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. If the Amount is 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 246/ 10s. amount to in 7 Years, at 5 per Cent. per Annum? (2) What will 500. amount to in 30 Years and 30 Days, at 4 per Cent? (3) What is the Amount of 5234. in 5 Years and 194 Days, at 5 per Cent? Case 2. When A, R, and T, are given, to find P. A THEOREM 2. Rt. =P. By the foregoing Tables, thus: Divide the Amount by the tabular Number for the given Time and Rate, and the Quo tient 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: 1. ixlog. r+log. p=log. A. 2. log. a-txiog. r=log. P. 3. log. a-log p. log. r. =T. 4. =log. R. t raise a Stock of 2431 2sd in 4 Years, at 5 per Cent. per Annum? (5) What Principal, being put to Interest, will amount to 346/ 17s in 7 Years, at 5 per Cent. per Annum? (6) What Principal, being put to Interest for 30 Years, at 44 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 685/ 71⁄2d at 5 per Cent: Annum ? Case 3. When P, A, and R, are given, to find T. a THEOREM 3. -=Rt. per Which being continually divided by r, till nothing remains, the Number of those Divisions will be equal to T, the Time. 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 246/ 10s amount to 346/ 17s at 5 per Cent. per Annum ? (9) In what Time will 530/ amount to 1872/ 13s 2d. at 4 per Cent. per Annum ? (10) In what Time will 510/ amount to Cent. per Annum? 6d at 5 per Gase 4. When A, P, and T, are given, to find R. THEOREM 4. a = Rt. Which being extracted by the 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 246/ 10s amount to 3461 17s in 7 Years? T. (12) At what Rate per Cent. will 500/ amount to 1872 13s 2d in 30 Years? (13) At what Rate will 523/ amount to 685/ 74d 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 11 Annuity for any Number of Years under 31, at 3, 34, 4, 44, and 5 per Cent. and is thus constructed: Take the first Year's Amount, which is 1/multiply by 1,05+1=2,05=2d Year's Amount, which also multiply by 1,054-1=3,1525=3d Year's Amount. The 4th Table shows the present Worth of 1/ due at any Number of Years, to commence under 31, Rebate at 3, 31⁄2, 4, 44, and 5 per Cent. and is made thus: 1÷1,05=,952381 first Year's present Worth, and,952381÷1,05=,9070295= 2d Year's, and,90703÷1,05=,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. 3per Cent. 4 per Cent. 4per Cent. 5 per Cent. 25 36.4592643 38.9498567 41.6459083 38.5530422 41.3131017 44.3117446 44.5652101 47.7270988 47.5706446 51.1134538 26 27 40.7096335, 43-7590602 47.0842144 50.7113236 54.6691265 28 42.9309225 46.290627349.9675830 | 53.9933332 58.4025828 29 45.2188502 48.9107993 52.9662863| 57.4230332 62.3227119 30 47-5754157 51.6226773 56.0849277 61.0070607 66.4388475 |