NOTE ON INSTALLMENT LOAN REBATES. - Stelson, Hugh E.; Snyder, Ralph W. (The Accounting Review, 1954)
The ultimate point of reference in any mathematical development in the field of installment finance is or at least ought to be the compound interest method. It is not implied that pure actuarial theory should be introduced into practical day-to-day usage in installment transactions. But it is asserted that the mathematical relation between pure theory and the various practical short-cuts and simplified methods in use should be clearly established in the literature on the subject. Several of the common formulas for determining the rate of interest in installment payment plans have been shown to be approximations to the actuarially determined rate. The present paper relates the so called "Rule of 78" method of figuring rebates in pay-offs, to the theoretically equitable rebate found by the compound interest method. The "Rule of 78" method has that name because on a 12-payment loan the sum of the integers from 1 to 12 equals 78. It is also known as the "Sum of Digits" method.