1 year, at the rate Ratio is the Simple Interest of £1 or $1 for per cent. agreed on, and is found by dividing the reducing it to a decimal. Thus, 06, and, = rate by 100, and .05, and so on. A TABLE for the ready finding of the decimal parts of a year, equal to any number of days, or quarters of a year. The principal, time, and ratio given, to find the interest and amount. RULE. Multiply the principal, time and ratio continually together, and the last product will be the interest, commission, brokerage, &c. to which add the principal, and the sum will be the amount. 6 *This is a contraction of the General Rule for Simple Interest. If the interest on £30 or $30 was required for 2 years at 6 per cent. by the general rule, 30X6 the interest is X2=30X06×2, which is the product of 100 principal, ratio. and time. 100 And the amount=30+30×06 × 2==£33-6 or $. EXAMPLES. 1. Required the amount of £537 10s. at £6 per cent. per annum, for 5 years? Or, 537-5X 06×5+537·5=£698 15s. 2. What is the simple interest of £917 16s. at £5 annnum, for 7 years? 3. What is the amount of £391 17s. at £5 for 31 years? per cent. per Ans. £321 4 7. per cent. per annum, Ans. £449 3 12. £41 per cent. per an 4. What is the amount of £235 3s. 9d. at aum, from March 5th, 1784, to Nov. 23d, 1784 ? Ans. £244 0 81. 5. If my correspondent is to have £2 per cent; what will his Ans. £19 12 101. commission on £785 15s. amount to? 6. What will be the interest and amount of £445 10s. in 3 years and 129 days, at £81 per cent. per annum ? Ans. Interest, £126 19 81, and the amount=£572 9 81. 7. If a broker disposes of a cargo for me, to the amount of £637 10s. on commission at £1 per cent. and procures me another cargo of the value £817 15s. on commission at £13 per cent.; what will Ans. £22 5 7. his commission, on both cargoes, amount to? 3. What is the simple interest of $66-666 for 13 years at 7 per Ans. $8 16c. 6m. cent.? 9. Find the amount of $1 for 9 years and 200 days, computing interest at 7 Ans. $1 66c. 8m. cent.? 10. What is the interest of $236 at 5 per cent. for one year and 300 days? per 11. Required the interest on $6485 at 6 per cent. for two years, six months and 20 days. CASE II. The amount, time, and ratio given, to find the principal. KULE. Multiply the ratio by the time; add unity to the product for a divisor, by which sum divide the amount, and the quotient will be the principal.* In the demonstration of the Rule for Case I. it was proved that the amount the principul added to the product of the principal, ratio, and time, or, taking EXAMPLES. 1. What principal will amount to £1045 14s. in 7 years, at £6 per cent. per annum? Ratio='06 Divisor 1.42)1045 7(736.4084+= £736 8 2. 1045.7 Or, •06x7+1 £736 8 2 Ans. 2. What principal will amount to £3810, in 6 years, at £41 per cent. per annum ? Ans. £3000. 3. What principal will amount to £666 9s. 01 in 34 years, at £51 per cent. per annum? Ans. £563. .4. What principal will amount to £335 7s. 3d. in 3 years and 97 days, at £91 per cent. per annum? Ans. £255 19 03. CASE III. The amount, principal, and time given, to find the ratio. RULE. Subtract the principal from the amount; divide the remainder by the product of the time and principal, and the quotient will be the ratio.* EXAMPLES. 1. At what rate per cent. will £543 amount to £705 18s. in 5 years? From the amount=705.9 Take the principal 543 Divide by 543x5=2715) 162.90(06 162.90 the same example, the amount, 33.6=30+30×·06×2, or which is the same thing, 106×2×30. Divide both by the same quantity, 1+06×2, and the expression will still be equal, and we have 33.6 1+06X2X30 1+06×21+06×2 cancel the equal terms in the last fraction, and then -30, that is, the a mount divided by the product of the ratio and time increased by 1, gives a quotient, which is the principal. The same may be shown in any other example, and, hence the rule is general. * Under case I. it was shown that the amount, 33·6=30-30×06 X2. Take the principal, 30, from both sides, and 33-6-30-30 X 06 × 2, or 3.6=30×2×·06. 3.6 30X2X.06 Divide both parts by the product of time and principal, and 30X2 30XL 3.6 or 30x2 06, the ratio, and illustrates the rule. 543X5 2. At what rate per cent. will £391 17s. amount to £449 3s. 138. 74qr. in 31 years? Ans. £4. 3. At what rate per cent. will £413 12s. 6d. amount to £546 4s. 101d. in 4 years? Ans. £63. 4. At what rate per cent. will £3000 amount to £3810 in 6 years? Ans. £44. CASE IV. The amount, principal, and rate per cent. given, to find the time. RULE. Subtract the principal from the amount; divide the remainder by the product of the ratio and principal; and the quotient will be the time.* EXAMPLES. 1. In what time will £543 amount to £705 18s. at £6 per cent. per annum ? From the amount=705.9 Take the principal=543 Divide by 543x 06=32.58) 162-9(5 years, Ans. 162 9 2. In what time will £3000 amount to £3810, at 41 per cent. per annum ? Ans. 6 years. 3. In what time will £391 17s. amount to £449 38. 13d. at £4 per cent. per annum? Ans. 31 years. To find the Interest of any Sum, at 6 per cent. per annum, for any number of months. If the months be an even number, multiply the principal by half that number; and if the months be uneven, halve the even months, to which annex; thus the half of 19 is 9.5; and multiply the principal as before, dividing by 100 or cutting off two figures more at the right hand, than there are decimals in both factors, which reduce to farthings, each time cutting off as at first. 4. What is the interest of £345 16s. 6d. for 9 years and 11months, at 6 per cent. per annum? 1 Tubie of decima! parts for every day in the twelfth part of a year, which consists of 3651 days. days. dec. pts.| days. \dec. pts.| days. \dec. pts.| days. \dec. pts.| days. \dec. pts. To find the Interest of any Sum, either for Months, or Months and Days at 6 per cent. per annum. RULE. Multiply the principal by the number of months, (or months and parts, answering to the given number of days in the table) and cut off one figure at the right hand of the product more than is required by the rule in decimals, and the product will be the interest for the given time, in shillings and decimal parts of a shilling.* In the Note, un ler the Goneral Rule for Simple Interest, it is shown that when the Rate is 6 per cent. the product of the principal and half the number of months divided by 100, gives the Interest. Whence, the product of the principal and the number of months divided by 100, must give twice the Interest. 30.5 X 17 Let then the principal £30-5 be put to interest for 17 months. Then 100 £5.185=2× £2·5925=twice the interest, and the interest is 2:5925. Multi: ply by 20 and the interest will be reduced to shillings and the decimal parts of 30-5X17X20 a shilling, and we have -=2× £2·5925×20. Divide by 2, and 30-5X17X10 100 -=£25925×20, and dividing both parts of the fraction by 10, 100 30.5 X 17 10 ·=£25925 × 20, that is, multiply the principal by the number of months and divide the product by 10, or, cut of only one figure more than the rule for K k |