20. A 75 days' note for $348.56, dated March 9, discounted April 3, at 6 %.

21. A 6 months' note for $ 2916.80, dated Apr. 19, discounted June 26, at 4%.

22. A 60 days' note for $285.75, dated Oct. 13, discounted Nov. 5, at 7 %.

23. A 5 months' note for $131.40, dated Sept. 30, discounted Dec. 1, at 7%.

24. A 45 days' note for $463.19, dated July 10, discounted Aug. 2, at 6 %.

25. A 3 months' note for $2500, dated July 16, discounted Aug. 22, at 8 %.

26. A 4 months' note for $ 916.80, dated Mar. 20, May 11, at 7 %.

$987.44.

discounted

BOSTON, Oct. 25, 1894.

For value received, I promise to pay William Simpson & Co., or order, nine hundred eighty-seven dollars and forty-four cents, six months from date, with interest at 8%. THOMAS P. Fox.

27. What are the avails of the above note if discounted at

date at 6%?

28. What are the avails if discounted Jan. 1, 1895, at 6 %? 29. What is the value at maturity?

30. What is the value Sept. 13, 1895?

31. What must be the face of a 60 days' note discounted on its date at 6% in order that the avails may be $150?

32. What must be the face of a 3 months' note discounted on its date at 7% in order that the avails may be $316?

33. If at 5% discount $223.75 is received July 12, 1895, on a note dated June 8, 1895, and maturing Sept. 2, 1895, what is its face?

34. If at 73% discount $75.15 is received on a 60 days' note 20 days after its date, what is the face?

EQUATION OF PAYMENTS.

379. Equation of Payments is the method of determining when several sums, payable at different times, may be paid at one time without loss to either debtor or creditor.

380. The equated time is the date of payment.

381. Written Exercises.

1. A owes B $900, of which $200 is due June 12, 1895, $300 Aug. 8, and $ 400 Sept. 19. When can A pay the $ 900 in one sum without loss to either A or B ?

June 12, 1895, +2 m. 2 d. Aug. 14, 1895, Ans.

=

If the amounts due were all paid June 12, the debtor would lose the interest on the $300 from June 12 to Aug. 8, or $2.85, and also the interest on $400 from June 12 to Sept. 19, or $6.47; that is, by paying the $900 June 12 the debtor would lose $ 2.85 + $6.47 = $9.32. Therefore, he can equitably retain the $900 as long after June 12 as it will take it to gain $9.32. As $900 gains $4.50 in one month it will take it as many months to gain $9.32 as $ 4.50 is contained times in $9.32, or 2 m. 2 d. 2 m. 2 d. after June 12 is Aug. 14.

NOTE 1. In finding the equated time interest may be computed from the date of the first bill or from any other date, but it is most convenient to compute the interest from the first day of the month in which the first bill is due, because the time for which interest is to be computed on the several bills is thereby most easily determined.

NOTE 2. Some accountants compute the interest between the dates for the exact number of days instead of for the calendar months and days. But as interest between merchants is usually computed for months and days, the above method is more equitable as well as expeditious, and will seldom produce a different result, and then will seldom change the equated time more than one day.

382. Hence, to find the equated time for the payment of several sums due at different times,

Rule.

Find the sum of the interests on each amount from the first day of the month in which the first bill is due to the time each bill is due. Divide the sum of these interests by the interest of the sum of the bills for one month, and the quotient will be the number of months from the selected date to the equated time.

NOTE 1. A fraction of a day less than is neglected; otherwise it is counted as a day.

2. Find the equated time for paying $2000 due Jan. 17, $3000 due Feb. 21, and $ 600 due June 6.

Jan. 1+1 m. 19 d. Feb. 20, Ans.

3. Jan 7, 1895, I purchased of Mr. James $75 worth of goods on a credit of 4 months; Jan. 28, $ 155, on a credit of 3 months; and Feb. 15, $98, on a credit of 2 months. What is the equita

ble time for paying the whole amount?

NOTE 2. First find the date at which each bill is due.

4. Jan. 1, A owes B $200 payable in 4 months and $600 payable in 8 months. Find the equated time for settlement.

5. July 6, 1895, I owe to John Smith $4550, payable in 2 m., $5075 in 3 m., and $3500 in 4 m. What is the equated time of payment?

6. $1500, $2100, and $2400 are due in 3, 4, and 5 months, respectively, from Nov. 15, 1895. What is the equated time of payment?

7. Required the equated time of paying the following bills of goods, each bought on a credit of two months. Mar. 12, 1895, $300; Mar. 18, $200; Apr. 6, $600; July 24, $100.

NOTE 3. Find the equated time without regard to the 2 months, and then add 2 months to this result.

8. Required the equated time of paying the following bills, each bought on 3 months' credit. June 5, 1895, $180; June 15, $84; July 12, $240; July 20, $96.

9. Bought the following bills on 2 months' credit: May 14, 1895, $400; June 4, $150; June 6, $80; June 14, $170. What is the equated time of payment?

10. Bought the following bills on 3 months: Feb. 18, 1895, $1200; Mar. 25, $472; Mar. 30, $468; Apr. 1, $500. What is the equated time of payment?

11. Bought the following bills on 2 months: Jan. 8, 1895, $12; Jan. 24, $20; Feb. 18, $1200; Mar. 6, $4000. What is the equated time of payment?

12. Bought the following bills on 30 days: Jan. 8, 1895, $4000; Jan. 14, $1200; Jan. 18, $20; Jan. 26, $12. What is the equated time of payment?

13. If Jan. 1, 1895, A owes B $400 due in 4 months, $600 due in 6 months, and $800 due in 8 months, what is the equated time of payment?

The $600 is due 2 months, and the $800 4 months after the $400 is due. The use of $600 for 2 months is equivalent to the use of $1200 for 1 month; and the use of $800 for 4 months is equivalent to the use of $3200 for 1 month. A, then, is entitled to keep, after the time the $400 is due, the whole sum, $1800, till it is equivalent to the use of $4400 for 1 month; that is, as many months after the $400 is due as $1800 is contained times in $4400, or 24 m. = = 2 m. 13 d. 2 m. 13 d. after Jan. 1, 1895, + 4 m. = July 14, 1895, Ans. Hence,

Rule.

Multiply each debt by the number expressing the time to elapse between its maturity and the earliest maturity of any debt, and divide the sum of these products by the sum of the debts. Add the time thus obtained to the date of the earliest maturity of any debt.

NOTE 4. The examples already given can be performed by the product method if preferred; but the interest method is considered the better.

383. To find the equated time for paying the balance of an account which has both debit and credit entries.

14. What is the equated time for paying the balance of $500 due on the following account?