day's nearly. Hence, the balance became due 136 days forward from August 8, 1856, or on December 22, 1856. The time was counted forward from the average date of the larger amount, since it became due last; but had that amount become due first, the time would have been counted backward from its average time. = December 23, 1856. 328 days forward from January 30, 1856 In the second operation, we take the earliest date on which any sum becomes due in the account, for the starting-point from which to reckon the days, by which to find the several products belonging either to the debit or credit side (Art. 435, Note 1). The sum of the debit products, 143183, denotes the number of days required for $1 to gain as much interest as all the items of debit would gain in the times of their becoming due, and the sum of the credit products, 8786, denotes the number of days required for $ 1 to gain as much interest as all the items of credit would gain in the times of their becoming due. The difference between the sums of debit and credit products is 134397, and the difference between the debit and credit items is $410. Then, if it requires 134397 days for $1 to gain a certain interest, it will require $ 410 to gain the same amount of 134397 days= 328 days nearly. 328 days forward from January 30, 1856= December 23, 1856, the time of the balance of the account becoming due; thus varying one day in the result, on account of the fractions. = RULE 1. 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 ac fount. The quotient will be the time of the balance becoming due, counted from the average date of the larger side, FORWARD when the amount of that side becomes due LAST, but BACKWARD when it becomes due FIRST. Or, RULE 2.- Multiply each sum of debit and credit by the number of days intervening between the date of its becoming due, and the earliest date on which any sum in the account becomes due. Then, the difference between the sums of debit and credit products, divided by the difference between the debit and credit item, will give the time, to be counted from the earliest date of any sum in the account becoming due, FORWARD when the larger sum of products is on the LARGER side of the account, but BACKWARD when it is on the SMALLER side. NOTE. The CASH VALUE of a balance of an account drawing interest, or whose items are on different terms of credit, depends upon the time of settlement, and is therefore either larger or smaller than the difference between the debit and credit items. The average time of a balance becoming due being known, its cash value may be found, when the balance is due BEFORE the time of settlement, by adding to the balance interest up to the time of settlement; and when due AFTER that time, by deducting from the balance interest for the time intervening between the time of settlement and the time of the balance becoming due. The deduction of interest, in the latter case, is the mercantile method, instead of that of finding the true present worth by deducting the true discount. EXAMPLES. 2. Required the time when the balance of the following accounts becomes subject to interest, allowing that each item was due from its date. 3. When did the balance of the following account become due, the merchandise items being on 6 months? 4. Allowing that each item of the following account draws interest from its date, at what time would the balance become due, and how much ready money should in equity discharge the same, September 21, 1856, interest being at 6 per cent.? Ans. November 21, 1856; cash value of balance, $ 27.73. 5. Required the time when the balance of the following account became subject to interest, allowing the merchandise to have been on 8 months; and the cash value of the balance on November 28, 1857, provided it drew 6 per cent. interest from the time of its becoming due. Dr. 1856. N. Chandler, 2d, in account with T. E. Lanman. May 1, To merchandise, $300.00 1857. Cr. July 7, 66 66 66 66 Jan. 1, By cash, 759.96 417.20 Mar. 19, Feb. 18, merchandise, $500.00 481.75 750 25 287.70 April 1, 5 1.10 May 25, draft, “cash, 210.00 100.00 Ans. July 28, 1857; cash value of balance, $ 299.88. 6. The following account was settled May 24, 1857; how long previous to date was the balance by average due, and what was the cash value of the balance at the time of settlement? Ans. May 19, 1856; cash value of balance, $ 364.93. 439. To find the true balance of an account current whose items draw interest. Ex. 1. Required the true balance of the following account, on November 1, 1857, the time of settlement, allowing that each item drew interest from its date, at the rate of 6 per cent. Ans. $430.04. The time in days intervening between the date of each item and the time of settlement is, evidently, the number of days each item is on interest. Then, if each item be multiplied by the number denoting its number of days, and divided by 6000, the result will be its interest (Art. 356, Note 1), and the sum of the interest of the several items of debit will be the aggregate interest of the debit side, and the same principle will hold in finding the aggregate interest of the credit side. But the same result may be obtained in a shorter way by dividing the sums of the debit and credit products by 6000, which is done most readily by pointing off three decimal places at the right of cach sum (Art. 78), and dividing by 6, as in the operation. Then the balance of items and the balance of interest we add together, and thus obtain the true balance. 2. Required the true balance of the following account, on October 1, 1857, the time of settlement, allowing the rate of interest to be 6 per cent. Ans. $189.81. *Introduced only to illustrate the manner of balancing the account. Dr. Grant & Barker in account and interest with J. Ritchie. Cr. We find the several products by multiplying, as in working the preceding example. The products belonging to items becoming due previous to settlement we arrange as belonging to their respective sides. One item, however, becomes due 9 days after the time of settlement, thus requiring its side to be diminished by the interest of that item for the 9 days, or that the opposite side should be increased by that interest. We, therefore, write the product of this item with the debit products. We may now find the interest of each side separately, and then subtract that of the one side from that of the other for the balance of interest; but we obtain the desired result by a shorter method by finding the interest corresponding to the difference of the sums of the debit and credit products. Hence the general RULE. Multiply each item of debit and credit by the number of days intervening between its becoming due and the time of settlement. Place the product of each item becoming due BEFORE the time of settlement on its own side of the account, and place the product of each item * Introduced only to illustrate the manner of settlement. |