Reconciling Compounding Periods and Payment Periods

Now that the concepts of nominal and effective interest rates are introduced, in addition to considering the compounding period (which is also known as the interest period), it is necessary to consider the frequency of the payments or receipts within the cash-flow time interval. For simplicity, the frequency of the payments or receipts is known as the payment period (PP). It is important to distinguish between the compounding period (CP) and the payment period because in many instances the two do not coincide. For example, if a company deposited money each month into an account that pays a nominal interest rate of 6% per year compounded semiannually, the payment period is 1 month while the compounding period is 6 months as shown in Figure (3-1). Similarly, if a person deposits money once each year into a savings account that compounds interest quarterly, the payment period is 1 year, while the compounding period is 3 months. Hereafter, for problems that involve either uniform-series or gradient cash-flow amounts, it will be necessary to determine the relationship between the compounding period and the payment period as a first step in the solution of the problem.

Figure (3-1): Cashflow diagram for a monthly payment period (PP) and semiannual compounding period (CP).

The next three sections describe procedures for determining the correct i and n values for use in formulas, and factor tables, as well as calculator and spreadsheet functions. In general, there are three steps:

1-      Compare the lengths of PP and CP.

2-      Identify the cash-flow series as involving only single amounts (P and F) or series amounts (A, G, or g).

3-      Select the proper i and n values.