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EXAMPLES FOR PRACTICE.
1. JAMES GORDON, 1860.
To HENRY LANCEY, Dr. Mar. 4. To 100 yd. Cassimere, @ $2 50...... $250 25. 66 300C « French Prints,“
.12,...... 360 66 1200 " Sheeting,
96 30. 400 “ Oil Cloth,
.50...... 200 May 17. Sundries,.......
350 When is the above bill due, per average ?
Ans. Apr. 12, 1860.
2. I sell goods to A at different times, and for different terms of credit, as follows:
Sept. 12, 1859, a bill on 30 days' credit, for $180
300 Nov. 16,
150 Dec. 20,
350 Jan. 25, 1860,
130 Feb. 24,
140 If I take his note in settlement, at what time shall interest commence ?
3. What is the average of the following account? 1860, Oct. 1. Mdse., on 60 da.,....
$240 Nov. 12.
500 Dec. 25.
436 1861, Jan. 16.
325 Feb. 24.
436 Mar. 17.
537 Ans. Mar. 10, 1861.
4. I have 4 notes, as follows: the first for $350, duė Aug. 16, 1859 : the second for $250, due Oct. 15, 1859; the third for 3300, due Dec. 14, 1859; the fourth for $248, due Feb. 12, 1860. When shall a note for which I may exchange the four, be made payable ?
29518 • 548 = 54 da., average term of interest.
Oct. 28 - 54 da. = Sept. 4, balance due. ANALYSIS.—In this operation we have written the dates of maturity on either side, allowing 3 days' grace to the draft. The latest date, Oct. 28, is assumed as the focal date for both sides, and the two columns marked da. show the difference in days between the focal date and each of the other dates. The products are obtained as in simple equations, and the balance found between the items on the two sides, and also between the products. These balances, being both on the Dr. side, show that there is due on the day of the focal date, $548, with interest on $29518 for 1 day. By division, this interest is found to be equal to the interest on $548 for 54 days. Hence this balance, $548, has been due 54 days; and reckoning back from the focal date, we obtain the equated time of payment, Sept. 4.
Had we taken the earliest maturity, June 12, for the focal date, we should have obtained 84 days for the interval of time; and since in this case the products would represent the credit to which the several items are entitled after June 12, we should add 84 days to the focal date, which would give Sept. 4, as before.
2. When is the balance of the following account due, per average ?
2199 • 235 = 9 da.; Mar. 30 + 9 da. = Apr. 8, Ans. ANALYSIS. We take the latest maturity, Mar. 30, for the focal date, and consequently the products represent the interest due upon the several items, at that date. We find the balance of the items upon the Dr. side, and the balance of the products upon the Cr. side. The debtor therefore owes, on Mar. 30, $235, but is entitled to such a term of interest on the same as will be equivalent to the interest on $2199 for 1 day, which by division, is found to be 9 da. Hence the balance is due Mar. 30 + 9 da. Apr. 8. Thus we see that when the balances are on opposite sides, the interval of time is counted from the other dates. If we take, in this example, the earliest date for the focal date, the balances will both be upon the Dr. side, and the interval of time will be 97 da., which reckoned forward from the focal date, will give the equated time as before.
620. From these examples we derive the following
RULE. I. Find the time when each item of the account is due, and write the dates, in two columns, on the sides of the account to which they respectively belong.
II. Use either the earliest or the latest of these dates as the focal date for both sides, ana find the products as in the last case.
III. Divide the balance of the products by the balance of the account; the quotient will be the interval of time, which must be reckoned from the focal date TOWARD the other dates when both balances are on the same side of the account, but FROM the other dates when the balances are on opposite sides of the account.
Notes. 1. Instead of the products, we may obtain the interest, at any per cent., on the several items for the corresponding intervals of time, and divide the balance of interest by the interest on the balance of the account for 1 day; the quotient will be the interval of time to be added to, or subtracted from the focal date, according to the rule. The tiine obtained will be the same, at whatever rate the interest be computed.
2. There may be such a combination of debits and credits, that the equated time will be earlier or later than any date of the account.
EXAMPLES FOR PRACTICE.
1. Required, the average maturity of the following account.
Int on $118.62 for 1 da. $.0198. 2.20 :-0198=111 da.; June 8—111 da. Feb. 17, 1859, Ans.
ANALYSIS. Taking the latest maturity, June 8, for the focal date, we find the interest of each item, at 6 %, from its maturity to the focal date; then, taking the balance, we find the interest due on the account to be $2.20. Dividing this interest by the interest on the balance of the items for 1 day, we obtain 111 da., the time required for the interest, $2.20, to accrue. The average maturity, therefore, is June 8 — 111 da. = Feb. 17, 1859.
It is evident that when the balances occur on opposite sides, the interval of time will be reckoned as in the method by products.
2. What is the balance of the following account, and when is it due ?
436 548 312 536
00 00 00 00
1860. March 1 To Sundries,
March 25 By draft, at 60 da. April 12 6 Mdse.
3066 July 16
June 20 Sept. 14
Ans. Balance, $498; due June 22, 1860. 3. When shall a draft for the settlement of the following account be made payable ? David Sanford.
If the above account were settled April 6, 1858, by draft on time, how many days' credit should be given ? Ans. 20 da.
5. I owe $1000 due Apr. 25. If I pay $560 Apr. 1, and $324 Apr. 21, when, in equity, should I pay the balance ?
Ans. Aug. 30. Note.—Make the $1000 the Dr. side of an account, and the payments the Cr. side, and then average.
6. A man owes $684, payable Aug. 12, and $468, payable Oct. 15. If he pay $839, Aug. 1, what will be the equated time for the payment of the balance ?
Ans. Dec. 15. 7. A man holds 3 notes, the first for $500, due March 1, the second for $800, due June 1, and the third for $600, due Aug. 1. He wishes to exchange them for two others, one of which shall be for $1000, payable Apr. 1; what shall be the face and when the maturity of the other?
Ans. Face, $900; maturity, July 28.