THE RATE OF INTEREST IN INSTALMENT PAYMENT PLANS. - Stelson, Hugh E. (The Accounting Review, 1952)
There are three relatively simple methods in common use for determining the rate of interest in installment payment plans. These are known as the Constant Ratio, Series of Payments and Interest at End methods. They have been developed from independent assumption, apparently without any thought that they might be approximations to the more complicated Compound Interest method. In a paper in the American Mathematical Monthly it is shown algebraically that the above methods are approximations to the Compound Interest Method. In order to obtain a better understanding, let us assume temporarily that we know the rate and form a schedule of the payment of the debt. The magnitudes of the rates for the approximate formulas may be compared by means of the areas of the trapezoids. The rate is inversely proportional to the area. The areas for the series of payments, constant ratio, and interest at end methods are in order. This solution is often approximated by means of interpolation in tables. It is the purpose however to compare the compound interest method with the above methods and to present a simple but more accurate approximate formula which can be used without knowledge of the theory of finance.