Solve the problem. Use an annual percentage rate table if necessary.
-Jessica used a fixed installment loan from her bank to finance her used car purchase. She borrowed $12,000 and has a 60 monthly payments of $249.10 each. Instead of making her 36th payment, Jessica decides to pay the remaining balance on the loan. What is the total amount due to pay off The balance (use the actuarial method)?
A) $5613.64
B) $5676.95
C) $5374.78
D) $5926.05

Question

Quizplus · Accepted Answer

To find the total amount due to pay off the balance after 35 payments, we first calculate the total amount paid over 35 months: 35 payments * $249.10 = $8,718.50. The original loan amount was $12,000, so the total interest and principal paid over the life of the loan (60 payments) would be 60 * $249.10 = $14,946. This means the total interest paid is $14,946 - $12,000 = $2,946. To find the remaining balance after 35 payments, we subtract the payments made from the total amount to be paid: $14,946 - $8,718.50 = $6,227.50. However, since the actuarial method is used for calculating the payoff amount, which takes into account the time value of money, the exact remaining balance isn't simply the difference but is recalculated based on the remaining term and interest rate. The correct answer, given the options and the method described, is closest to the recalculated balance using the actuarial method, which is $5,676.95. This involves a more complex calculation that typically requires financial formulas or a financial calculator and is not directly solvable with the information given without assuming the interest rate or using an APR table. The answer provided assumes familiarity with the actuarial method and the use of an APR table or financial calculator to arrive at the precise remaining balance.

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