various terms of credit, as by the statement annexed. When is the medium time of payment? 1, a bill amounting to $ 360, on 3 months' credit. Jan. do. March 1, do. do. May 15, 186, on 4 months' credit. do. do. do. do OPERATION. 44= 91= 300 × 136 = Nov. 20, 500 × 233 = 1796 8184 40950 40800 116 500 )206434 (11 48 days. 1796 2683 1796 8874 7184 1690 We first find the time when each of the bills will become due. Then, since it will shorten the operation, we take the first time when any bill becomes due, instead of its date, for the period from which to compute the average time. Now, since April the period from which the average time is computed, no time will be reckoned on the first bill, but the time for the payment of the second bill extends 44 days beyond April 1, and we multiply it by 44. (Art. 230.) Proceeding in like manner with the remaining bills, we find the average time of payment to be 115 days nearly, from April 1, or on the 25th of July. Hence, • Find the time when each of the sums becomes due. Multiply each sum by the number of days intervening between the date of its becoming due and the earliest date on which any sum becomes due. Then proceed as in the rule (Art. 230), and the quotient will the average time required, in days forward, from the date of the earliest sum becoming due. NOTE. -In the work, if there be a fraction of a day less than, it may be rejected; but if, or more than, it may be reckoned as 1 day. 231. The rule for finding the average time, when there are different dates? By what other method can you obtain nearly the same result? EXAMPLES FOR PRACTICE. 2. I have purchased several parcels of goods, at sundry times, and on various terms of credit, as by the following statement. What is the average time for the payment of the whole ? Jan. 1, 1856, a bill amounting to $175.80, on 4 months' cr. 66 16, 66 66 do. do. do. do. 66 do. do. 96.46, on 90 days' 78.39, on 3 months' "6 49.63, on 60 days' 114.92, on 6 months' "6 Ans. May 30, or in 45 da. do. do. Feb. 11, 66 28, Mar. 19, 3. Sold S. Dana several parcels of goods, at sundry times, and on various terms of credit, as by the following statement: Jan. 7, 1854, a bill amounting to $375.60, on 4 months' cr. April 18, June 66 do. do. do. do. Sept. 25, do. do. Nov. 5, of do. do. Dec. do. do. 66 7, 687.25, on 4 months' 568.50, on 6 months' 300.00, on 6 months' 675.75, on 9 months' 100.00, on 3 months' 66 1, What is the average time for the payment of all the bills? Ans. Dec. 24, or in 231 da. May 1, June 15, July 5, Sept. 25, Dec. 1, 4. The following is my account against G. M. Holbrook, and I wish to ascertain the average time of payment. Jan. 1, 1857, 97 yards of broadcloth, at $ 4.50, on 3 mos.' cr. Feb. 10, 7 bales of cotton cloth," 18.50, on 60 days' 66 66 9 tons of iron, 45.00, on 4 mos.' 66 66 66 66 11 hhds. of molasses, 66 8 doz. shovels, 14cwt. of sugar, 66 8 chests of tea, 66 མ མ མ མ མིའི 66 12.00, on 30 days' 9.00, on 2 mos.' " 6.50, on 1 mo.'s " "15.00, on 90 days' " Ans. July 16, or in 106 da. do. do. 66 66 do. do. 66 5. The following is an account of my bills against J. Crowell. Jan. 1, 1854, a bill amounting to $300, on 6 months' credit. June 1, 500, on 5 months' 66 Sept. 1, Feb. 1, 1855, do. July 1, 1856, do. Dec. 1, 66 do. May 1, 1857, do. do. 66 do. 200, on 6 months' 66 do. 66 do. 66 What is the average time of payment on the above bills? Ans. March 9, 1856, or in 20 mo. 8 da. 232. When partial payments have been made before the debt is due. Ex. 1. I have purchased goods to the amount of $ 800, on a credit of 6 months. At the end of 2 months I pay $100, and at the end of another month I pay $200 more. How long, in equity, after the expiration of the 6 months, ought the balance to remain unpaid? Ans. 2 months. 2 m. The interest on the $100 for 4 months is equal to the interest of $1 for 400 months; and the interest of the $200 for 3 months, to that of $1 for 600 months; and thus the interest on both $800-$300-$500. partial payments, at the expiration of the 6 months, is equal to the interest of $1 for 400+600, or 1000 months. To equal this credit of interest, the balance of the debt, which we find to be $ 500, should remain unpaid, after the 6 months, of 1000 months, or 2 months. RULE. - Multiply each payment by the time, in months or days, it was made before it became due, and divide the sum of the products by the balance remaining unpaid. The quotient will be the required time. EXAMPLES FOR PRACTICE. 2. Sold, March 11, 1855, James Stone goods to the amount of $1850, on a credit of 4 months. I received from him, April 7, $400; May 15, $ 270; and June 20, $ 350. When in equity should I receive the balance? Ans. Sept. 22, 1855. 3. Bought, June 12, 1855, of William Jones, goods to the amount of $1200, on a credit of 8 months. I paid him, September 1, $400; November 1, $200; and December 1, $100. When in equity can he require the balance of me? Ans. Aug. 17, 1856. 4. I sold, September 25, 1855, John Eckles 144 barrels of flour, at $12 per barrel, and 370 bushels of wheat, at $3 per bushel, on 6 months' credit. I received of him, September 25, $1000; November 1, $800; and December 21, $ 600. When ought I to be paid the remainder? Ans. June 14, 1858. 232. The rule for finding the average time of paying the balance of a debt, when partial payments have been made? 5. Wilson Seymour bought March 20, 1855, of a merchant in Troy, merchandise to the amount of $2000, on 6 months' credit. He paid down $ 500; May 10, $350, and June 7, $ 400. When I did the balance become due? Ans. May 18, 1856. 233. When an account containing items of both debit and credit. Ex. 1. At what time did the balance of the following account become due, allowing that each item drew interest from its date? Cr. Dr. 1856. Jan. 22, To merchandise, 66 66 24, Feb. 20, "" Martin Jordan in account with David Hill & Co. 1856. "" Jan. 4, By merchandise, "6 23, April 4, = $89 00 234 )24994 (40 2476 210 00 189 00 OPERATION. days. Average date of purchase, 40 days from Jan. 22, or on March 2. Difference between March 2 $619-$260-$359, or balance, Credits. Jan. 4, 77 April 16, 40×103= 4120 Ans. February 9, 1856. 260 260 620 359 days. )22853(87288 2080 2053 1820 $77 00 40,00 143,00 233 Average of credits, 88 days from 859)7800(21 days. 718 261 22 days back from March 2= February 9. 233. How do you equate an account having items of debit and credit? On equating each side of the account (Art. 230), we find the debits $619, became due 40 days from January 22, or on March 2; and the credits, $260, became due 88 days from January 4, or on April 1. If the account had been settled on March 2, it is evident the credits. $260, would have been paid 30 days, or the time from March 2 to April 1, before having become due. This would have been a loss of the use or interest of that sum to the credit side of the account, and a corresponding gain to the debit side. Now, as the settlement is required to be one of equity, we find how long it will take the balance of the account, $ 359, to gain the same interest that $ 260 would gain in the 30 days. If it takes $ 260 to gain a certain interest in 30 days, it would take $1 to gain the same interest-260 times 30 days, or 7800 days; and $ 359 to gain the same amount of interest of 7800 days, or 22 days nearly. Hence, the balance became due 22 days back of March 2, or on February 9. In this example, the time was counted back from the average date of the larger amount, since it became due first; but when that amount becomes due last, the time is counted forward from its average time. RULE. Find the average time of each side becoming due. Multiply the amount of the smaller side by the number of days between the two average dates, and divide the product by the balance of the account. The quotient will be the time of the balance becoming due, counted from the average date of the larger side, BACK when the amount of that side is due FIRST, but FORWARD when it is due LAST. NOTE. Having the average time of a balance becoming due, its CASH VALUE can be ascertained when the balance is due before the time of settling the account, by adding to it the interest up to the time of settlement, and when due after that time, by finding the present worth (Art. 213) from the time of settlement to the time of the balance becoming due. EXAMPLES FOR PRACTICE. 2. In settling the following account, when did the balance become due, the merchandise items being on 6 months' credit? Dr. Hiram Lewis in account with Joseph Warren. 1854. 66 Mar. 20, By cash, " merchandise. Ans. March 3, 1855. 1854. Feb. 16, To merchandise, $375 80 66 66 432 18 66 66 April 8, May 17, July 13, 320 15 66 "" 158 12 Cr. $300 00 371 50 200 00 85,20 323. What is the rule? How can the cash value of the balance of an account be found } |