Simple and Compound Interest.—As to its method of calculation, interest may be simple or compound. Simple or single interest is figured on the single base known as the principal, the only other element being the length of time. Compound interest periodically adds the unpaid interest to the previous principal, and so secures interest not only on the original principal but on all unpaid interest as well.

In accounting both kinds of interest are recorded under the common title Interest. Some applications of the interest principle to certain special accounts will be discussed.

Equation of Payments.—The practice of averaging accounts is occasionally met with at the present time in American business. In proceedings in bankruptcy, all claims against the bankrupt on open or running account comprising several items, when filed with the trustee, must show the average due date of the items if interest is to be secured on the overdue amounts.

The problem involved may best be shown by an example. The following account appears on A’s books, showing charges against B:

B
Jan.  5 Mdse. 2/10, n/30.100.00
Feb.  1 Mdse. 2/10, n/60.350.00
Apr. 10 Mdse. net200.00
June  2 Mdse. 2/10, n/60.2,000.00

If B does not settle the various amounts as they come due, A is deprived of the use of his money longer than contemplated in the sale contract. In justice to him, interest on the overdue amounts ought to be allowed. If B should pay any of the amounts earlier than the terms of sale require, he should be allowed a discount, i.e., a rebate equal to the interest for the time of prepayment. Further, shortly after the last purchase on June 2 at 60 days, amounting to $2,000, B may desire to settle his entire account, taking his discount for prepayment on the $2,000 and allowing A interest on the overdue amounts. If the date of settlement is fixed, the amount necessary for an equitable settlement may be determined by the method used for the account current in the previous chapter.

Average Due Date.—But B may want to know the date on which he can settle equitably by paying the exact amount of the account without either paying interest on the overdue items or taking discount on the $2,000. The problem involved is that of averaging or equating accounts. The equated date, due date, or average date of payment are the terms variously applied to the date of equitable settlement. If the account has only debits or only credits, the equation is called a simple or single equation or average; if it has both debits and credits, the equation is called a compound or double equation.

In order to determine the equated date, an arbitrary one, called the focal date, is taken for the purpose of computing the interest charges and credits, and from that date the days of interest are counted backwards or forwards according to the result arrived at through use of the arbitrary date. Interest is calculated at an arbitrary rate, usually 6% (100% per day is used by another method of calculation), and in the case of compound equation the same rate must be used on both debits and credits.

To illustrate the method of calculation for the simple equation and the interest principle involved, the account above cited will be equated. In order that the expired time between the focal date and each date of value may be easily computed, the last day of the previous year is taken as the focal date. Interest is at 6%.

Date of
Entry		 Date of
Value		 Expired
Time		 Amount Int. on Total
Amount for
1 Day		 Int. on Each
Amount for
Expired Time
1/52/435 da.$ 100 $ .58
2/14/292 ” 350 5.37
4/10 4/10 100 ” 200 3.33
6/28/1213 ”  2,000 71.00
$2,650.44⅙)$80.28
182 da.