Time Value of Money
If a cash flow is compounded more frequently than annually, then intrayear compoundingIntrayear Compounding:More frequent compounding than annual. is being used. To adjust for intrayear compounding, an interest rate per compounding periodInterest Rate per Compounding Period:Annual rate ÷ times-per-year compounding. must be found as well as the total number of compounding periodsNumber 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