$500. New Orleans, May 1st, 1850. 28. Twelve months after date I promise to pay to Caleb Strong, Five hundred dollars, with interest, for value received. James Mindful. Endorsements.-May 1st, 1851, received $200. June 10th, 1852, received $100.50. July 15th, 1853, received $50.75. What balance was due, September 20th, 1854? Ans. $217.16' Partial Payments on Accounts. (179.) The following method is frequently adopted for computing the Balance due on an account, bearing interest on which partial payments have been made. 1. Compute the interest on the account from the time it became due, and the interest on each payment from the time it was made, to the time of settlement. 2. Subtract the sum of all the payments and their interest from the sum of the account and its interest; the remainder will be the balance due. But The same result may also be obtained, and frequently with greater convenience, as follows: 1. Multiply the Principal due at first, and the remainders after the payments are successively subtracted, each by the number of days it was separately at interest. 2. Divide the sum of the products by 6000. The quotient will be the interest, at 6 per cent. (from which may be found the interest at any other rate), to be added to the last re mainder, for the balance due. EXAMPLE. A merchant's account arnounting to $230 was due January 1st, 1854; on which there was paid, March 20th, 1854, $80, and June 30th, 1854, $100. What was the balance due, October 15th, 1854, allowing interest at 6 per cent. ? From Jan. 1st to March 20th, is 78da.; $230 × 78=17940 80 From March 20th to June 30th, 102da.; 150 X 102=15300 From June 30th to Oct. 15th, 107da.; The sum of these products is 38590; 6000)38590(6.43; 100 50 × 107 5350 then $50+$66.81=$56.43 was the required balance. Only one of the days of the two given dates must be included in the interval of time for which interest is computed; and it will be most convenient to find such intervals by means of the following Table, which shows (180.) The Number of Days between any two Dates, to the extent of one Year. From any To the corresponding day of the following day of Jan. Feb. [Mar. |Ap. May. June July Aug Sept Oct. Nov. Dec. 365 31 59 90 120 151 181 212 243 273 304 334 89 120 150 181 212 242 273 303 Jan. Feb. 334 365 28 59 Aug. Sept. Oct. Nov. Dec. 153 184 212 243 273 304 334 365 31 61 92 122 91 61 30 Each of the numbers in the preceding Table is the number of days from any day of the month standing opposite on the left, to the corresponding day of the month which stands above. The use of the table will be seen from the following Example. To find the number of days from June 20th to March 13th. Opposite to June and under March, we find 273, which is the number of days from June 20th to March 20th; and since March 13th is 7 days short of March 20th, the required number of days is 273-7-266. In Leap years, the numbers in the preceding Table will be 1 more, after the 28th of February, because, in such years, February has 29 days. 29. An account for $350 was due, January 1st, 1854; on which $120 was paid, June 10th, and $100, September 25th, 1854. What balance was due on the 20th of December, 1854, allowing interest at 6 per cent. ? Ans. $145.29'. 30. An account for $485 became due, July 1st, 1854, on which was paid, October 1st, 1854, $100, December 15th, 1854, $180, and May 26th, 1855, $90. What balance is due, August 1st, 1855, allowing interest at 6 per cent. ? Ans. $134.06'. 31. With the same items as in the preceding question, what balance would be due, if the computation were made according to the method adopted for partial payments on Notes or Bonds? (178). Ans. $134.37'. Why should this last Answer be greater than the preceding one? (181.) Rate per cent., or Time of Interest,-how found 1. The Rate per cent. is found by dividing the given Interest by the interest of the given Principal, at 1 per cent., for the given time. 2. The Time, in years, months, or days, is found by divid ing the given Interest by the interest of the given Principal, at the given rate, for 1 year, month, or day, respectively. 3 32. At what rate per cent. would $250 amount to $287.50 in 2y. 6m.? The given interest is $287.50-250=$37.50; and the interest of $250, at 1 per cent,, for 2y. 6m., is $6.25 (176); then the required rate per cent. is $37.50÷÷÷6.25. Ans. 6 per cent. 33. In what time will $300 amount to $373.50, at 7 per cent. interest ? The given interest is $373.50-300-$73.50; and the interest of $300, at 7 per cent. for 1 year, is $21 ; then the required number of years is 73.50-21. Ans. 3.5 years. 34. At what rate per cent. must $1000 be put at interest, to amount to $1120 in 1 year and 6 months? Ans. 8 per cent. 35. In what time will $475.37 amount to $532.42, if the rate of interest be 6 per cent. ? Ans. 2 years. 36. In what time will $100, or any other principal, double itself, if put on interest at 6 per cent. ? Ans. 16 years. 37. In what time will $1000, or any other principal, double itself, if the rate of interest be 7 per cent. ? Ans. 14 years. Present Worth of a Future. Debt. (182.) The PRESENT WORTH of a debt not due, and not bearing interest, is that principal which, put at interest, would amount to the debt by the time the debt becomes due. The present worth subtracted from the future debt leaves the discount, which is the deduction that should be made for the present payment of the debt. RULE XLIII. (183.) To find the Principal, or Present Worth of a future debt, when the Amount, Time, and Rate of interest are given. Divide the given Amount by the amount of $1, at the given rate of interest, for the given time; the quotient will be the principal required. 38. A debt of $500 will be due in 3 years, without interest. What is the present worth of the debt, allowing the rate of interest to be 6 per cent.? The amount of $1, at 6 per cent., for 3y., is $1.18; then $5001.18 gives the present worth, that is, the principal which would amount to the debt by the time the debt becomes due. Ans. $423.72. 39. What principal would amount to $650 in 2 years if the rate of interest be 5 per cent. ? Ans. $590.909. 40. What is the present worth of $750 due in 2 years 3 months, 20 days, allowing the rate of interest to be 7 per cent.? Ans. $645.827'. 41. What discount should be allowed for the present payment of a debt of $1000, due in 1 year and 6 months, when the interest is 8 per cent. ? Ans. $107.143 |