Brian took eight years to pay off his $71,900 loan. The loan had an interest rate of 8.16%, compounded quarterly. If Brian paid quarterly and made the same payment every time, how much was each payment that he made?

The quarterly interest rate is 8.16% ÷ 4 = 2.04%, and eight years of quarterly payments means 8 × 4 = 32 payments. For a loan repaid with equal payments, use payment = loan amount × rate ÷ [1 − (1 + rate)^−number of payments]. Substituting gives $71,900 × 0.0204 ÷ [1 − (1.0204)^−32] ≈ $3,081.54 per payment. The correct choice is $3,081.54.

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