Say you are considering two loans. Loan F has a nominal interest rate of 5.66%, compounded monthly. Loan G has a rate of 6.02%, compounded semiannually. Which loan will give the lower effective interest rate, and how much lower will it be?

For a nominal rate compounded monthly, Loan F’s effective rate is (1 + 0.0566/12)^12 − 1 ≈ 5.809%. For Loan G, compounded semiannually, it is (1 + 0.0602/2)^2 − 1 ≈ 6.111%. Loan F’s effective rate is lower by about 6.111% − 5.809% = 0.302 percentage points, so the correct choice is “Loan F’s effective rate will be 0.302 percentage points lower than Loan G’s.”

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