CASE 1. The principal, time, and rate given, to find the amount, or interest: RULE. Multiply the principal by the ratio involved to the time, (found either by involution, or in table II.) and the product will be the amount; from which subtract the principal, for the compound interest. EXAMPLES. 1 What will 225 L. amount to in 3 years, at 5 per cent. per annum ? per 1.05×1.05×1.05-1.157625 raised to the third power; then, 1.157625×225=260 L. 9 s. 3 d. 3 qrs. the Ans. 2. What will 480 L. amount to in 6 years, at 5 cent. per annum ? Ans. 643 L. 4 s. 11.0178 d. 3. What is the amount of 500 1. at 44 per cent. per annum, for 4 years? Ans. 590 L. 11 s. 5 d. 2.95+qrs. 4. What is the compound interest of a bond for 764 dollars, for 4 years and 9 months, at 6 per cent. per annum? Ans 243 dols. 61 cts + CASE 2. Or, the amount, rate, and time given, to find the principal: RULE. Divide the amount by the ratie involved to the time. EXAMPLES. 1. What principal must be put to interest, to amount to 260 L. 9 s. 3 d. 3 qrs. in 3 years, at 5 per cent. per annum ? 260 L. 9 s. 3 d. 3 qrs. 260.465625 1.. 1.05×1.05×1.05=1.157625 ratio raised to the 3d power. 1.157625)260.465625(225 L. Ans. 2. What principal will amount to 547 L. 9 s. 10 d. 2.0528 qrs. in 5 years, at 4 per cent. per annum? 3. What principal will amount to 3.809 qrs. in 4 years, at 5 per cent.? Ans. 450 L 619 L. 88. 2 d. Ans. 500 L. An annuity is a sum of money payable yearly, half yearly, or quarterly, for a number of years, during life, or for ever; and may draw interest if it remain unpaid after it becomes duc. Tables to facilitate the calculations of Annuities. TABLE III. Showing the amount of 1 L. annuity. Y. 4 per cent. 4 per cent. 5 per cent. 5 per cent. 6 per cent. 7.898294 9.214226 10.582795 8.019152 8.142008 8.266894 9.380014 9.549109 9.721573 10.802114 11.026564 11.256259 10 12.006107 12.28821 11 13.486351 13.841179 12 15.025805 15.464032 13 16.626838 17.159913 14 18.291911 18.932109 15 20.023588 20.784054 16 21.824531 22.719337 23.657492 8.393837 7 9.897468 8 11.491316 9 12.577892 12.875354 13.180795 10 14.206787 14.583498 14.971643 11 16.38559 16.869942 12 18.286798 18.882138 13 26.855084 18 25.645413 27 47.084214 50.711324 54.669126 58.989109 30 56.084938 61.007069 2 62.701469 68.666245 36.833378 38.505214 40.864309 43.392291 22 47.570645 51.113454 54.965979 59.156383 26 63.705766 27 36 77.598314 86.163966 95.836323 106.765188 91.041344 101.628139 113.637274 96.138205 107.709546 120.887324 135.904206 38 101.464424 114.095023 128.536127 145.058458 39 40 95.025516| 107.030329| 120.799774 136.605146 154.761966 40 39 90.40915 TABLE IV. Showing the present worth of 1L. annuity for any number of years, from 1 to 40. 4 per cent. | 44 per cent. 5 per cent. | 5 per cent. 6 per cent. Y 10.03759 9.71225 15 13.7986 15 11.41839 10.73954 10.37965 21 14.02916 13.40472 12.82115 9.10589 16 10.47726 17 10.8276 18 11.15811 19 13.48857 14.09354 26 15.98277 15.14661 14.37518 13.66250 13.00316 26 13.21053 27 28 16.66306 15.74287 14.89313 14.12142 14.53375 13.76483 30 13.92908/31 14.90420 14.08404 32 15.07507 14.23023 33] 14.36814 34 14.49825 35 TABLE V. payments. Quarterly The construction of this table is from an algebraic theorem, given by the learned A. De Moivre, in his treatise of Annuities on Lives, which may be in words, thus: 3 1.007445 1.011181 1.008675 1.013031 1.009902 1.014877 3 4 4 5 6 6 7 1.0111261.016720 1.0123481.018559 For half yearly payments take a unit from the ratio, and from the square root of the ratio; half the quotient of the first remainder divided 1.013567 1.020395 by the latter, will be the tabular number. For quarterly payments use the 4th root as above, and take one quarter of the quotient. G CASE 1. The annuity, time, and rate of interest given, to find the amount. RULE. From the ratio involved to the time take a unit, or one, for the dividend; which divide by the ratio less one; and multiply the quotient by the annuity, for the amount or answer. Or, by Table III. Multiply the number under the rate, and opposite to the time, by the annuity, and the product will be the amount for yearly payments. If the payments be half yearly or quarterly, the amount for the given time, found as above, multiplied by the proper number in Table V., will be the true amount. EXAMPLES. 1. What will an annuity of 50 L. per annum, payable yearly, amount to in 4 years at 5 per cent.? 1.05×1.05×1.05×1.05-1=.21550625 1.05-1.05).21550625 4.310125 50 Ans. L. 215.506250=215 L. 10 s. 1 d. 2 qrs. 2. What will an annuity of 30L. per annum, payable yearly, amount to in 4 years, at 5 per cent. per annum, and what would be the respective amounts, if the payments were to be half yearly or quarterly' Ans. L. 130.CC04 Amount for yearly payments is L. 129.30375 L. 131.7035 3 If a salary of 35L. per annum to be pad yearly, be omitted for 6 years at 5 per cent. what is the amount? Ans. 241L. 1s. 7d. 2.5+qrs. CASE 2. The annuity, time, and rate given, to find the present worth: RULE. Divide the annuity by the ratio involved to the time, and subtract the quotient from the annuity; divide the remainder by the ratio less one, and the quotient will be the present worth: Or, by Table IV. Multiply the number under the rate, and opposite the time by the annuity, and the product will be the present worth. When the payments are half yearly or quarterly, multiply the present worth so found, by the proper number in Table V. EXAMPLES. 1. What is the present worth of a pension of 30L. per annum for 5 years, at 4 per cent.? Number from Table IV. 4.45182 Ans. 133L. 11s. 1d. ×30 annuity. L. 133.55460 Or, 133L. 11s. 1.104d. 2. What is the present worth of 20L. a year for 6 years, payable either yearly, half yearly, or quarterly, computing at 5 per cent. per annum? L. Present worth for yearly payments, 101.5138 Ans. for half yearly 102.7673 103.3978 |