3. I owe $480 payable in 90 days, and $320 payable in 60 days. My creditor consents to an extension of time to 1 year, and offers to take my note for the whole amount on interest at 6 per cent. from the equated time, or a note for the true present worth of both debts, on interest from date. How much will I gain if I choose the latter condition? Ans. $1.14. $280 on 3 mo.,

4. Bought merchandise April 1, as follows: $300 on 4 mo., $200 on 5 mo., $560 on 6 mo.; what is the equated time of payment?

CASE II.

Ans. Aug. 24.

618. When the terms of credit begin at different dates.

1. When does the amount of the following bill become due, per average?

ANALYSIS. The three items of the bill are due Jan. 12, Mar. 16, and Apr. 20, respectively. In the first operation we use the earliest maturity, Jan. 12, for a focal date, and find the difference in days between this date and each of the others; thus, from Jan. 12 to Mar.

16 is 64 da.; from Jan. 12 to Apr. 20 is 99 da. Hence, from Jan. 12 the first item has no credit, the second has 64 days' credit, and the third 99 days' credit, as appears in the column marked da. We now proceed to find the products as in Case I, whence we obtain the average credit, 55 da., and the equated time, Mar. 7.

In the second operation, the latest maturity. Apr. 20, is taken for a focal date, and the work may be explained thus: Suppose the account to be settled Apr. 20. At that time the first item has been due 99 days, and must therefore draw interest for this time. But interest on $400 for 99 days the interest on $39600 for 1 day. The second item must draw interest 35 days; but interest on $600 for 35 days= interest on $21000 for 1 day. Taking the sum of the products, we find that the whole amount of interest due Apr. 20 equals the interest on $60600 for 1 day; and this is found, by division, equal to the interest on $1375 for 44 da., which is the average term of interest. Hence the account would be settled Apr. 20, by paying $1375, with interest on the same for 44 days. This shows that the $1375 has been used 44 days, that is, it falls due Mar 7, without interest. Hence we have the following

RULE. I. Find the time at which each item becomes due, by adding to the date of each transaction the term of credit, if any be specified, and write these dates in a column.

II. Assume either the earliest or the latest date for a focal date, and find the difference in days between the focal date and each of the other dates, and write the results in a second column.

III. Write the items of the account in a third column, and multiply each by the corresponding number of days in the preceding column, writing the products in a fourth column.

IV. Divide the sum of the products by the sum of the items. The quotient will be the average term of credit or interest, and must be reckoned from the focal date TOWARD the other dates, to find the equated time of payment.

NOTES.-1. When dollars and cents are given, it is generally sufficient to take only dollars in the multiplicand, rejecting the cents when less than 50, and.carrying 1 to the dollars, if the cents are more than 50.

2. Months in any terms of credit are understood to be calendar months; the time must therefore be carried forward to the same day of the month in which the term of credit expires.

EXAMPLES FOR PRACTICE.

1. JAMES GORDON,

1860.

Mar. 4. To 100 yd. Cassimere, @ $2 50,...... $250

.12,...... 360
.08,.....

TO HENRY LANCEY, Dr.

96

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

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

500

436

325

436

537

Ans. Mar. 10, 1861.

4. I have 4 notes, as follows: the first for $350, due Aug. 16, 1859 the second for $250, due Oct. 15, 1859; the third for $300, 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?

2951854854 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?

21992359 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