Tiffany has taken out a loan with a stated interest rate of 8.145%. How much greater will Tiffany’s effective interest rate be if the interest is compounded weekly than if it is compounded semiannually?

For a nominal annual rate of 8.145%, the effective rate is (1 + 0.08145/n)^n − 1, where n is the number of compounding periods per year. Weekly compounding (n = 52) gives about 8.4790%, while semiannual compounding (n = 2) gives about 8.3109%. The difference is about 8.4790% − 8.3109% = 0.1681 percentage points, so the correct choice is 0.1681 percentage points.

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