$1 for 4800 months. It is evident that a note for the balance, $1200-$1000 = $200, must be dated 5 of 4800 months, or 24 months previous to the time the $1000 was due, or must draw interest from that time.

6. July 10, 1858, A paid B $600; Sept. 12, 1858, B paid A $800. When ought A to pay the balance?

NOTE.-Sept. 12, B owed A $600+its interest for 64 days. He paid A $600+ $200. Hence, A is entitled to the use of the balance ($200) until its interest equals the interest of $600 for 64 days, or 192 days. 192 days from Sept. 12, 1858, is March 23, 1859.

7. July 10, 1868, A paid B $800; Sept. 12, 1868, B paid A $600. What should be the date of a note for the balance?

NOTE.-Sept. 12, B owed A $800+its interest for 64 days. He paid A but $600. Hence, he owes A the balance ($200) and the interest of $800 for 64 days, or the interest of $200 for 256 days. A note for the balance must therefore begin to draw interest 256 days previous to Sept. 12, 1868, which is Dec. 30, 1867.

Remark. The above seven examples, if well understood, will aid the student in equating accounts which contain both debits and credits.

EQUATION OF ACCOUNTS.

687. 1. Equation of accounts (also called "Averaging of Accounts," and "Compound Equation of Payments") is the process of finding at what time the balance of an account can be paid without loss to the debtor or creditor.

2. The balance of an account is the difference between the sum of the debits and credits, or what one party owes the other in excess.

3. It is a principle of common law that a debt does not draw interest after it falls due, with the exception of negotiable paper. If the balance of an account is not paid when it is demanded, still it does not draw interest. In consequence of the hardship the common law imposes on the creditor, many of the States have passed statutes giving him the right to compute interest on the balance of his account, after he has submitted a statement of it to the debtor, and obtained his acknowledgment of its correctness. The courts would not enforce the payment of interest on the balance of account from the equated date to the commencement of the suit, nor would they defer the payment of the balance until the equated date, should it fall subsequent to the last transaction. All that

can be claimed is simply the balance without interest, which is due at any time, unless changed by express agreement of the parties, or by a statutory provision giving interest, provided the conditions of the statute have been strictly complied with.

4. Since the debit and credit sides of an account are respectively equivalent to the sum of their several items, due at the equated time (Art. 684, Ex. 3, Note), the first step in equating accounts is to find the time when each side of the account becomes due.

5. This may be found by equating each side of the account, without any reference to the other, commencing either at the first or the last date of each, or by using the first or last date of the account as a common starting-point for both sides.

The date from which the intervals of time are reckoned is commonly called the focal date.

When each side of the account is equated separately, the process may be called that of double equation; when both sides are equated from one focal date, the process may be called that of single equation.

688. Ex.

Dr. D. B. CLARK & Co. in account with G. C. Cook. Cr.

1. First Method by Double Equation. In the following solution we have taken the earliest date when any item became due on each side of the account for the focal date of that side, and have equated each side by itself.

By thus equating each side, the account will stand as follows:

Dr.

Due, Nov. 21, 1870, $875. Due, Oct. 10, 1870,

.

2. Second Method by Double Equation. In this operation we use the earliest date when any item of either side of the account becomes due, as a focal date.

3. The next step is to find when the balance of the account, as thus equated, becomes due.

Using 12% as the most convenient rate for computation, we have

Discount or interest of $650 for 42 da. $650 x .014=$9.10. Time that the balance $225 should be kept = ($9.10÷$225) × 3 =121 days; or $9.10.075 (disc't of $225 for 1 day)=121 days. Thus the balance is due 121 days from Nov. 21, 1870, which is March 22, 1871.

5. Explanation.-Assume the account settled Nov. 21, the latest date. The credit side of the account has been due from Oct. 10 to Nov. 21, or 42 days. Nov. 21, the credit side is equal

to $650 and the interest of the same 42 days. That the debit side of the account may be increased by an equal amount of interest, it is evident that the balance of the account must remain unpaid 121 days after Nov. 21, or the 121 days must be counted forward from Nov. 21.

6. Or thus:

The above account may be stated as follows: Oct. 10, 1870, G. C. Cook paid D. B. Clark & Co. $650; Nov. 21, 1870, D. B. Clark & Co. paid G. C. Cook $875. Now, since D. B. C. & Co. had the use of $650 for 42 days, G. C. C. is entitled to the use of $225 (the balance) until its interest equals the interest of $650 for 42 days, which is 121 days. 121 days from Nov. 21, 1870, is March 21, 1871.

Suppose the account be reversed so as to stand thus:

$650. Due Oct. 10, 1870,

$875.

Due Nov. 21, 1870 8. What is the equated time for the payment of the balance now due ?

Balance due 163 days previous to Nov. 21, 1870, which is June 11, 1870.

9. Explanation.-Suppose the account settled Nov. 21. The credit side is equal to $875 and its interest from Oct. 10 to Nov. 21, or 42 days. That the debit side of the account may be increased by an equal amount of interest, the balance of the account must be regarded as due 163 days previous to Nov. 21, or June 11.

10. Or thus:

Oct. 10, 1870, G. C. Cook paid D. B. Clark & Co. $875; Nov. 21, 1870, D. B. C. & Co. paid G. C. C. $650. Since D. B. C. & Co. had the use of $875 for 42 days, G. C. C. is entitled to the interest of $225 (the balance) for 163 days. Hence, the balance must be regarded as due 163 days previous to Nov. 21. The simple question is: How long must $225 be on interest to equal the interest of $875 for 42 days?

NOTE. If D. B. Clark & Co. should wish to give their note for the balance, it is evident the note may in equity be dated June 11, 1870, or may draw interest from that time.

First find the equated time for each side of the account separately. Then multiply the amount due on that side of the account which falls due FIRST, by the number of days between the dates of equated time, and divide the product by the balance of the account. The quotient will be the number of days to be counted FORWARD from the LATEST DATE when the SMALLER side of the account falls due FIRST; and BACKWARD when the LARGER side falls due First.

NOTE.-Some authors give the following rule:-Multiply the smaller side of the account by the number of days between the dates of equated time, and divide the product by the balance of the account. The quotient will be the time for consideration. From the equated date of the larger side, count FORWARD when that side becomes due last, but BACKWARD when it becomes due first.

690. Method by Single Equation. The equated time for the payment of the balance of an account may be found directly without averaging the debit and credit items separately, by the following method: