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? 1.05 X 1.05 X 1.05 1.157625 raised to the third power; then, 1.157625 × 225 = 260 L. 9s. 3d. 3 qrs. the Ans. 2. What will 480 L. amount to in 6 years, at 5 per cent. per annum? Ans. 643 L. 4s. 11.0178d. 3. What is the amount of 500 L. at 41 per cent. per ann. for 4 years? Ans. 590 L. 11s. 5d. 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. DISCOUNT, Or, the amount, rate, and time given, to find the principal: RULE. Divide the amount by the ratio involved to the time. EXAMPLES. 1. What principal must be put to interest to amount to 260 L. 9s. 3d. 3qrs. in 3 years, at 5 per cent. per annum? 260 L. 9s. 3d. 3qrs. H 260.465625 L. 1.05 X 1.05 X 1.05 = 1.157625 ratio raised to the 3d power. 1.157625)260.465625(225 L. Ans. 2. What principal will amount to 547L. 9s. 10d. 2.0528 qrs. in 5 years, at 4 per cent. per annum? Ans. 450L. 3. What principal will amount to 619 L. 8s. 2d. 3.808qrs. in 4 years, at 51 per cent.? Ans. 500L. ANNUITIES AT COMPOUND INTEREST. 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 due. Tables to facilitate the calculations of annuities. TABLE III. Shewing the amount of L. 1 annuity. yr 4 per ct.4 per ct. 5 per ct. 51 per ct. 6 per ct. fyr 9.10.582795 10.802114 11.026564 11.256259 11.491316 9 10 12.006107 12.28821 12.577892 12.875354 13.180795 10 1113.486351 13.841179 14.206787 14.583498 14.971643 11 12 15.025805 15.464032 15.917126 16.38559 16.869942 12 13 16.626838 17.159913 17.712983 18.286798 18.882138 13 14 18.291911 18.932109 19.598632 20.292572 21.015066 14 15 20.023588 20.784054 21.578563 22.408663 23.275971 15 16 21.824531 22.719337 23.657492 24.64114 25.672528 16 17 23.697512 24.741707 25.840366 26.996402 28.212881 17 18 25.645413 26.855084 28.132385 29.481205 30.905653 18 19 27.671229 29.065562 30.539004 32.102671 33.759993 19 20 29.778078 31.371423 33.065954 34.868318 36.785592 20 21 31.969202 33.783137 35.719252 37.786075 39.992728 21 22 84 247970 36.833378 38.505214 40.864309 43.392291 22 23 36.617888) 38.93703 41.430475 44 111846 46.99582823 24 39.082604 41.689196 44.501999 47.537998 50.815578 24 25 41.645908 44.56521 47.727099 51.152588 54.864513 25 26 44.311745 47.570645 51.113454 54.965979 59.156383 26 27 47.084214 50.711324 54.669126 58.989109 63.705766 27 28 49 967582 53.993333 58.402583 63.23351 68.528117 28 29 52.966286 57.423033 62.322712 67.711353 73.639798 29 30 56.084938 61.007069 66.438847 72.435478 79.058186 30 3159.328335 64.752388 70.76079 77.419429 84.801677 31 3262.701469 68.666245 75.298829 82.677498 90.889778 32 33 66.209527 72.756226 80.063771 88.22476 97.343165 33 34 69.857904 77.030256 85.066959 94.077122 104.183754 34 35 73.652225 31.496618 90.320307 100.251363 111.434780 35 3677.598314 86.163966 95.836323 106.765188 119.120867 36 37 81.702246 91.041344 101.628139 113.637274127.268118 37 38 85.970336 96.138205 107.709546 120.887324 135.904206 38 39 90.40915 101464424 114.095023 128.536127 145.058458 39 4095.025516107030329 120.799774 136.605146/154.761966 40 TABLE IV. Shewing the present worth of L. 1 annuity for any number of years, from 1 to 40. " yr 4 per ct. 41 per ct. 5 per ct. 51 per ct. 6 per ctyr 10.96154 0.95694 0.95231 0.94786 0.94339 19 2 1.88609 1.87267 1.85941 1.84632 1.83339 2 32.77509 2.74876 2.72325.2.69793 2.67301 3 4 3.62989 3.58752 3.54595 3.50514 3.4651 4 5 4.45182 4.38997 4.32988 4.27028 4.21236 5 6 5.24214 5.15787 5.07569 4.99553 4.91732 6 7 6.40205 5.8927 5.78637 5.68297 5.58238 7 8 6.73274 6.59589 6.46321 6.33457 6.20979 8 9 7.43533 7.26879 7.10782 6.95220 6.80169 9 10 8.11089 7.91272 7.72173 7.53762 7.36008 10 11 8.76048 8.52892 8.3064 8.09254 7.88687 11 12 9.38500 9.11858 8.86325 8.61852 8.3838412 13 9.98565 9.68285 9.39357 9.11708 8.85268 13 14 10.5631210.22282 9.89864 9.58965 9.29498 14 15 11.41839 10.73954 10.37965 10.03759 9.71225 15 1611.65229 11.23401 10.83777 10.46216 9.1058916 17 12.1656711.70719 11.27407 10.86461 10.47726 17 1812.65929 12.15999 11.68958 11 24607 10.8276 18 19 13.1339412.59329 12.08532 11.6076511.1581119 20 13.59032 13.00793 12.4622111.95034 11.4699220 21 14.0291613.40472 12.82115 12.2752411.76407/21 22 14.4511113.78442 13.163 12.58317 12.04158 22 23 14.85684 14.14777 13.48857 12.8750412.30338 23 24 15.24696 14.49548 13.79864 13.15170 12.55035 24 25 15.62208 14.82821 14.09394 13.4139112.7833525 26 15.98277 15.1466114.37518 13.66250 13.0031626 27 16.32959 15.45 130 14.64303 13.89810 13.2105327 28 16.66306 15.74287 14.89813 14.1214213.4061628 29 16.98371|16.02189 15.14107 14.33310 13.5907229 30 17.29203 16.28889 15.37245 14.5337513.7648330 3117.58849 16.54439 15.59281 14.7239313.92908 31 32 17.87355 16.78889 15.80268 14.90420 14.08404 32 33 18.14764 17.02286 16.00255 15.07507 14.2302333 34 18.4112617.24676 16.1929 15.23703 14.36814 34 35 18.6646117.4610116.37419 15.39055 14.4982535 36 18.9082817.66604 16.54685 15.53607 14.6209836 37 19.14258 17.8622416.71129 15.67400 14.7367837 38 19.36786 18.04999 16.86789 15.80474 14.84602 38 39 19.58448 18.22965 17.01704 15.92866 14.9490739 40 19.79277 18.40158 17.15909 16.0461214.92€40 40 ་ The annuity, time, and rate of interest given, to find the amount: RULE. From the ratio involved to the time take an 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 x 1.05 x 1.05 x 1.05 -1.21550625 4.310125 50 Ans. L. 215.506250215 L. 10s. 1d. 2qrs. 2. What will an annuity of 30 L. 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. fAmount for yearly payments is L. 129.30375. for half yearly L. 130.9004. L. 131.7035. 3. If a salary of 35 L. per annum to be paid yearly, be omitted for years at 5 per cent., what is the amount? Ans. 241 L. Is. 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, mul, tiply the present worth so found, by the proper number in Table V. EXAMPLES. 1. What is the present worth of a pension of 30 L. per annum for 5 years, at 4 per cent.? Ans. 133 L. 11s. 1d. Number from Table IV. 4.45182 X30 annuity. L. 133.55460 Or, 133 L. 11s. 1.104d. 2. What is the present worth of 201.. a year for 6 years, payable either yearly, half yearly, or quarterly, computing at 5 per cent. per annum? |