On the Proper Use of Compound Interest Factors—A Technical Note

Abstract

Five of the seven factors in most common use for compound interest calculations involve a uniform series of payments (or receipts). These interest factors, for use when interest is compounded at discrete points in time, are commonly referred to as the uniform series present worth factor, the uniform series compound amount factor, the capital recovery factor, the sinking fund factor and the uniform series gradient conversion factor. The proper use of these five factors requires that the period of time between the compoundings of interest coincide with the period of time between the uniform payments. If the interest is compounded more frequently (assume by an integer number of times) than the payments, then the best way to apply the compound interest factors is to determine the effective interest rate between payments. If interest is compounded less frequently than the payments (assume there are an integer number of payment periods within each compounding period), the correct solution procedure is not well known. Three methods are discussed for solving problems when interest is compounded less frequently than payments are made. It is argued that the method proposed in this note is better than the other two methods in popular use from both a theoretical and practical standpoint.