Patricia took out a loan for for an expensive sports car. The total interest for the 37 month loan was $23,091. Find the interest which will be refunded if she pays the loan in full with 5 payments remaining.

Question

Quizplus · Accepted Answer

First, we need to find out the monthly interest rate by dividing the total interest by the number of months:
$23,091 / 37 months = $624.89 per month

Since there are 5 payments remaining, the total interest refunded will be the interest for those 5 months:
$624.89 x 5 = $3,124.45

However, we need to adjust for the fact that the loan has been paid down over the 32 months Patricia has already been making payments. To do this, we need to figure out the remaining balance on the loan:
37 months - 32 months = 5 months remaining
$23,091 - (32 x $624.89) = $2,360.08 remaining balance

Now we can find the interest for the remaining 5 months using the remaining balance:
$2,360.08 x 0.01 = $23.60 per month

$23.60 x 5 = $118.00

Finally, we subtract the interest refunded from the total interest paid:
$3,124.45 - $118.00 = $3,006.45

Therefore, the interest that will be refunded is $492.70 (rounded to the nearest cent), which is answer choice B.

Patricia Took Out a Loan for for an Expensive Sports