 At rates per cent, per annum. 
 
 nf 
 
 
 \JL 
 
 years. 
 
 5#. 
 
 5#. 
 
 6. 
 
 6X- 
 
 6 
 
 6#. 
 
 X 
 
 97324 
 
 .97205 
 
 .97087 
 
 .96970 
 
 .96852 
 
 .96735 
 
 I 
 
 1 .92042 
 
 1.91694 
 
 i -9 i 347 
 
 1.91001 
 
 1.90656 
 
 1.90312 
 
 1% 
 
 2.84226 
 
 2.83542 
 
 2.82861 
 
 2.82183 
 
 2.81507 
 
 2.80834 
 
 2 
 
 3-73943 
 
 3.72824 
 
 3.71710 
 
 3.70601 
 
 3.69498 
 
 3.68401 
 
 2^ 
 
 4.61258 
 
 4.59610 
 
 4-57971 
 
 4.56341 
 
 4.54720 
 
 4.53108 
 
 3 
 
 5.46237 
 
 5-43971 
 
 5.41719 
 
 5.39482 
 
 5-37259 
 
 5.35050 
 
 3^ 
 
 6.28941 
 
 6.25974 
 
 6.23028 
 
 6.20104 
 
 6.17200 
 
 6.14317 
 
 4 
 
 7.09431 
 
 7.05686 
 
 7.01969 
 
 6.98282 
 
 6.94625 
 
 6.90996 
 
 4 1 A 
 
 7.87768 
 
 7.83169 
 
 7.78611 
 
 7.74092 
 
 7.69612 
 
 7.65171 
 
 S 
 
 8.64008 
 
 8.58488 
 
 8.53020 
 
 8.47604 
 
 8.42240 
 
 8.36925 
 
 S/2 
 
 9.38207 
 
 9.31701 
 
 9.25262 
 
 9.18889 
 
 9.12581 
 
 9.06336 
 
 6 
 
 10.10420 
 
 10.02869 
 
 9.95400 
 
 9.88014 
 
 9.80708 
 
 9.7348i 
 
 6^ 
 
 10.80701 
 
 10.72048 
 
 10.63496 
 
 10.55043 
 
 10.46690 
 
 10.38434 
 
 7 
 
 11.49101 
 
 11.39293 
 
 11.29607 
 
 11.20042 
 
 11.10596 
 
 11.01266 
 
 7/2 
 
 12.15670 
 
 12.04659 
 
 n-93794 
 
 11.83071 
 
 11.72490 
 
 1 1 .62047 
 
 8 
 
 12.80457 
 
 12.68198 
 
 12.56110 
 
 12.44190 
 
 12.32436 
 
 12.20844 
 
 8X 
 
 1 3-435 1 1 
 
 13.29962 
 
 13.16612 
 
 I3-03457 
 
 12.90495 
 
 12.77721 
 
 9 
 
 14.04877 
 
 13.89999 
 
 I3-7535I 
 
 . 13.60928 
 
 13.46726 
 
 13-32741 
 
 9> 
 
 14.64600 
 
 14.48359 
 
 14.32380 
 
 14.16658 
 
 14.01188 
 
 13.85964 
 
 10 
 
 15.22725 
 
 15.05088 
 
 14.87748 
 
 14.70698 
 
 H-53935 
 
 14.37450 
 
 ioX 
 
 15.79295 
 
 15.60231 
 
 15.41502 
 
 15.23101 
 
 15.05021 
 
 14.87256 
 
 ii 
 
 16.34350 
 
 16.13833 
 
 15.93692 
 
 i5-739!7 
 
 15.54500 
 
 15-35435 
 
 H l /2 
 
 16.87932 
 
 16.65938 
 
 16.44361 
 
 16.23192 
 
 16.02422 
 
 15.82041 
 
 12 
 
 17.40080 
 
 17.16586 
 
 16.93554 
 
 16.70974 
 
 16.48834 
 
 16.27125 
 
 l2/ 2 
 
 17.90832 
 
 17.65819 
 
 i7-4i3 I 5 
 
 17.17308 
 
 16.93786 
 
 16.70738 
 
 13 
 
 18.40226 
 
 18.13675 
 
 17.87684 
 
 17.62238 
 
 I7-37323 
 
 17.12927 
 
 *3# 
 
 18.88297 
 
 18.60195 
 
 18.32703 
 
 18.05807 
 
 17.79490 
 
 17.53738 
 
 14 
 
 19-35083 
 
 19.05414 
 
 18.76411 
 
 18.48055 
 
 18.20329 
 
 17.93217 
 
 i4# 
 
 19.80616 
 
 19.49370 
 
 19.18846 
 
 18.89023 
 
 18.59883 
 
 18.31407 
 
 15 
 
 20.24930 
 
 19.92097 
 
 19.60044 
 
 19.28749 
 
 18.98192 
 
 18.68350 
 
 i5# 
 
 20.68059 
 
 20.33630 
 
 20.00043 
 
 19.67272 
 
 I9-35295 
 
 19.04087 
 
 16 
 
 21.10033 
 
 20.74003 
 
 20.38877 
 
 20.04628 
 
 19.71230 
 
 19.38658 
 
 i6# 
 
 21.50883 
 
 21.13247 
 
 20.76579 
 
 20.40851 
 
 20.06034 
 
 19.72099 
 
 17 
 
 21.90641 
 
 21.51394 
 
 21.13184 
 
 20.75977 
 
 20.39742 
 
 20.04449 
 
 I7X 
 
 22.29334 
 
 21.88475 
 
 21.48722 
 
 21.10038 
 
 20.72389 
 
 20.35743 
 
 18 
 
 22.66992 
 
 22.24520 
 
 21.83225 
 
 21.43067 
 
 21.04009 
 
 20.66015 
 
 i8# 
 
 23.03642 
 
 22.59558 
 
 22.16724 
 
 21.75095 
 
 21.34634 
 
 20.95298 
 
 19 
 
 23-393II 
 
 22.93617 
 
 22.49246 
 
 22.06153 
 
 2 1 .64294 
 
 21.23626 
 
 i9# 
 
 23.74025 
 
 23.26723 
 
 22.80822 
 
 22.36270 
 
 21.93021 
 
 21.51029 
 
 20 
 
 24.07810 
 
 23.58905 
 
 23.11477 
 
 22.65474 
 
 22.20843 
 
 21.77537 
 
 20^ 
 
 24.40691 
 
 23.90187 
 
 23.41240 
 
 22.93793 
 
 22.47790 
 
 22.03180 
 
 21 
 
 24.72692 
 
 24.20595 
 
 23.70136 
 
 23.21254 
 
 22.73889 
 
 22.27985 
 
 2I# 
 
 25.03837 
 
 24.50153 
 
 23.98190 
 
 23.47882 
 
 22.99166 
 
 22.51981 
 
 22 
 
 25-34I47 
 
 24.78885 
 
 24.25427 
 
 23-73704 
 
 23.23647 
 
 22.75193 
 
 22^ 
 
 25.63647 
 
 25.06814 
 
 24.51871 
 
 23-98743 
 
 2347358 
 
 22.97647 
 
 23 
 
 25-92357 
 
 25-33963 
 
 24-77545 
 
 24.23024 
 
 23.70323 
 
 23.19369 
 
 23X 
 
 26.20299 
 
 25.60353 
 
 25.02471 
 
 24.46568 
 
 23.92564 
 
 23.40381 
 
 24 
 
 26.47493 
 
 25.86005 
 
 25.26671 
 
 24.69400 
 
 24.14106 
 
 23.60707 
 
 24X 
 
 26.73959 
 
 26.10940 
 
 25.50166 
 
 24.91539 
 
 24.34969 
 
 23.80370 
 
 25 
 
 26.99717 
 
 26.35179 
 
 25.72976 
 
 25.13008 
 
 24.55176 
 
 23-99390 
 
TABLE VIII. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 
 f.e 
 
 At rates per cent, per annum. 
 
 OI 
 
 years. 
 
 s#. 
 
 5tf 
 
 6. 
 
 6# 
 
 6tf. 
 
 6Jf. 
 
 25X 
 
 27.24785 
 
 26.58740 
 
 25.95123 
 
 25.33826 
 
 24.74747 
 
 24.17790 
 
 26 
 
 27.49183 
 
 26.81643 
 
 26.16624 
 
 25.54013 
 
 24.93702 
 
 24-35589 
 
 26X 
 
 27.72927 
 
 27.03906 
 
 26.37499 
 
 2573588 
 
 25.12060 
 
 24.52806 
 
 27 
 
 27.96036 
 
 27.25546 
 
 26.57766 
 
 25.92570 
 
 25.29840 
 
 24.69462 
 
 27X 
 
 28.18527 
 
 27.46582 
 
 26.77443 
 
 26.10977 
 
 25.47060 
 
 24.85574 
 
 28 
 
 28.4041 5 
 
 27.67030 
 
 26.96546 
 
 26.28826 
 
 25-63739 
 
 25.01 160 
 
 - 28^ 
 
 28.61718 
 
 27.86906 
 
 27.15094 
 
 26.46135 
 
 25.79892 
 
 25.16237 
 
 2 9 
 
 28.82451 
 
 28.06227 
 
 27.33101 
 
 26.62918 
 
 2 5-95537 
 
 25.30822 
 
 2 9 X 
 
 29.02628 
 
 28.25008 
 
 27.50583 
 
 26.79194 
 
 26.10690 
 
 25.44930 
 
 30 
 
 29.22266 
 
 28.43264 
 
 27.67556 
 
 26.94976 
 
 26.25366 
 
 25.58578 
 
 3oX 
 
 29.41378 
 
 28.61010 
 
 27.84035 
 
 27.10279 
 
 26.39579 
 
 25.71781 
 
 3i 
 
 29.59979 
 
 28.78260 
 
 28.00034 
 
 27.25119 
 
 26.53346 
 
 25.84552 
 
 3'X 
 
 29.78082 
 
 28.95028 
 
 28.15567 
 
 27.39510 
 
 26.66679 
 
 25.96906 
 
 32 
 
 29.95700 
 
 29.11328 
 
 28.30648 
 
 27.53464 
 
 26.79592 
 
 26.08857 
 
 32^ 
 
 30. 1 2846 
 
 29.27171 
 
 28.45289 
 
 27.66995 
 
 26.92099 
 
 26.20418 
 
 33 
 
 30-29534 
 
 2942573 
 
 28.59504 
 
 27.80117 
 
 27.04212 
 
 26.31602 
 
 33X 
 
 30-45775 
 
 29-57543 
 
 28.73305 
 
 27.92841 
 
 27.15944 
 
 26.42420 
 
 34 
 
 30.61582 
 
 29.72095 
 
 28.86704 
 
 28.05179 
 
 27.27306 
 
 26.52885 
 
 34X 
 
 30.76965 
 
 29.86241 
 
 28.99712 
 
 28.17143 
 
 27.38311 
 
 26.63009 
 
 35 
 
 30.91937 
 
 29.99991 
 
 29,12342 
 
 28.28745 
 
 27.48970 
 
 26.72802 
 
 35X 
 
 31.06508 
 
 3013357 
 
 29.24604 
 
 28.39995 
 
 27.59293 
 
 26.82275 
 
 36 
 
 31.20689 
 
 30.26350 
 
 29.36509 
 
 28.50904 
 
 27.69291 
 
 26.91439 
 
 36X 
 
 3 * -3449 i 
 
 30.38979 
 
 29.48067 
 
 28.61483 
 
 27-78974 
 
 27.00304 
 
 37 
 
 3I-47923 
 
 30.51255 
 
 29.59288 
 
 28.71741 
 
 27.88352 
 
 27.08879 
 
 37X 
 
 31.60995 
 
 30.63189 
 
 29.70183 
 
 28.81688 
 
 27.97436 
 
 27.17174 
 
 38 
 
 3I-737I8 
 
 30.74789 
 
 29.80760 
 
 28.91334 
 
 28.06233 
 
 27.25199 
 
 38X 
 
 31.86100 
 
 30.86064 
 
 29.91029 
 
 29.00687 
 
 28.14754 
 
 27.32961 
 
 39 
 
 31.98151 
 
 30.97025 
 
 30.00999 
 
 29.09758 
 
 28.23006 
 
 27.40470 
 
 39X 
 
 32.09880 
 
 31.07679 
 
 30.10679 
 
 29.18553 
 
 28.30999 
 
 27-47734 
 
 40 
 
 32.21294 
 
 31.18035 
 
 30.20076 
 
 29.27081 
 
 28.38740 
 
 27.54761 
 
 4oX 
 
 32.32403 
 
 31.28103 
 
 30.29200 
 
 29-35352 
 
 28.46237 
 
 27.61559 
 
 4i 
 
 32.43214 
 
 31.37888 
 
 30.38059 
 
 2943371 
 
 28.53498 
 
 27.68134 
 
 4iX 
 
 32.53737 
 
 31.47400 
 
 30.46659 
 
 29.51148 
 
 28.60531 
 
 27-74495 
 
 42 
 
 32.63977 
 
 31.56647 
 
 30.55009 
 
 29.58689 
 
 28.67342 
 
 27.80648 
 
 42^ 
 
 32-73944 
 
 31-65635 
 
 30.63115 
 
 29.66001 
 
 28.73939 
 
 27.86600 
 
 43 
 
 32.83644 
 
 3I-74372 
 
 30.70986 
 
 29.73092 
 
 28.80329 
 
 27.92358 
 
 43^ 
 
 32.93084 
 
 31.82864 
 
 30.78627 
 
 29.79968 
 
 28.86517 
 
 27.97928 
 
 44 
 
 33.02271 
 
 3i'.9ii20 
 
 30.86045 
 
 29.86636 
 
 28.92510 
 
 28.03316 
 
 44K 
 
 33-11213 
 
 31.99144 
 
 30.93248 
 
 29.93102 
 
 28.98315 
 
 28.08528 
 
 45 
 
 33-I99I5 
 
 32.06945 
 
 31.00241 
 
 29.99371 
 
 29.03937 
 
 28.13570 
 
 45X 
 
 33-28385 
 
 32.14527 
 
 31.07030 
 
 30.05451 
 
 29.09382 
 
 28.18448 
 
 46 
 
 33.36628 
 
 32.21897 
 
 31.13621 
 
 30.11346 
 
 29.14656 
 
 28.23166 
 
 46X 
 
 33.44650 
 
 32.29062 
 
 31.20021 
 
 30. 1 7063 
 
 29.19764 
 
 28.27730 
 
 47 
 
 33-52457 
 
 32.36026 
 
 31.26234 
 
 30.22607 
 
 29.24710 
 
 28.32145 
 
 47^ 
 
 33.60056 
 
 3242796 
 
 31.32266 
 
 30.27982 
 
 29.29502 
 
 28.36416 
 
 48 
 
 33- 6 745 I 
 
 3249376 
 
 31.38122 
 
 30.33195 
 
 29.34142 
 
 28.40548 
 
 48^ 
 
 33-74648 
 
 32.55773 
 
 31.43808 
 
 30.38249 
 
 29.38636 
 
 28.44544 
 
 49 
 
 33.81652 
 
 32.61990 
 
 31.49328 
 
 3043151 
 
 29.42989 
 
 28.48410 
 
 49^ 
 
 33.88469 
 
 32.68034 
 
 31.54687 
 
 30.47904 
 
 29.47205 
 
 28.52150 
 
 50 
 
 33-95 10 4 
 
 32.73910 
 
 31.59891 
 
 30.52513 
 
 29.51288 
 
 28.55768 
 
TABLE IX. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 t 
 
 At rates per cent, per annum. 
 
 of 
 years. 
 
 7- 
 
 rA- 
 
 8. 
 
 Btf. 
 
 9- 
 
 10. 
 
 '/* 
 
 .96618 
 
 .96386 
 
 .96154 
 
 95923 
 
 95694 
 
 .95238 
 
 I 
 
 1 .89969 
 
 1.89287 
 
 1.88609 
 
 1.87936 
 
 1.87267 
 
 1.85941 
 
 I# 
 
 2.80164 
 
 2.78831 
 
 2.77509 
 
 2.76198 
 
 2.74896 
 
 2.72325 
 
 2 
 
 3.67308 
 
 3-65138 
 
 3.62990 
 
 3.60861 
 
 3-58753 
 
 3-54595 
 
 2^ 
 
 4.51505 
 
 4.48326 
 
 4.45182 
 
 4.42073 
 
 4.38998 
 
 4.32948 
 
 3 
 
 5-32855 
 
 5.28507 
 
 5.24214 
 
 5-19974 
 
 5.15787 
 
 5.07569 
 
 3* 
 
 6.11454 
 
 6.05790 
 
 6.00205 
 
 5.94699 
 
 5.89270 
 
 5.78637 
 
 4 
 
 6.87396 
 
 6.80280 
 
 6.73275 
 
 6.66378 
 
 6.59589 
 
 6.46321 
 
 4X 
 
 7.60769 
 
 7.52077 
 
 7-43533 
 
 7-35I35 
 
 7.26879 
 
 7.10782 
 
 5 
 
 8.31661 
 
 8.21279 
 
 8.11090 
 
 8.01089 
 
 7.91272 
 
 7.72173 
 
 5X 
 
 9.00155 
 
 8.87980 
 
 8.76048 
 
 8.64354 
 
 8.52892 
 
 8.30641 
 
 6 
 
 9-66334 
 
 9.52269 
 
 9.38507 
 
 9.25039 
 
 9.11858 
 
 8.86325 
 
 6X 
 
 10.30274 
 
 10.14236 
 
 9.98565 
 
 9.83251 
 
 9.68285 
 
 9-39357 
 
 7 
 
 10.92052 
 
 10.73962 
 
 10.56312 
 
 10.39090 
 
 10.22283 
 
 9.89864 
 
 7/2 
 
 11.51741 
 
 11.31530 
 
 11.11839 
 
 10.92652 
 
 10.73955 
 
 10.37966 
 
 8 
 
 12.09412 
 
 11.87017 
 
 11.65230 
 
 11.44031 
 
 11.23401 
 
 10.83777 
 
 8X 
 
 12.65132 
 
 12.40498 
 
 12.16567 
 
 H-933I5 
 
 11.70719 
 
 11.27407 
 
 9 
 
 1 3- tf968 
 
 12.92046 
 
 12.65930 
 
 12.40590 
 
 12.15999 
 
 11.68959 
 
 9^ 
 
 13.70984 
 
 1341731 
 
 I3.I3394 
 
 12.85938 
 
 12.59329 
 
 12.08532 
 
 10 
 
 14.21240 
 
 13.89620 
 
 I3.59033 
 
 I3-29437 
 
 13.00794 
 
 12.46221 
 
 10^ 
 
 14.69798 
 
 14-35779 
 
 14.02916 
 
 13.71162 
 
 13.40472 
 
 12.82115 
 
 II 
 
 15.16713 
 
 14.80269 
 
 14.45112 
 
 14.11187 
 
 13.78442 
 
 13.16300 
 
 n% 
 
 15.62041 
 
 15-23151 
 
 14.85684 
 
 14.49580 
 
 14.14777 
 
 13.48857 
 
 12 
 
 16.05837 
 
 15.64482 
 
 15.24696 
 
 14.86407 
 
 14.49548 
 
 13.79864 
 
 I2# 
 
 16.48152 
 
 16.04320 
 
 15.62208 
 
 15.21734 
 
 14.82821 
 
 14.09394 
 
 13 
 
 16.89035 
 
 16.42719 
 
 15.98277 
 
 15.55620 
 
 15.14661 
 
 14.37518 
 
 I3tf 
 
 17.28537 
 
 16.79729 
 
 16.32959 
 
 15.88124 
 
 15.45130 
 
 14.64303 
 
 14 
 
 17.66702 
 
 17.15401 
 
 16.66306 
 
 16.19304 
 
 15.74287 
 
 14.89813 
 
 I4# 
 
 18.03577 
 
 17.49784 
 
 16.98372 
 
 16.49212 
 
 16.02189 
 
 15.14107 
 
 15 
 
 18.39205 
 
 17.82925 
 
 17.29203 
 
 16.77902 
 
 16.28889 
 
 I5.37245 
 
 I5# 
 
 18.73628 
 
 18.14867 
 
 17.58849 
 
 17.05421 
 
 16.54439 
 
 15.59281 
 
 16 
 
 19.06887 
 
 18.45655 
 
 17.87355 
 
 17.31819 
 
 16.78889 
 
 15.80268 
 
 1 6^ 
 
 19.39021 
 
 18.75330 
 
 18.14765 
 
 17.57140 
 
 17.02286 
 
 16.00255 
 
 17 
 
 19.70069 
 
 19-03933 
 
 18.41120 
 
 17.81430 
 
 17.24676 
 
 16.19290 
 
 i7# 
 
 20.00066 
 
 19.31501 
 
 18.66461 
 
 18.04729 
 
 17.46101 
 
 16.37419 
 
 18 
 
 20.29050 
 
 19.58074 
 
 18.90828 
 
 18.27078 
 
 17.66604 
 
 16.54685 
 
 i# 
 
 20.57053 
 
 19.83685 
 
 19.14258 
 
 18.48516 
 
 17.86224 
 
 16.71129 
 
 19 
 
 20.84109 
 
 20.08371 
 
 19.36787 
 
 18.69080 
 
 18.04999 
 
 16.86789 
 
 19^ 
 
 21.10250 
 
 20.32165 
 
 19.58449 
 
 18.88806 
 
 18.22966 
 
 17.01704 
 
 20 
 
 21.35507 
 
 20.55099 
 
 19.7927^7 
 
 19.07727 
 
 18.40158 
 
 17.15909 
 
 20> 
 
 21.59911 
 
 20.77204 
 
 19.99305 
 
 19.25878 
 
 18.56611 
 
 17.29437 
 
 21 
 
 21.83488 
 
 20.98510 
 
 20.18563 
 
 19.43288 
 
 18.72355 
 
 17.42321 
 
 2I# 
 
 22.06269 
 
 21.19046 
 
 20.37080 
 
 19.59988 
 
 18.87421 
 
 17.54591 
 
 22 
 
 22.28279 
 
 21.38839 
 
 20.54884 
 
 19.76008 
 
 19.01838 
 
 17.66277 
 
 22^ 
 
 22.49545 
 
 21.57917 
 
 20.72004 
 
 I9-91375 
 
 19.15635 
 
 17.77407 
 
 23 
 
 22.70092 
 
 21.76306 
 
 20.88465 
 
 20.06115 
 
 19.28837 
 
 17.88007 
 
 23X 
 
 22.89944 
 
 2 1 .94030 
 
 21.04294 
 
 20.20254 
 
 19.41471 
 
 17.98101 
 
 24 
 
 23.09125 
 
 22.IIII3 
 
 21.19513 
 
 20.33817 
 
 19.53561 
 
 18.07716 
 
 24^ 
 
 23.27657 
 
 22.27579 
 
 21.34147 
 
 20.46827 
 
 19.65130 
 
 18.16872 
 
 25 
 
 23.45562 
 
 22.43449 
 
 21.48219 
 
 20.59306 
 
 19.76201 
 
 18.25592 
 
TABLE X. 
 
 PRESENT VALUE OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 ^t 
 
 At rates per cent, per annum. 
 
 01 
 years. 
 
 7- 
 
 1%. 
 
 8. 
 
 SJ*. 
 
 9- 
 
 10. 
 
 ^A 
 
 23.62862 
 
 22.58746 
 
 21.61749 
 
 20.71277 
 
 19.86795 
 
 18.33898 
 
 26 
 
 23-79577 
 
 22.73490 
 
 21.74758 
 
 20.82760 
 
 I9.96933 
 
 18.41807 
 
 26X 
 
 23.95726 
 
 22.87702 
 
 21.87268 
 
 20.93774 
 
 20.06634 
 
 18.49340 
 
 27 
 
 24.11330 
 
 23.01399 
 
 21.99296 
 
 21.04340 
 
 20.15918 
 
 18.56514 
 
 27X 
 
 24.26405 
 
 23.14602 
 
 22.10861 
 
 21.14474 
 
 20.24802 
 
 18.63347 
 
 28 
 
 24.40971 
 
 23.27327 
 
 22.21982 
 
 21.24196 
 
 20.33303 
 
 18.69854 
 
 2 8>/ 2 
 
 24.55045 
 
 23-39592 
 
 22.32675 
 
 21.33521 
 
 20.41439 
 
 18.76052 
 
 29 
 
 24.68642 
 
 23.51414 
 
 22.42957 
 
 21.42467 
 
 20.49224 
 
 18.81954 
 
 29^ 
 
 24.81780 
 
 23.62809 
 
 22.52843 
 
 21.51047 
 
 20.56673 
 
 18.87575 
 
 3 
 
 24.94474 
 
 23.73792 
 
 22.62349 
 
 21.59278 
 
 20.63802 
 
 18.92929 
 
 30^ 
 
 25.06738 
 
 23.84377 
 
 22.71490 
 
 21.67173 
 
 20.70624 
 
 18.98027 
 
 3i 
 
 25.18587 
 
 23.94581 
 
 22.80278 
 
 21.74746 
 
 20.77152 
 
 19.02883 
 
 y% 
 
 25.30036 
 
 24.04415 
 
 22.88729 
 
 21.82011 
 
 20.83399 
 
 19.07508 
 
 32 
 
 25.41098 
 
 24.13894 
 
 22.96855 
 
 21.88979 
 
 20.89377 
 
 I9.II9I2 
 
 32^ 
 
 25.51785 
 
 24.23030 
 
 23.04668 
 
 21.95663 
 
 20.95098 
 
 I9.l6l07 
 
 33 
 
 25.6211 1 
 
 24-31837 
 
 23.12181 
 
 22.02075 
 
 21.00572 
 
 I9.2OIO2 
 
 33^ 
 
 25.72088 
 
 24.40324 
 
 23.19405 
 
 22.08226 
 
 21.05811 
 
 19.23907 
 
 34 
 
 25.81728 
 
 24.48505 
 
 23.26351 
 
 22.14125 
 
 21.10824 
 
 19.27530 
 
 34^ 
 
 25.91041 
 
 24.56391 
 
 23-33030 
 
 22.19784 
 
 21.15621 
 
 19.30981 
 
 35 
 
 26.00040 
 
 24.63991 
 
 23.39452 
 
 22.25213 
 
 21. 2021 1 
 
 19.34268 
 
 35X 
 
 26.08734 
 
 24.71317 
 
 23.45627 
 
 22.30420 
 
 21.24604 
 
 I9.37398 
 
 36 
 
 26.17134 
 
 24-78378 
 
 23.51564 
 
 22.35415 
 
 2I.288o8 
 
 I9-40379 
 
 36K 
 
 26.25251 
 
 24.85183 
 
 23.57273 
 
 22.40206 
 
 21.32830 
 
 I9432I8 
 
 37 
 
 26.33092 
 
 24.9I743 
 
 23.62763 
 
 22.44802 
 
 2 1 .36680 
 
 1945922 
 
 37X 
 
 26.40669 
 
 24.98065 
 
 23.68041 
 
 22.49211 
 
 21.40363 
 
 1948497 
 
 33 
 
 26.47989 
 
 25.04159 
 
 23.73116 
 
 22.53439 
 
 21.43888 
 
 19.50949 
 
 38X 
 
 26.55062 
 
 25.10033 
 
 2377996 
 
 22.57496 
 
 21.47262 
 
 19.53285 
 
 39 
 
 26.61896 
 
 . 25.15695 
 
 23.82689 
 
 22.61387 
 
 21.50490 
 
 19.55510 
 
 39X 
 
 26.68498 
 
 25.21152 
 
 23.87201 
 
 22.65119 
 
 21-53579 
 
 19.57628 
 
 40 
 
 26.74878 
 
 25.26411 
 
 23.91539 
 
 22.68700 
 
 21.56534 
 
 19.59646 
 
 40^ 
 
 26.81041 
 
 25.31481 
 
 23.95711 
 
 22.72134 
 
 21.59363 
 
 19.61568 
 
 4i 
 
 26.86996 
 
 25.36367 
 
 23.99722 
 
 22.75428 
 
 2I.62O7O 
 
 1 9-63398 
 
 4i# 
 
 26.92750 
 
 25.41076 
 
 24.03579 
 
 22.78588 
 
 21.64660 
 
 19.65141 
 
 42 
 
 26.98309 
 
 25.45616 
 
 24.07287 
 
 22.81619 
 
 21.67139 
 
 19.66801 
 
 42^ 
 
 27.03681 
 
 25.49991 
 
 24.10853 
 
 22.84527 
 
 21.69511 
 
 19.68382 
 
 43 
 
 27.08870 
 
 25.54208 
 
 24.14282 
 
 22.87316 
 
 21.71781 
 
 19.69887 
 
 43X 
 
 27.13884 
 
 25.58273 
 
 24.17579 
 
 22.89991 
 
 21-73953 
 
 I97I32I 
 
 44 
 
 27.18729 
 
 25.62191 
 
 24.20749 
 
 22.92558 
 
 21.76032 
 
 19.72687 
 
 44^ 
 
 27.23409 
 
 25.65967 
 
 24.23797 
 
 22.95019 
 
 2I.7802I 
 
 19.73987 
 
 45 
 
 27.27932 
 
 25.69607 
 
 24.26728 
 
 22.97381 
 
 21.79924 
 
 1975226 
 
 45 % 
 
 27.32301 
 
 25.73115 
 
 24.29546 
 
 22.99646 
 
 21.81746 
 
 19.76406 
 
 46 
 
 27.36523 
 
 25.76497 
 
 24-32256 
 
 23.01818 
 
 21.83489 
 
 1977529 
 
 4 6X 
 
 27.40602 
 
 25.79756 
 
 24.34861 
 
 23-03903 
 
 21.85156 
 
 19.78599 
 
 47 
 
 27.44543 
 
 25.82897 
 
 24.37367 
 
 23.05902 
 
 21.86753 
 
 19.79618 
 
 47^ 
 
 27.48351 
 
 25.85925 
 
 24.39776 
 
 23.07819 
 
 21.88280 
 
 19.80589 
 
 48 
 
 27.52030 
 
 25.88843 
 
 24.42092 
 
 23.09659 
 
 21.89742 
 
 19.81513 
 
 48^ 
 
 27.55584 
 
 25.91656 
 
 24.44319 
 
 23.11423 
 
 2I.9II4O 
 
 19.82394 
 
 49 
 
 27.59018 
 
 25.94367 
 
 24.46461 
 
 23.13116 
 
 21.92479 
 
 19.83232 
 
 49X 
 
 27.62337 
 
 25.96981 
 
 24.48520 
 
 23.14740 
 
 21.93760 
 
 19.84030 
 
 50 
 
 27.65543 
 
 25-99499 
 
 24.50500 
 
 23.16297 
 
 21.94985 
 
 19.84791 
 
TABLE XI. 
 
 AMOUNT OF ONE DOLLAR EVERY HALF YEAR. 
 
 No. 
 
 At rates per cent, per annum. 
 
 No. 
 
 At rates per cent, per annum. 
 
 nf 
 
 
 nf 
 
 
 UI 
 
 years. 
 
 3#. 
 
 4- 
 
 Ui 
 
 years. 
 
 3/2. 
 
 4- 
 
 % 
 
 I.OOOOO 
 
 I.OOOOO 
 
 25^ 
 
 81.28301 
 
 87.27099 
 
 I 
 
 2.01750 
 
 2.O2OOO 
 
 26 
 
 8370547 
 
 90.01641 
 
 iK 
 
 3.05281 
 
 3.06040 
 
 26^ 
 
 86.17031 
 
 92.81674 
 
 2 
 
 4.10623 
 
 4.12161 
 
 27 
 
 88.67829 
 
 95.67307 
 
 2^ 
 
 5.17809 
 
 5.20404 
 
 27X 
 
 91.23016 
 
 98.58653 
 
 3 
 
 6.26871 
 
 6.30812 
 
 28 
 
 93.82669 
 
 101.55826 
 
 3/2 
 
 7.37841 
 
 743428 
 
 28/ 2 
 
 96.46866 
 
 104.58943 
 
 4 , 
 
 8.50753 
 
 8.58297 
 
 29 
 
 99.15686 
 
 107.68122 
 
 4^ 
 
 9.65641 
 
 975463 
 
 29X 
 
 101.89210 
 
 110.83484 
 
 5 
 
 10.82540 
 
 10.94972 
 
 30 
 
 104.67522 
 
 114.05154 
 
 5X 
 
 12.01484 
 
 I2.I6872 
 
 30^ 
 
 107.50703 
 
 117.33257 
 
 6 
 
 13.22510 
 
 I34I209 
 
 31 
 
 110.38841 
 
 120.67922 
 
 6^ 
 
 14.45654 
 
 14.68033 
 
 3# 
 
 113.32020 
 
 1 24.0928 1 
 
 7 
 
 1 5.70953 
 
 15-97394 
 
 32 
 
 116.30331 
 
 127.57466 
 
 7K 
 
 16.98445 
 
 17.29342 
 
 32X 
 
 119.33861 
 
 131.12615 
 
 8 
 
 18.28168 
 
 18.63929 
 
 33 
 
 122.42704 
 
 134.74868 
 
 8/2 
 
 19.60161 
 
 2O.OI2O7 
 
 33/2 
 
 125.56951 
 
 138.44365 
 
 9 
 
 20.94463 
 
 21.41231 
 
 34 
 
 128.76698 
 
 142.21252 
 
 9/2 
 
 22.31117 
 
 22.84056 
 
 34X 
 
 132.02040 
 
 146.05677 
 
 10 
 
 23.70161 
 
 24.29737 
 
 35 
 
 I35-33076 
 
 I49-9779 1 
 
 10^ 
 
 25.11639 
 
 25.78332 
 
 3S/2 
 
 138.69905 
 
 153-97747 
 
 ii 
 
 26.55593 
 
 27.29898 
 
 36 
 
 142.12628 
 
 1 58.05702 
 
 n/2 
 
 28.02065 
 
 28.84496 
 
 36K 
 
 145.61349 
 
 162.21816 
 
 12 
 
 29.51102 
 
 30.42186 
 
 37 
 
 149.16173 
 
 166.46252 
 
 I2# 
 
 31.02746 
 
 32.03030 
 
 37/2 
 
 152.77206 
 
 170.79177 
 
 13 
 
 32.57044 
 
 33.67091 
 
 38 
 
 156.44557 
 
 175.20761 
 
 I3# 
 
 34.14042 
 
 35-34432 
 
 3*/2 
 
 160.18336 
 
 179-71176 
 
 14 
 
 35.73788 
 
 37.05121 
 
 39 
 
 163.98657 
 
 184.30599 
 
 I4# 
 
 37.36329 
 
 38.79223 
 
 39 1 A 
 
 167.85634 
 
 188.99211 
 
 15 
 
 39.01715 
 
 40.56808 
 
 40 
 
 171.79382 
 
 193.77196 
 
 JStf 
 
 40.69995 
 
 42.37944 
 
 40^ 
 
 175.80022 
 
 198.64740 
 
 16 
 
 42.41220 
 
 44.22703 
 
 4i 
 
 179.87672 
 
 203.62034 
 
 i6tf 
 
 44.15441 
 
 46.11157 
 
 4U* 
 
 184.02456 
 
 208.69275 
 
 I? 
 
 45.92712 
 
 48.03380 
 
 42 
 
 188.24499 
 
 213.86661 
 
 I7# 
 
 47.73084 
 
 49.99448 
 
 42^ 
 
 192.53928 
 
 219.14394 
 
 18 
 
 49.56613 
 
 51-99437 
 
 43 
 
 196.90872 
 
 224.52682 
 
 1 8% 
 
 51.43354 
 
 54.03425 
 
 43/2 
 
 201.35462 
 
 230.01735 
 
 19 
 
 53.33362 
 
 56.11494 
 
 44 
 
 205.87833 
 
 235.61770 
 
 I9# 
 
 55.26696 
 
 58.23724 
 
 44/2 
 
 210.48120 
 
 241.33005 
 
 20 
 
 57.23413 
 
 60.40198 
 
 45 
 
 215.16462 
 
 247.15666 
 
 20# 
 
 59-23573 
 
 62.61002 
 
 45X 
 
 219.93000 
 
 253-09979 
 
 21 
 
 61.27236 
 
 64.86222 
 
 46 
 
 224.77877 
 
 259.16178 
 
 2I# 
 
 63.34462 
 
 67.15947 
 
 46^ 
 
 229.71240 
 
 265.34502 
 
 22 
 
 65.45315 
 
 69.50266 
 
 47 
 
 23473237 
 
 271.65192 
 
 22^ 
 
 67.59858 
 
 71.89271 
 
 47/2 
 
 239.84018 
 
 278.08496 
 
 23 
 
 69.78156 
 
 74.33056 
 
 48 
 
 245-03739 
 
 284.64666 
 
 23^ 
 
 72.00274 
 
 76.81718 
 
 48/2 
 
 250.32554 
 
 29I-33959 
 
 24 
 
 74.26278 
 
 79-35352 
 
 49 
 
 255.70624 
 
 298.16638 
 
 24X 
 
 76.56238 
 
 81.94059 
 
 49X 
 
 261.18110 
 
 305.12971 
 
 25 
 
 78.90222 
 
 84.57940 
 
 50 
 
 266.75177 
 
 312.23230 
 
WORKS BY THE SAME AUTHOR. 
 
 VALUES OF BONDS, WITH SINKING FUNDS FOR PREMIUMS, ETC., 
 
 AT 4$, ........ per copy, $50.00 
 
 VALUES* OF UNITED STATES GOVERNMENT BONDS, SINKING 
 
 FUNDS FOR PREMIUMS, AT 4$, . . per set of 3, i.oo 
 
 DEPRECIATION, APPRECIATION, DISCOUNT, INTEREST AND AN- 
 NUITY TABLES, ....... per copy, 5.00 
 
 CAR TRUST, BUILDING LOAN ASSOCIATION AND INSTALMENT 
 
 PLAN MONTHLY TABLES, .... per copy, 5.00 
 
 VALUES OF BONDS AT 4$ ANNUAL INVESTMENTS, 
 
 10.00 
 
05544 
 
 UNIVERSITY OF CALIFORNIA LIBRARY