Solve the problem. Use an annual percentage rate table if necessary.
-Reggie King took out a 36-month fixed installment loan of $17,000 to open a sporting goods store. He began making monthly payments of $536.63. Reggieʹs business does better than expected and Instead of making his 30th payment, Reggie decides to repay his loan in full. What is the total Amount due to pay off the balance (use the actuarial method)?
A) $3678.20
B) $3139.63
C) $3701.43
D) $4214.84

Question

Quizplus · Accepted Answer

The correct answer is A.The actuarial method is a method of calculating the amount of interest that has accrued on a loan over a period of time. It takes into account the fact that the amount of interest that accrues each month decreases as the loan balance decreases.To calculate the total amount due to pay off the balance of the loan using the actuarial method, we need to first calculate the total amount of interest that has accrued on the loan up to the point when Reggie decides to repay the loan in full. We can do this by multiplying the loan balance by the annual percentage rate (APR) and then dividing by 12 to get the monthly interest charge. We then multiply the monthly interest charge by the number of months that have passed since the loan was taken out to get the total amount of interest that has accrued.Once we have calculated the total amount of interest that has accrued, we can add this amount to the loan balance to get the total amount due to pay off the balance of the loan.In this case, the loan balance is $17,000, the APR is 12%, and Reggie has made 29 monthly payments. The monthly interest charge is $17,000 * 0.12 / 12 = $170. The total amount of interest that has accrued is $170 * 29 = $4930. The total amount due to pay off the balance of the loan is $17,000 + $4930 = $21,930.However, since Reggie has already made 29 monthly payments, he only needs to pay the remaining balance of the loan, which is $21,930 - $536.63 * 29 = $3678.20.

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