Oct. 7, Merchandise, on 90 days, $1000.

$600, are, respect

ively, 0, 51, and

Nov. 15, 186645 days Dec. 30, 1866, Ans.

95 days, from Nov 15.

The average term of these credits, by Case I., is 45 days; hence, 45 days from Nov. 15, 1866, or Dec. 30, 1866, is the equated time.

RULE. Select the earliest date at which any one of the debts became due, and therefrom reckon the terms of credit. Multiply the terms of credit of each item by the number denoting its item, and divide the sum of the products by the num ber denoting the sum of the items; the quotient will be the average term of credit.

The average term of credit, added to the selected date, will give the equated time.

Examples.

2. Purchased the following bills of goods: July 1, a bill of $200, on 2 months; July 20th, a bill of $600, on 60 days; Aug. 1, a bill of $1000, on 30 days. What is the equated time of payment? Ans. September 6th.

Explain the operation. Repeat the Rule.

3. I owe Oliver Bates as follows: April 1, for cash, $1400; May 1, for merchandise $500; June 1, for flour, $1100. What is the average date of the items? Ans. April 28th.

4. R. Hicks & Co. have sold a merchant the following bills: Jan. 1, merchandise, $735; Jan. 21, corn, on 30 days, $649.50; Feb. 1, lumber, $100; March 12, merchandise, on 30 days, $200. If they should receive in settlement for the whole, a note, from what date ought it to draw interest?

Ans. February 3d.

343. When the items have the same term of credit, we may First find their average date, and then add the common term of credit, for the equated time.

5. Purchased goods, on 4 months, as follows:- April 1, a bill of $1450; May 7, a bill of $1250; June 5th, a bill of $850. Required the equated time of payment.

Ans. August 29th.

6. Sold the following bills of goods, on 6 months: Jan. 15, a bill of $3750; Feb. 10, a bill of $3000; March 6, a bill of $2400; June 8, a bill of $2250. At what time should a note be made payable, that will settle for the whole?

344.

Ans. Sept. 2d

AVERAGING OF ACCOUNTS.*

The Balance of an account is the difference between its debtor and creditor sides.

Accounts are subjecí to interest after the expiration of the term of credit.

345. The Averaging of an Account is the process of finding the equated time of paying the balance, or the date at which the balance of the account becomes due, or subject to interest.

How may we proceed when the items have a common term of credit? What is the Balance of an Account? When are accounts subject to inter est ? What is the Averaging of an Account?

* Optional.

346. To find the equated time of the balance of an account.

1. When does the balance of the following account become due ?

Balances,

200

19200 April 196 days=July 6, Ans. We select, for convenience, April 1, the earliest date at which any of the items of account is due, as the point of reckoning, and find the aggregate of the terms of credit of the debit items, with reference to the selected date, to be equal to the credit of $1 for 48800 days; and the aggregate of the terms of credit of the credit items to be equal to the credit of $1 for 29600 days.

Striking the balance, it appears that at the selected date, $200 subject to a credit equal to the credit of $1 for 19200 days, is against Franklin Fuller. But the credit of $1 for 19200 days is equal to that of $200, for 2 of 19200 = 96 days; hence, the $200 is not due in equity till 96 days after April 1, or till July 6.

If, however, the balance of items and of terms of credit had been on different sides of the account, the balance of items would have been due before, instead of after, the selected date.

RULE. Select the earliest date at which any of the items of account become due, and therefrom reckon the terms of credit. Multiply each term of credit by the number denoting th corresponding item, and divide the balance of the sums of the products by the balance of the sums of the items of the ac

ount.

The quotient will be the time, which must be ADDED to the selected date, when the two balances are on the same side of account, but SUBTRACTED from the selected date, when the balances are on different sides, to obtain the equated time of THE

ACCOUNT.

Examples.

2. What is the balance of the following account, and, allowing each item to be on 30 days, when does it become due ?

3. Required the date, at which a note, given for the balance of the following account, should begin to draw interest.

4. Required the face of a note which must be given for the balance of the following account, and the date at which it should begin to draw interest.

Dr.

1866.

J. F. Gould.

1866.

Cr.

May 16, To Mdse. on 60 d.,|| $300 00 ||May 20, By Mdse. on 30 d., $200 00

Ans. Face of note $99.60; on interest from June 2.

What is the Rule?

SETTLEMENT OF ACCOUNTS.*

347. Merchandise Balance is the balance of the items without interest.

348. Interest Balance is the balance of the interest of the items of the two sides of an account.

349. Cash or Net Balance is the balance when the merchandise and interest balances have been added to the proper sides of the account.

350. The Settlement of an account is ascertaining the balance at any specified time.

351. Since the merchandise balance is understood to be subject to interest from the date of its being due (Art. 344), it follows, that

The cash or net balance, at any date subsequent to the equated time, may be found by ADDING to the merchandise balance its interest up to date; or at any date previous to the equated time, by SUBTRACTING from the merchandise balance its interest for the time intervening.

INTEREST METHOD.*

352. The cash balance of an account drawing interest may be determined by means of the interest on the items of the two sides.

1. Let it be required, on January 1, 1867, to find the cash balance of the following account; and, also, the equated time, allowing each item to draw interest from date, at 6 per cent. P. T. Montgomery & Co.

Dr.

Cr.

ance ? The Settlement of an Account? How may the cash or net balance be found?

* Optional.