bills, we find the average time of payment to be 43 days, nearly, from May 1, or on June 13. Rule. — Multiply cach payment by its own term of credit, and divide the sum of the products by the sum of the payments. NOTE 1. When the date of the average time of payment is required, as ir. Example 2, 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, and the quotient will be the average time required, in days forward from the date of the earliest sum becoming due. Note 2. In the result, it is customary, if there be a fraction of a day less than ), to reject it; but if more than 1, to reckon it as 1 day. In practice the work may be somewhat abridged, without varying materially the result, by disregarding, in performing the multiplications, the cents in the several sums, when they are less than 50, and by calling them $1, when more than 50. When a payment is made at the time of purchase, it has no product, but it must be added with the other products in finding the average time. Note 3. — The method of the rule, or that generally adopted by merchants, as has been intimated (Art. 384), is not perfectly correct. For if I owe a man $ 200, $ 100 of which I am to pay down, and the other $ 100 in two years, the equated time for the payment of both sums would be one year. It is evident that, for deferring the payment of the first $ 100 for one year, I ought to pay the amount of $ 100 for that time, which is $ 106; but for the $ 100 which I pay a year before it is due, I ought to pay the present worth of $ 100, which is $ 94.335), and $ 106 + $ 94.335) $ 200.335}; whereas, by the mercantile method of equating payments, I only pay $ 200. EXAMPLES 3. There is owing a merchant $ 1000; $ 200 of it is to be paid in 3 months, $ 300 in 5 months, and the remainder in 10 months. What is the equated time for the payment of the whole sum ? Ans. 7mo. 3d. 4. I have bought a farm for $ 6500; $ 2000 of which is to be paid down, $ 500 in one year, and the remainder in 2 years. But if a note for the whole amount had been preferred, in what time would it have become due ? 5. A owes B $ 300, of which $ 50 is to be paid in 2 months, $ 100 in 5 months, and the remainder in 8 months. What is the equated time for the payment of the whole sum ? Ans. 6 months. 6. I have sold H. W. Hathaway several bills of goods, at different times, and on various terms of credit, as by the following statement. What is the average time for the payment of the whole? 66 66 66 66 66 Feb. 10, 66 66 66 66 Jan. 1, a bill amounting to $ 600, on 4 months. 370, on 5 months. 560, on 4 months. April 20, 420, on 6 months. Ans. July 11. 7. Purchased goods of J. D. Martin, at different times, and on various terms of credit, as by the statement annexed. What is the equated time of paying for the same? March 1, 1855, a bill amounting to $ 675.25, on 3 months. July 4, " 376.18, on 4 months. Sept. 25, 821.75, on 2 months. Oct. 1, 961.25, on 8 months. Jan. 1,1856, 144.50, on 3 months. 811.30, on 6 months. 567.70, on 5 months. April 15, 369.80, on 4 months. Ans. March 16, 1856. 436. To find the time of paying the balance of a debt, when partial payments have been made before the debt is due. Ex. 1. I have bought of Leonard Johnson goods to the amount of $ 1728, on 6 months' credit. At the end of one month I pay him $ 300, and at the end of 5 months, $ 800. How long, in equity, after the expiration of 6 months, should the balance remain unpaid ? Ans. 3mo. 20d. The interest on the $ 300 300 x 5 1 5 0 0 for 5 months is equal to the 800 X 1 800 interest of $1 for 1500 months, and the interest of $ 800 for 1 1100 2 3 0 0 month is equal to that of $ 1 $17 28 $1100 for 800 months; and thus the $ 6 2 8; interest on both partial pay2 3 0 0 ; 6 2 8 = 3ino. 20d. ments, at the expiration of the 6 months, is equal to the interest of $ 1 for 1500 + 800 = 2300 months. To equal this credit of interest, the balance of the debt, which we find to be $ 628, should remain unpaid, after the 6 months, rig of 2300 months, or 3 months and 20 days. Rule. — Multiply each payment by the time it was made before it becomes due, and divide the sum of the products by the balance remaining unpaid ; and the quotient will be the required time. OPERATION. EXAMPLES. 2. A merchant has $ 144 due him, to be paid in 7 months, but the debtor agrees to pay one half ready money, and two thirds of the remainder in 4 months. What time should be allowed for paying the balance ? Ans. 2y. 10mo. 3. March 23, 1856, I sold John Morse goods to the amount of $ 8000 on a credit of 8 months. April 5, he paid me $1200; July 4, $ 1500; September 25, $ 1800; October 1, $ 1000; November 20, $ 500. When, in equity, should I receive the balance ? 4. There is due to a merchant $ 800, one sixth of which is to be paid in 2 months, one third in 3 months, and the remainder in 6 months; but the debtor agrees to pay one half down. How long may the debtor retain the other half so that neither party may sustain loss? Ans. 83 months. 5. I have sold Charles Fox goods to the amount of $3051, on a credit of 6 months, from September 25, 1856. October 4, he paid $ 476; November 12, $375; December 5, $ 800; January 1, 1857, $ 200. When, in equity, ought I to receive the balance ? Ans. October 8, 1857. AVERAGING OF ACCOUNTS. 437. An Account Current is a statement of the mercantile transactions of one person with another, when immediate payments are not made. An account is marked Dr. on the left, to indicate that the person with whom the account is kept is debtor for the items on that side; and is marked Cr. on the right, to indicate that he is creditor for the items on that side. Accounts current are generally made up or settled at the end of every six months or year. 438. To find the equated time when the balance of an account current will be due. Ex. 1. In the following account when did the balance become due, the merchandise articles being on 6 months' credit ? Ans. December 22, 1856. Dr. Messrs. James Dutton & Co. in account with David Hale. Cr. 66 1856. 1856. Jan. 4. To merchandise, $ 96.51 Jan.30. By cash, $ 240.00 " 18. 57.67|Apr. 3. 48.88 Feb. 4. " cash paid draft, 80.00 May22. 50.00 • merchandise, 38.96||July 7. “ Note,* June 22, 6mo. 410.01 9. 6 cash paid draft, 50.26 Mar. 3. “ merchandise, 154.46 .6 24. “ 42.30 23.60 May15. 28.46 " 21. “ 177.19 Apr. 9. “ 66 Errors excepted. Settled as above, Boston, July 7, 1856. DAVID HALE, FIRST OPERATION. Debits. 66 66 66 66 1856. Credits. Due July 4, 97 X 151 = 14647 Due Jan. 30, 240 18, 58 X 165 = 9570 Apr. 3, 49X 64 = 3136 May 22, 50x113 5650 $ 339 8786 days. Feb. 9, 50 x 5 250 8786 5 339 32648 Sept. 3, 154X212 = 2533) days. 24, 42X 233 9786 Credits due 26 days from January 30, Oct. 9, 24 X 248 5952 or on February 25, 1856. Nov. 15, 28X285 7980 Difference between February 25 and 21, 177X291 51507 August 8 = 165 days. $ 749 139438 days. $ 749 — $ 339 $ 410, balance. 139438 = 749 186449 days. 339 X 165 = 55935; Debits due 186 days from February 4, or on August 8, 1856. 55935 – 410 = : 1363 days. 136 days forward from August 8, 1856 = December 22, 1856. On equating each side of the account (Art. 435), we find the debits became due 186 days from February 4, or on August 8; and the credits became due 26 days from January 30, or on February 25. If the account had been settled on February 25, it is evident the debits would have been paid 165 days, or the time from February 25 to August 8, before having become due. This would have been a loss of interest to the debit side of the account, and a corresponding gain to the credit side. Now, as the settlement should be one of equity, we find how long it will take the balance, $ 410, to gain the same interest that $ 339 would gain in the 165 days. If it take $ 339 to gain a certain interest in 165 days, it would take $ 1 to gain the same interest 339 times 165 days 55935 days; and it would take $ 410 to gain the same amount of interest aid of 55935 days - 136 * Included only to illustrate the manner of settling an account. days 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. SECOND OPERATION. 66 400 500 15132 9860 7293 87 86 Debits. Credits. Due Feb. 4, 80 X Due Jan. 30, 240 April 3, 49 x 64 = 3136 “ May 22, 50 X 113 = 5650 $339 8786 days. Aug. 4, 39 X 187 Sept. 3, 154 X 217 = 33418 $ 749 $ 339 $ 410, balance of the 24, 42 X 238 9996 items. Oct. 9, 24 X 253 = 6072 143183 134397, balance of “ Nov. 15, 28 X 290 8120 products. 21, 177 X 296 52392 134397 - 410 = 3274 i7 days. $ 749 143183 days. 328 days forward from January 30, 1856 = December 23, 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 to 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 account. 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 |