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Effective AnnuaI lnterest Rate

Different investments may provide returns based on various compounding periods. If we want to compare alternative investments that have different compounding periods, we need to state their interest on some common, or standardized, basis. This leads us to make a distinction between nominal, or stated, interest and the effective annual interest rate. The effective annual interest rate is the interest rate compounded annually that provides the same annual interest as the nominal rate does when compounded m times per year.

By definition then,

(1 + effective annual interest rate) = (1 + [i/m])(m)(1)

Therefore, given the nominal rate i and the number of compounding periods per year m, we can solve for the effective annual interest rate as follows:

effective annual interest rate = (1 + [i/m])m - 1

For example, if a savings plan offered a nominal interest rate of 8 percent compounded quarterly on a one-year investment, the effective annual interest rate would be

(1 + [0.08/4])4 - 1 = (1 + 0.02)4 - 1 = 0.08243

Only if interest had been compounded annually would the effective annual interest rate have equaled the nominal rate of 8 percent.

Table 3.7 contains a number of future values at the end of one year for $1,000 earning a nominal rate of 8 percent for several different compounding periods. The table illustrates that the more numerous the compounding periods, the greater the future value of (and interest earned on) the deposit, and the greater the effective annual interest rate.

 

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