Miles and Nick each separately apply for and receive loans worth $5,000 apiece. Miles has a very good credit score, so his loan has an APR of 7.75%, compounded monthly. Nick’s credit score is rather low, so his loan has an APR of 13.10% interest, compounded monthly. If both of them repay their loans over a four year period, making equal monthly payments based on their own loan, how much more will Nick have paid than Miles? (Round all dollar values to the nearest cent.)
Use the fixed-payment loan formula with 48 monthly payments: payment = 5,000r ÷ [1 − (1 + r)⁻⁴⁸], where r is the APR divided by 12. Miles’s monthly payment rounds to $121.48, and Nick’s rounds to $134.39. The difference is $12.91 per month, so over 48 months Nick pays $12.91 × 48 = $619.68 more. The best choice is $619.68.
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