Case 1. When P, T, and R are given, to find A. * THEOREM 1. pxrt=A. By the foregoing tables, thus: Multiply the principal by the tabular number for the given time and rate; and the product will be the amount required. C T If the amount be required for any number of years or days that are not in the tables, then observe this rule. Divide the given number of years or days into such numbers as are in the table; then multiply the amounts answering to each, into each other, continually, and the product by the principal, which will be the amount required. EXAMPLES. (1) What will 2467. 10s. amount to in 7 years, at 5 per cent. per annum? (2) What will 500l. amount to in 30 years and 30 days, at 44 per cent. ? (3) What is the amount of 5231. in 5 years and 194 days, at 5 per cent. ? Case 2. When A, R, and T are given, to find P. By the foregoing tables, thus: Divide the amount by the tabular number for the given time and rate, and the quotient will be the principal required. EXAMPLES. (4) What principal, or sum of money, must be put out to * The most convenient way of giving the four Theorems in Compound Interest is by Logarithms, as follows: raise a stock of 2431. 2s. d. in 4 years, at 5 per cent, per annum? (5) What principal, being put to interest, will amount to 3467. 17s. in 7 years, at 5 per cent. per annum? (6) What principal, being put to interest for 30 years at 4 per cent. per ann. will amount to. 1872. 13s. 2d.? (7) What principal, being put to interest for 5 years and 194 days, will amount to 6851. 71⁄2d. at 5 per cent. per annum? 心 Case 3. When P, A, and R are given, to find T. By the foregoing tables, thus: Divide the amount by the principal, and the quotient will be the amount of 11. at the given rate, which will be found under the rate, even with the time required. EXAMPLES. (8) In what time will 2467. 10s. amount to 3461. 17s. at 5 per cent. per annum ? (9) In what time will 5301. amount to 1872l. 13s. 2d. at 4 per cent. per annum ? (10) In what time will 510l. amount to 6851. 71d. at 5 per cent. per annum? Case 4. When A, P, and T are given, to find R. a THEOREM 4. =Rt. Which being extracted by the rules of Extraction (the time given to the question showing the power) will give the rate. By the foregoing tables, thus: Proceed as with the last, and even with the given time is under the rate required. EXAMPLES. (11) At what rate per cent. will 2467. 10s. amount to 3467. 17s. in 7 years? (12) At what rate per cent. will 5001. amount to 18721. › 13s. 2d. in 30 years? (13) At what rate will 5231. amount to 6851, 71⁄2d. in 5 years and 195 days? LXVIII. ANNUITIES, PENSIONS, in ARREARS. HERE U represents the annuity, pension, or yearly rent, A, R, and T, as before. The 3d Table shows the amount of 17. annuity for any number of years, under 31, at 3, 34, 4, 4, and 5 per cent. and is thus constructed: Take the first year's amount, which is 1, multiply by 1,05+12,052d year's amount; which also multiply by 1,05+13,1525 3d year's amount. The 4th Table shows the present worth of 14 due at any number of years, to commence under 31, rebate at 3, 31, 4, 4, and 5 per cent, and is made thus: 11,05=952381 first year's present worth, and ,952381÷1,05=9070295= 2d year's, and ,907031,05,8638376, the third year's present worth, &c. TABLE III. The Amount of One Pound per Annum, or Annuity, for Years. Years. 3 per Cent. 31 per Cent. 4 per Cent.44 per Cent. 5 per Cent. 11,0000000 1,0000000 1,0000000 1,0000000 1,0000000 1112,8077957 13,1419919|13,4863514 13,8411788|14,2067871 |1518,5989139|19,2956809|20,023587620,7840543/21,5785636| 22 30,5367803|32,3289022|34,2479698|36,503377988,5052144 TABLE IV. -The Present Worth of one Pound for Years. Years. 3 per Cent. 34 per Cent. 4 per Cent. 4 per Cent. 5 per Cent. 1,9708738 ,9661836 ,9615385 ,9569378 ,9523809 2,9425959 ,9331507 ,9245562 ,9157299 ,9070295 3,9151417 ,9019427 ,8889964 ,8762966 ,8638376 4,8884870 ,8714422 ,8548042 ,8385613 ,8227025 5,8626088 ,8419732 ,8219271 6,8374843 ,8135006 ,7903145 7,8130915 ,7859910 ,7599178 8,7894092 ,7594116 ,7306902 9,7664167 ,7337310 ,7025867 10,7440939 ,8024511 ,7835262 ,7678957 ,7462154 ,7348285 ,7106813 ,7031851 ,6768394 ,6729044 ,6446089 ,7809183 ,6755642 ,6439277 ,6139133 11,7224213 ,6849457 ,6495809,6161988 ,5846703 12,7013799 ,6617833 ,6245971 ,5896639 ,5568374 13,6809513 ,6394041 14,6611178 6177818 15,6418619 ,5968906 16,6231669,5767059 ,6005741 ,5642716 ,5303214 ,5774751,5399729,5050679 ,5552645 ,5167204 ,4810171 ,5339082 ,4944693 17,6050164,7572038 ,5133733 ,4581115 ,4731764 ,4362967 ,4155207 ,4333018 ,3957340 ,3768895 ,3489424 ,3418479 ,3255713 ,3100639 18,5873846 ,5383611 ,4936281 ,4528004 19,5702960 ,5201577 ,4746424 20,5536758 ,5025659 ,4563870 ,4146429 21,5375493 ,4855709 ,4388336 ,3967874 22,5218925 ,4691506 ,4219554 ,3797009 23,5066917 ,4532856 ,4057263 ,3633501 24,4919337 ,4379571 ,3901215 ,3477035 25,4776056 ,4231470 ,3751168 26,4636947 ,4088378 ,3606892 27,4501891 ,3950123 ,3468166 28,4370768 ,3816543 ,3334775 ,2915707,2550936 29,4243464 ,3687482 ,3206514 ,2790150 ,2429463 30,4119868- ,3562784,3083187,2670000 $2315775 |