E. 20. per annum? In what time will 1327. amount to 1717. 125, at 5 per cent. 132 Principal 5 Rate per cent, 6160 £. s. 12 : I CAEE 9. When the principal, amount, and time are given, to find the rate per cent. RULE. 1. Say, as the principal is to the intereft for the whole time, fo is 100l. to the intereft for the fame time. 2. Divide that intereft by the given time, and the quotient will be the rate per cent. required. E. 21. At what rate per cent. per annum, will 5287. amount to 6861. 8s. in 6 years? Quest. 1. Lent at Christmas 1771, the fum of 5oool. at 4 per cent. after which time I lent feveral fums at the fame rate, and drew upon the borrower as bufinefs required; viz. on Lady-day 1772, I drew for 185 guineas; on Midfumer-day following I lent 500 moidores, and drew for 700l. and on Michaelmas-day in the fame year, I lent 5697. 175. I demand what calh the borrower owed me at that time? .56 55. Intereft due to Lady-day, which is a quarter and by proceeding in this manner with each new principal, you will gain the refpective interefts; as in the work following: Queft. 2. Lent to John Jemefon, per bill, dated 18th of Jan. 1771. payable one day after date, 8781. 195, 10d. which I received back in the following partial payments, viz. on the 27th of Feb. 577. 155. 7d. on the 18th of March 374. 145. on the 29th of April 34/. 115. on the 12th of May 1361. 155. 7d. on the 19th of June 67%. 135. 4d. on the 15th of July 15 guineas and 6d. on the 25th ditto 1117. 115. 11d. on the 3d of October 78%. 75. 4d. on the 19th of November 100%. on the 23d ditto 100%. and on the 30th of Dec. received the balance of the principal; how much intereft ought I to claim, at 5 per cent.? Note. The refpective products are found by multiplying each prin. cipal by the number of days it was employed; fee the following operation, Balance 338 15 7 47 15922 12 5 Nov. 19, Received 100 O O 4 2 78 7 4 5160 4 73|00)206|40(2 qrs. 146 604 Answer, 23, Received 100 O O Balance 138 15 737 5134 16 7 Dec. 30, Rd. in 1 full of the prin. 138 15 7 The total fum of the products 187327 6 8 Note. The reafon of dividing by 73 in the above operation, is this; as 100 3655, or any other rate to the fourth term. Or, as 100 731, that is 365 73, and 1. Hence the fecond and third terms will allways admit of the fame abbreviations. Quef 3. June 23d, 1745, bought 900l. of New South Sea annuities at 11 per cent, viz. the day before the clofing the books, the brokerage whereof is always 2s. 6d. per cent, on the capital, whether you buy or fell; the Midfummer dividend 2 per cent. became due and payable on the 10th of Auguft following, by which time the rebellion growing confiderable in the North, the faid annuities where down at 92 per cent. In the general alarm, fold 400/, capital at that price; but continued the remainder, till a fecond, third, fourth, and fifth dividend, 125 dividend, as before, came due; and on opening the books on the 10th of Auguft, 1747, fold out at 1023 per cent. Now reckoning I might have made 5 per cent. of my money, had I kept it out of the stocks, how ftood this article in point of profit and lofs? First 900l. at 111 per cent. Brokerage of ditto, at 2s. 6d. per cent. = Midfummer dividend, at 2 per cent, £. s. d. 1002 7 6 I 2 6 £. 1003 10 Intereft of 10037. 10s. for 49 days. at 5 per cent. Sold 400/. at 921 per cent. 18 O 985 10 6 14 Intereft for half a year, due Feb. 10, 1746 Dividend received at that time Intereft due to Angust 10th 644 O 634 649 17 ΙΟ O O 639 17 2 Anfwer, Loft in the whole . 133 2 I XIX. COMPOUND INTEREST. IS that which arifes from any principal, and its intereft put together, as that intereft becomes due but not paid, the fame intereft is allowed upon that intereft unpaid, fo it becomes part of the principal, for which reason it is called intereft upon intereft, or compound intereft. 1. Find the amount of the given fum by fimple intereft for the first year, which is the principal for the fecond year; then find the amount of that principal for the fecond year, and that is the principal for the third year; and fo on for any number of years. RULE. 2. Subtract 2. Subtract the given principal from the last amount, and the remainder is the compound interest required. EXAMPLES. What is the compound intereft of 900/ forborne 3 years, annum ? 900 ft year's principal 45 Interest 945 2d year's principal 5 12/25 12 3/00 XX. REBATE OR DISCOUNT. S the fatisfying any fum of money due at fome time to come, by paying given fum, in the fame space of time. RULE. I. Find the intereft for 100l. for the time given, and rate per cent. which intereft add to rol. 2. Then fay, as that fum is to the interest of 1007. fo is the debt, or fum propofed, to the rebate, or prefent worth required. Or when the prefent worth is fubtracted from the given fum, the remainder is the rebate required. EXAMPLE. |