Compounding under varying interest rates

Abstract

The arithmetic of investment analysis presently in use presumes that cash flows generated by an investment are capable of earning successively period after period at a uniform rate throughout the chosen time horizon. This presumption may work out only rarely, for the rates of reinvestment available in one period may vary from those in another and. due to size constraints on opportunities, the rates of reinvestments may be different even during the same period. There is, therefore, a need to establish methods by which cash flows can be priced when reinvestment opportunities offer varying rates. This paper suggests a method of pricing the cash flows where rate of potential earning varies over time while the size of opportunity at any one point of time can be taken as large enough to accommodate the flows available then. The model developed in the paper offers, incidentally, a simple computational process to the bankers who have to compound interest accruals on deposits at interest rates varying with maturity.