This is “Effective Interest Rates”, section 6.6 from the book Finance for Managers (v. 0.1).
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If you are searching for the lowest interest rate for a loan, and one advertisement proclaims a 6% APR while another offers a 5.9% APR, should you always opt for the latter? It turns out to not be so straightforward because of the potential differences in compounding periods. If the 5.9% is compounded daily but the 6% is compounded yearly, you’ll have the following:
Figure 6.11 Effect of Daily Compounding
Per dollar of principal, the 6% loan is .08 cents, or .08%, better over a year. Because of more frequent compounding, the realized rate of the second, 5.9% APR loan is actually 6.08%! This is called the effective interest rateThe equivalent interest rate of a loan if it were to be compounded annually., or the equivalent rate if the loan were to be compounded annually.
The easiest way to find the effective interest rate is to take a PV of $1 and compare to the FV in one year, given the terms of the loan. Subtracting the $1 principal from the loan nets the interest, which also equals the effective interest rate. Of course, if the compounding period is annual to begin with, the APR is the effective interest rate. Typically, however, compounding is more frequent, causing effective interest rates higher than the quoted APR (much to the chagrin of many credit card holders!). Most financial calculators include a function that computes the effective interest rate. For spreadsheet users, the function is:=EFFECT(APR, # of periods in a year) =EFFECT(5.9%, 365) 0.0608
Using effective interest rates allows two or more offers to be directly compared without the need for further consideration of the compounding period.