Compounding Interest Periods Shorter Than a Year

The present value examples all involved periods of one year. In many situations, however, interest is compounded over shorter periods. For example, the interest rate on bonds is usually stated as an annual rate but interest is often paid every six months (semiannually).

This means that the present value of interest payments from such bonds must be computed using interest periods of six months.
Assume that a borrower wants to know the present value of a series of 10 semiannual payments of $4,000 made over five years at an annual interest rate of 12%.

The interest rate is stated as an annual rate of 12%, but it is actually a rate of 6% per semiannual interest period. To compute the present value of this series of $4,000 payments, go to row 10 of Exhibit 14A.6 and across to the 6% column to find the factor 7.3601. The present value of this annuity is $29,440 (7.3601 × $4,000).

Example: If this borrower makes five semiannual payments of $8,000, what is the present value of this annuity at a 12% rate? Answer: 4.2124 × $8,000 = $33,699