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AVERAGE OR EQUATION OF PAYMENTS.

237

603. Examples. 139. What is the average date for paying three bills due as follows: March 31, $400; April 30, $ 300; May 30, $200 ?

140. What is the average date of maturity of three notes of $ 800 each, due respectively Nov. 5, Dec. 8, and Feb. 3 ?

141. What is the average date of maturity of the following items of account, viz., $ 900 due Sept. 10; $ 2250.48 due Oct. 21; and $ 1049.65 due Oct. 28 ?

142. Find the equated time for paying $ 430 due in 5 months; $ 270 due in 9 months; and $ 300 due in 8 months ?

143. Average the above, having the first item due in 3 months, the others in 9 months each.

144. A gentleman purchased a farm for $ 3600, agreeing to pay $ 600 down, and the remainder in five equal semi-annual instalments. At what time may the whole be paid at once ?

145. When shall a note to settle the following account be made payable ? J. R. INGERSOL

To R. FISH & CO., Dr.

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NOTE. First find at what time each item falls due by adding the time of credit to the date of the item.

146. What is the equated date of maturity of the following?

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AVERAGE OF ACCOUNTS.

NOTE. Younger pupils may omit this subject.
604. ILLUSTRATIVE EXAMPLE. What is the

average

date of maturity of the following account? Dr.

PHILIP ARCHER in Acct, with E. GRANGER. Cr.

1877. Mar. 18 To Mdse $250 30

600

1877.
Apr. 1 By Cash...

20 66 Real Estate

$700 300

66

66

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1 day's int. of 150=0.05 0.05) 4.17

83 March 18 + 83 d. = June 9. Ans. June 9, 1877. Explanation. — The payment of all these items at the earliest date, March 18, would involve a loss, at 1% a month, to the debtor of $2.40 of interest, and to the creditor of $ 6.57, or $4.17 more to the creditor than to the debtor.

Now, as the balance of the account, $ 150, is due from the creditor, he may, to avoid loss of interest, defer payment of the balance as many days after March 18 as will be required for $ 150, at 1% a month, to gain $ 4.17 of interest, which is 83 days. 83 days after March 18 is June 9. Ans. June 9, 1877.

In this case it will be seen that the balance of the account and of the interest are on the same side of the account.

605. Suppose, on the contrary, the first item in the foregoing account to be $ 500, instead of $ 250, what would then be the average date of its maturity ?

Explanation. — In this case the loss of interest to both debtor and creditor is the same as before, but the balance of the account, $ 100. is due from the debtor, who, to cancel the excess of interest lost by the creditor, should pay the balance of the account as many days before March 18 as will be required for $ 100, the balance, to gain $ 4.17 of interest, which is 125 days. 125 days before March 18, 1877, is Nov. 13, 1876. Ans. Nov. 13, 1876.

In this case the balance of the account and of the interest are on opposite sides of the account.

606. From the above illustrations we derive the following

Rule. To find the average or equated time for the settlement of an account when there are both debit and credit items :

1. Find the interest on the several items of the account from the earliest date at which any item becomes due to their several maturities.

2. Find the balance of interest of the debit and credit sides of the account, also the balance of the items.

3. Divide the balance of interest by the interest of the balance of the items for one day. The quotient will be the time in days between the selected date and the average time of settlement.

4. Count this time FORWARD from the selected date, when the balance of the account and of the interest are on the same side of the account, and BACK when on opposite sides. The result will be the date of settlement.

NOTE I. When settlement takes place after the equated time of payment, interest on the balance is charged ; when before the equated tinie, discount is allowed.

NOTE II. The balance due on an account at any day selected for settlement may be, and usually is, found without averaging the account, by computing the interest of the items on each side of the account from their several dates of maturity to the day of settlement. The interests so found on each side of the account are then added to that side. If any item matures after the day of settlement, the discount is computed and added to the opposite side of the account (which is equivalent to subtracting it from the side on which it occurs). When the two sides of the account have been so increased, their difference is the balance due.

607. Examples. 147. At what date can the balance of the following ledger account be paid without loss to either party? Dr. EDWIN C. CASTLETON.

Cr. 1877.

q 1877. April 1 To Mdse... 100000 || April 14 By Mdse... 1393 00 July 8 66 Cash .

118 98 || Aug. 10 66 Real Estate 94 33

148. What is the average date of maturity for the following account? Dr. RUDE, ALDRICH, & CO.

Cr. 1876.

1876.

Q Apr. 5 | To Sundries on 2 mo. 400|00|| June 1 Mdse on 60 d. 25000 Aug. 5

"1

600|00|| July 8 Mdse 30 d. 700 00 1

20000 | Aug. 13 Cash ........ 20000 149. Find the average date of maturity of the following account: Dr. EARL INGALLS.

Cr.

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66 Mdse 66 Mdse

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SECTION XVI.

EXCHANGE.

608. To avoid the risk and expense of sending money to make payments in distant places, merchants and others make use of drafts or bills of exchange. What these are, and how they are used, will best be shown by an example.

Suppose that J. G. Ames, in Boston, wishes to pay $200 to William Smith, in New Orleans. He may pay the money to a banker, James A. Dupee, in Boston, who will write an order on his correspondent, George Flint, a banker in New Orleans, in the following form :

of 200.

Boston, July 18. 1877. Thirty days after sight, st pay to William Smith, or order, Iwo Hundred Dollars, and place the same to the account of

Your obedient servant,
James A. Dupee

.

To George Flint, Esq.,

New Orleans.

609. Such a written order for the payment of money is a draft, or bill of exchange. The method of making payments by drafts or bills of exchange is exchange.

Ames will take this draft and send it to Smith, who, when he receives it, will present it to Flint for acceptance. If Flint is willing to obey the order and pay the money, he writes the word “ Accepted” across the face of the draft, adds the date, and signs his name. In due time Smith gets the money from Flint, gives up the draft, and the transaction is complete.

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