950,75x5=4753,75)285,2250,06-6 per cent. 285,2256 2. At what rate por cent. will 5671. 10$, amount to 3731. 195. in 9 years ? Ans. 6 per cent. 3. At what rate per cent. will 3-10 dols. 25 tis. amount to 626 dols. 6 cts. in 12 years ? Ans. 7 per cent. 4. At what rate per cent. will 6151. 15s. bount to 9501. 10s. 4,125d. in 87 years ? Ins. 5 por cont. CASE IV. The amount, principal, and rate per cent. given, to find the time. RULE. Subtract the principal from the amonnt ; diviele the remainder by the product of the ratio and principal ; and the quotient will be the time. EXAMPLES. 1. In what time will 950 dois. 75 cts. amount to 1235 dollars, 97,5 cents, at 6 per cent. per annum ? From the amount $1235,075 Take the principal 950,75 Ans. 950,75X06=57,0450 285,2250(5 years, 285,2250 Ans. 9 years. Ans. 12 ycdis. 2. In what time will 5671. 10s. amount to 8737. 198 at 6 per cent. per annum ? 3. In what time will 340 dols. 25 cts. amount to 620 dols. 6 cts. at 7 per cent. per annum ? 4. In what time will 6451. 15s. amount to 9561. 10s. 4,125d. at 5.3 per ct. per annum ? Ans. 8,75=$7 years. **990, RULE. Multiply the principal by the given number of days, and that product by the ratio ; divide the last product by 365 (the number of days in a year) and it will give the interest required. Ans. $10,53cts. + £. s. d. grs. EXAMPLES. 1. What is the interest of 3601. 10s. for 146 days, ar 6 -=8652=8 13 0 1,9 Ans. 2. What is the interest of 640 dols. 60 cts. for 100 days, Ans. £4,1235=41. 28. 5d.+ 3. Required the interest of 2501. 17s. for 120 days at 5 4. Required the interest of 481 dollars 75 cents, for 25 £. days, at 7 per cent. per annum ? Ans. $2, 30cts. In. + 360,5 X 146x,06 365 at 6 per cent. per annum ? per cent. per annum ? per cent. ? + A TABLE, showing the number of Days from any day of one month, to the same day of any other month. FROM ANY DAY OF 6131 59 281 365 334 304 273 243 212 181 151 120 901 89 30 365 334 304 273 242 212 181 151 31 365 335 Dec. ! 334 3031 275! 244 214| 183 1531 122 91 61 90' 36.) 19 19 When interest is to be calculated on cash accounts, &c. where partial payments are made ; multiply the several balances into the days they are at interest, then multiply the sum of these products by the rate on the dollar, and di vide the last product by 365, and you will have the whole interest due on the account, &c. EXAMPLES. Lent Peter Trusty, per bill on demand, dated 1st of June, 1800, 2000 dollars, of which I received back the 19th of August, 400 dollars ; on the 15th of October, 600 dollars ; on the 11th of December, 400 dollars ; on the 17th of February, 1801, 200 dollars; and on the 1st of June, 400 dollars ; how much interest is due on the bill, reckoning at 6 per cent. ? 1800 dolls. days. products. June 1, Principal per bill, 2000 79 | 158000 August 19, Received in part, 400 Balance, 1600 91200 October 15, Received in part, 600 57 57 57000 Balance December 11, Received in part, 1000 1801, Balance, 600 February 17, Received in part, 200 Balance, 400 June 1, Rec'd in full of principal, 400 388600 Then 388600 ,06 Ratio. $ cts. m. 365 23316,00(63,879 Ans. = 63 87 9+ The following Rule for computing interest on any note, or obligation, when there are payments in part, or endorsements, was established by the Superior Court of the State of Connecticut, in 1784. RULE. " • Compute the interest to the time of the first mave ment; if that be one year or more from the time the intrres, commenced, add it to the principal, and deduct the pay ment from the sum total. If there be after payments made, compute the interest on the balance due to the next pay iment, and then deduct the payment as above; and in libe manner from one payment to another, till all the payments are absorbed ; provided the time between one payment and another be one year or more. But if any payment be made before one year's interest bath accrued, then compute the interest on the principal sun due on the obligation for one year, add it to the principal, and compute the interest on the sum paid, from the time it was paid, up to the end of the year : add it to the sun paid, and deduct that sum from the principal and interest added as above.* " If any payments be made of a less sum than the in. terest arisen at the time of such payment, no interest is to be computed but only on the principal sım for any period Kirby's Reporis, page 49. EXAMPLES. A bond, or note, dated January 4th, 1797, was given for 1000 dollars, interesi at 6 per cent. and there were pay. ments endorsed upon it as follows, viz. $ 1st payment February 19, 1798. 200 2d payment June 29, 1799. 500 3d payment November 14, 1799. 260 I demand how much remains due on said note the 24th of December, 1800 ? 1000,00 dated January 4, 1797. 67,50 Interest to February 19, 1798 513} months. 1067,50 amount. [Carried up * If a year does not extend beyond the time of final settlement ; but if it does, then find the arnount of the principal sum due on the obligation, up to the time of settlement, and likewise find the amount of the sum paid, from the time it was paid, up to the time of final settlement, and deduct this amount from the amount of the principal. But if there be several pay. ments made within the said time, find the amount of the several payments, from the time they were paid, to the time of settlement, and deduct their amount from the amount of the principale [Brought up. 1067,50 amount. 867,50 balance due, Feb. 19, 1798. 938,345 amount. 438,345 balance due, June 29, 1799. 26,30 interest for one year. 464,645 amount for one year. mo, da, 194,895 balance due June 29, 1800. 5,687 interest to December 24, 1800. 5 25 200,579 balance due on the Note, Dec. 24, 1800. RULE II. Established by the Courts of Law in Massachusetts for computing interest on notes, fc. on which partial payments have been endorsed. « Compute the interest on the principal sum, from the time when the interest commenced to the first time when a payment was made, which exceeds either alone or in conjunction with the preceding payment (if any) the interest at that time due : add that interest to the principal, and from the sum subtract the payment made at that time, together with the preceding payments if any) and the remainder forms a new principal ; on which compute and subtract the payments as upon the first principal, and proceed in this manner to the time of final settlement." $ cts. *260,00 third payment with its interest from the time it ! 9,75 was paid, up to the end of the year, or from Nov. 14, 1799 to June 29, 1800, which is 71 269,75 amount. [months. 1 |