Dave is considering two loans. Loan U has a nominal interest rate of 9.97%, and Loan V has a nominal interest rate of 10.16%. If Loan U is compounded daily and Loan V is compounded quarterly, which loan will have the lower effective interest rate, and how much lower will it be?

Use the effective-rate formula: (1 + nominal rate ÷ compounding periods)^(periods per year) − 1. Loan U’s daily compounding gives an effective rate of about 10.4824%, while Loan V’s quarterly compounding gives about 10.5536%. Loan U’s rate is therefore lower by about 10.5536% − 10.4824% = 0.0712 percentage points, which rounds to 0.0713 percentage points. The correct choice is “Loan U’s effective rate will be 0.0713 percentage points lower than Loan V’s.”

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