Jocelyn is considering taking out one of the two following loans. Loan H is a three-year loan with a principal of $5,650 and an interest rate of 12.24%, compounded monthly. Loan I is a four-year loan with a principal of $6,830 and an interest rate of 10.97%, compounded monthly. Which loan will have the smaller monthly payment, and how much smaller will it be? Round all dollar values to the nearest cent.

Use the monthly loan-payment formula: payment = principal × monthly rate ÷ [1 − (1 + monthly rate)^−number of payments]. Loan H has 36 payments at 12.24% ÷ 12 = 1.02% per month, giving a payment of about $188.31. Loan I has 48 payments at 10.97% ÷ 12 per month, giving a payment of about $176.43. Loan I’s payment is $188.31 − $176.43 = $11.88 smaller, so the correct choice is “Loan I's monthly payment will be $11.88 smaller than Loan H's.”

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