.

(c.) RULE.-I. Find the time when each item of the account is due, and their respective amounts.

II. ASSUME the EARLIEST date at which any of the items of the account become due, and FROM IT calculate the terms of credit.

III. Multiply each item by its own term of credit, and divide the balance of the sum of the products by the balance of the sum of the items of the account; the quotient will be the interval of time, which must be reckoned from the asSUMED DATE FORWARD, when the balances are on the same side of the account, but BACKWARD from the ASSUMED DATE, when the balances are on opposite sides of the account: this will be the date at which the balance becomes due.

IV. When the balance of the account becomes due BEFORE the time of settlement, calculate the interest at the given per cent. for the interval of time between the date at which the balance becomes due and the time of settlement; add it to the balance: the result will be the cash balance.

V. When the balance of the account becomes due AFTER the time of settlement, calculate the BANK discount on the balance at the given rate per cent., for the interval of time between the settlement and the date at which the balance becomes due; deduct it from the balance of the account: the remainder will be the cash balance.

QUESTIONS.-Give the rule for finding the cost of a bill of exchange on England. (286., a.) How is English exchange quoted? (286., a., 1.) Give the analysis of finding the cost of a bill of exchange on France. (290., a.) How is exchange on France quoted? (287., a., 2.) How are bills of exchange usually drawn? (287., a., 3.) What is the exchange value of the pound sterling? (286.) What How are bills on is the exchange value of the franc? (287.) England drawn? (286.) How are bills on France drawn? (287.)

What is the cash balance of the above account Jan. 1,

What is the date at which the balance of the above ac

What is the cash balance, of the above account Dec. 25,

66

Apr. 4 By Mdse. on 30 da., 475
July 6 Cash,

66

450

Aug. 26" Mdse. on 60 da., 375

Cr.

July 18" Mdse. on 60da., 350 Aug. 18 90 420 What is the cash balance of the above account Jan. 1, 1865?

QUESTIONS.-What is exchange? (270.) What is a bill of exchange? (271.) Who is the drawer or maker? (272.) The drawee? (273.) The payee? (274.) The buyer or remitter? (275.) What is an acceptance? (276.) What, an indorsement? (277.) What is the difference between an inland bill and a foreign bill? (278.) What is the course of exchange? (280.) What is par of exchange? (281.) When is exchange said to be at a premium? (282.) When at a discount? (283.)

LESSON XCVII.

300.* AVERAGING ACCOUNTS BY INTEREST. (a.) What is the date at which the following bill is due? (b.) What is the cash balance at 6 per cent., Dec. 12. JERRIE L. FORDHAM, To G. W. HOWELL, Dr.

*NOTE-For the following brief, practical method of averaging, or of finding the cash balance of accounts, we are indebted to R. S. Delisser, Esq., of N. Y. city. who has kindly permitted us to use it in this work.

The advantage of this method is, that, by ruling an interest column in the ledger, and by the aid of an appropriate interest table, the amount of interest on each item, from the assumed date to the date of purchase, may be entered while posting. Upon settlement, either the average or the cash balance may be found by adding the item and the interest column, and, at a single operation, determining the equated time or cash balance, the whole work requiring but a few moments of time.

This method is now used by the principal merchants in New York, and other large cities, and a more complete exposition of the system, with tables, &c., may be found in Mr. Delisser's published work.

3. July 3, +30 da≈Aug. 2, Ans. $37.083+$1690=1727.08, Ans. ANALYSIS.-(a.) By the table (298., b.) find the term of credit of each item from July 3, the assumed date, and write it in the column of days.

By the table (298., c.) find the interest on each item for its term of credit, and write it in the interest column.

1. If the interest on $6. for one day is 1 mill, the interest on $1690 for one day will be as many mills as $6. are contained times in $1690, which are 281,8.

2. If 1690 require one day to give $0.2816 interest, to give $8.547 interest it will require as many days as $0.2816 are contained times in $8.547, which are 30.

3. 30 days added to July 3d, equals Aug. 2d, the equated time.

(b.) The interest on $1690 from July 3, the assumed date, to Dec. 12, the time of settlement (162 da.), is $45.63.

If the interest on the several items to the dates at which they become due is $8.547, then $8.547 deducted from $45.63, the interest of $1690 to Dec. 12th, leaves $37.083, the required interest, which added to $1690 amounts to 1727.08, the cash bal

ance.

What is the date at which the balance of the following account becomes due?

NOTE.-The cash balance of this account may be found as follows:-Deduct $13.034 from the interest of $5700 from Feb. 8 to the time of settlement, and add the remainder to $5700 on the debit side of the account. In the same manner proceed with the credit side, and the balance of the account will be the cash balance.

ANALYSIS.-Assume Feb. 8, 1864, from which to calculate credits. Write the interest on each credit, in the interest column, and find the balance of interest and the balance of items. This balance shows that Chas. Rockwood owes me $4250, and the value of his credit in the account amounts to $29.923 more than mine, consequently the balance of the account should become due previous to Feb. 8, 1864, for a time sufficient to produce $29.923.

1. If $4250 require one day to give $.7083 interest, it will require as many days to give $29.923 interest as $0.7083 is contained times in $29.923, which is 42.

2. 42 days previous to Feb. 8, 1864, is Dec. 28, 1863, the equated time.

Hence, to find the equated time of an account by interest, we have the following

RULE.-I. Find the interest by the table on each item from the ASSUMED date to the time at which it becomes due.

II. Divide the balance of interest by the interest of the balance for 1 day and the quotient will be the average term of credit.

III. Add the average term of credit to the assumed date, if both interest and item balance are on the same side of the account; but subtract it if they are on the opposite sides of the account.