## Time Value of Money

Self-Paced Overview

### Intrayear Compounding

If a cash flow is compounded more frequently than annually, then intrayear compounding*Intrayear Compounding:*More frequent compounding than annual. is being used. To adjust for intrayear compounding, an interest rate per compounding period*Interest Rate per Compounding Period:*Annual rate ÷ times-per-year compounding. must be found as well as the total number of compounding periods*Number of Compounding Periods:*Number of years × number of times-per-year compounding..

The interest rate per compounding period is found by taking the annual rate and dividing it by the number of times-per-year the cash flows are compounded. The total number of compounding periods is found by multiplying the number of years by the number of times-per-year cash flows are compounded.

For instance, suppose someone were to invest $5,000 at 8% interest, compounded semiannually, and hold it for five years.

The interest rate per compounding period would be 4%.

The number of compounding periods would be 10.

(8% ÷ 2)

(5 × 2)

To solve, find the future value of a single sum looking up 4% and 10 periods in the TVM Table 1: Future Value Factors.

FV = PV(FVIF)

FV = $5,000(1.480)

FV = $7,400