Note 1.-The 4th root of the ratio will be the quarterly amount; the square root, the half-yearly amount; and the product arising from the half-yearly and quarter-yearly, multiplied together, the three-quarter-yearly amount; as follows: Thus: 1.01.014674 quarterly amount. And 1.06 =1.029536 half-yearly amount. Then. 1.014674×1.029536 =1.044671, amount for 3 qrs. of a year, at 6 per cent. Note 2.-The 4th root is found by extracting the square root of the square root. The ratio involved to the power whose index is the time, is the amount of 1 dollar or pound for that time; as, a square for 2 years, a cube for 3 years, & c. 1.06 X 1.06 X 1.06=1.1910160, amount of 1 pound or dollar for 3 years, at 6 per cent. When the ratio is to be involved to years and quarters, the power for the years must be multiplied by the quarterly amount. Thus: 1.1910160 × 1.014674=1.2184929, amount for 31 years at 6 per cent. The power of 1 dollar or pound may also be obtained for months and days, nearly, by adding the monthly simple interest of 1 pound or dollar, or proper parts thereof, to the amount of the quarter next preceding the given time for what that time exceeds the said quarter, as follows: Amt. for year. Int. of $1, for 1 mo. .005000 for 5 days 1.029563 .000833 for 43 years 1.311873 .005000 .000833 for 7 mo. 5 days 1.034396 Amt. for 4 Y.10m.5d.1.324706 TABLE I. Amount of 11. or dollar for a year, and for quarters, at Compound Interest Simple Interest of 11. For 3 quarters. For 2 quarters. For 1 quarter. for 1 month. 1.022416 1 014889 1.007417 .002500 31 1.035 1.026173 1.017349 1.008637 .002917 TABLE II. Showing the amount of £1 or $1, from 1 year to 46. yr. 3 per cent. 4 per cent. 4 per cent. 5 per cent. 5 per cent.6 per cent. 1 234567890 1.3312256 1.0350000 1.0400000 1.0450000 1.0500000 1.0550000 1.0600000 1.0712250 1.0816000 1.0920250 1.1025000 1.1130250 1.1236000 1.1087178 1.1238640 1.1411661 1.1576250 1.1742413 1.1910160 1.1475230 1.1698585 1.1925186 1.2155062 1.2388246 1.2624769 1.1876863 1.2166529 1.2461819 1.2762815 1.3069598 1.2292553 1.2653190 1.3022601 1.3400956 1.3788426 1.2722792 1.3159317 1.3608618 1.4071004 1.4546789 1.3168093 1.3685690 1.4221006 1.4774554 1.3621973 1.4233118 1.4860951 1.5513282 10 1.4105987 1.4802442 1.5529694 1.6288946 1.7081440 1.7908476 11 1.4599697 1.5394540 1.6228530 1.7103393 1.8020919 1.8982985 1.4185191 1.5036302 1.5938480 1.5346862 Questions. What is the ratio in compound interest, and how is it obtained? What is to be noticed, respecting three-quarterly, halfyearly, and quarterly amounts? What is the amount of a dollar or pound for any given time? What must be done, when the ratio is to be involved to years and quarters? for How may the power of a dollar or pound be obtained years and days? See TABLES III. and IV. Case 1. The principal, time, and rate, given to find the amount. Rule. Multiply the principal by the ratio involved to the time, which, for convenience, may be taken from Table II., and the product will be the amount; from which subtract the principal for the compound interest. Case 2. The amount, time, and rate per cent., given, to find the principal. Rule. Divide the amount by the ratio involved to the time. Questions. By what rule do you work in compound interest by decimals? When the principal, time, and rate per cent., are given, to find the amount? How do you proceed, when the amount, time, and rate per cent., are given, to find the principal? |