4
QuizMultiple Choice

Installment Loans

Question 4 • Applications and Modeling

# of Monthly PaymentsAnnual Percentage Rate (APR) 10%11%12%13%14%15%16%17%18%177.678.459.2410.0310.8211.6212.4213.2314.04188.108.939.7710.6111.4512.2913.1413.9914.85Your friend just purchased a new hybrid for $25,236. She received $3,110 for her trade in and used that money as a down payment for the new hybrid car. She financed the vehicle at 12% APR over 48 months. She received a stipend from school and paid off the loan after making 30 payments. Use the actuarial method formula and the table above to determine the amount of unearned interest given that her monthly payment is $582.74.

Answer
A
$1,402.00
B
$1,230.72
C
$933.59
D
$582.74

Explanation

After 30 of 48 payments, 18 payments remain, totaling 18 × $582.74 = $10,489.32. Under the actuarial method, discount those remaining payments at the monthly rate of 12% ÷ 12 = 1% to find the payoff balance: $582.74 × [1 − (1.01)⁻¹⁸] ÷ 0.01, which is about $9,555.73. The unearned interest is $10,489.32 − $9,555.73 = about $933.59, so the answer is $933.59.

AI-written and checked against the verified answer.

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