RULE II. Multiply the principal by the days; divide by 6083 for 6 per cent. and 7300 for 5 per cent. (the days in which any sum wil! double at those rates) and the quotient is the interest. For months, multiply the principal by them, and divide by 200 for 6 per cent. or 240 for 5 per cent. (the months in which any sum will double at those rates) and the quotient is the answer. Hence, when interest is to be calculated on cash accounts, or accounts current, where partial payments are made, or partia! debts contracted; multiply the several balances into the days they are at interest, which should be done at every transaction, and the sum of these products divided by 6083 and 7300 will give the interest at 6 and 5 per cent. For any other rate, make the proper addition or deduction, or find a divisor as before directed. When partial payments are made at short periods, subtract the several payments from the original sum in their order, placing their dates in the margin. 16. Suppose a bill of $359 was due January 1, 1807; that $75 was paid February 3d, $50 March 5th, $80 April 9th, and June 7th, $145: What interest is due at 5, 6 and 7 per cent.? After the dates are placed in the margin, the number of days in each of those periods is to be computed and marked against its respective sum: lastly, divide the sum of the products by 6083, &c. Interest on accounts current is calculated nearly in the same manner. 17. Compute the interest at 6 per cent. on the following account to August 10th. Dr. 1807. Mr. A. Jones, his account current, with B. Carr, Jan. 1, To Cash, Feb. 10, To do. July 25, To do. D. 1807. 560 March 10, By Cash, 300 April 25, By do. Ds. Days. Products | Dr. Cr. 1807. Jan. Feb. 10, Dr. 300 300 130 140 450 Here the sums on either side are introduced according to the order of their dates; those on the Dr. side are added to the former balance, and those on the Cr. side subtracted. Before we calculate the days, we try if the last sum $250 be equal to the balance of the account, which proves the additions and subtractions. And before multiplying we try if the sum of the column of days be equal to the number of days from January 1 to August 10. When payments are made at considerably distant periods, it is usual to calculate the interest to the date of each payment, and add it to the principal, and then subtract the payment from the amount. 18. A note was given for $540 the 18th August, 1804, and there was paid the 19th of March, 1805, $50, and the 19th of December, 1805, $25; and the 23d of September, 1806, $25; and the 18th of August, 1807, $110: Required the interest, and balance due on the 11th of November, 1807, at 6 per cent.? A note given 18th August, 1804, for Interest to 19th March, 1805, 218 days, $19.352 Paid 19th March, 1805, $540 19.352 559.352 50 19. A owes B the following sums, with interest at 6 per cent. per annum: $60 for 7 months, $150 for 9 months, $75.50 for 3 months, $365-25 for 8 months, and 510-20 for 5 months: Required the amount? 20. A note for $1000 is given January 1, 1803, with interest at 6 per cent per annum; February 19, 1803, $100 are paid; June 7, 1803, $150; April 14, 1804, $37-50; July 11, 1804, $75; Sept. 29, 1804, $250; Dec. 17, 1805, $39; March 4, 1806, $175; Aug. 7, 1806. $105; Oct. 30, 1806, $50; May 12, 1807, $40, and Nov. 17, 1807, $72: How much is due, January 1, 1808? SIMPLE INTEREST BY DECIMALS. A TABLE OF RATIOS, FROM One pound, &c. TO TEN POUNds. Rate per cent. ratios. rate per cent. | ratios. | rate per cent. | ratios. Ratio is the Simple Interest of £1 or $1 for 1 year, at the rate per cent. agreed on, and is found by dividing the rate by 100, and reducing it to a decimal. Thus, T=06, and, 1505, 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. Days. 1 decimal parts. | days. | decimal parts. | days. dec. parts. 123456789 027397 | 100 | 273973 054794 200 •547945 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. * 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 6 100 -x2=30x· X2=30×·06×2, which is the product of 100 principal, ratio, and time. 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? Ans. £321 4 7. 2. What is the simple interest of £917 16s. at £5 per cent. per annnum, for 7 years? 3. What is the amount of £391 17s. at £44 per cent. per annum, for 31 years? Ans. £449 3 12. 4. What is the amount of £235 3s. 9d. at £51 per cent. per annum, 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 commission on £795 15s. amount to? Ans. £19 12 101. 6. What will be the interest and amount of £445 108. in 3 years and 129 days, at £83 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 Os. on commission at £1 per cent, and procures me another cargo of the value £917 15s. on commission at £13 per cent.; what will his commission, on both cargoes, amount to? Ans. £22 5 7. 8. What is the simple interest of $66-666 for 12 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 per cent.? Ans. $1 66c. 8m. 10. What is the interest of $236 at 5 per cent. for one year and 300 days? 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. RULE. 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 principal added to the product of the principal, ratio, and time, or, taking |