Question

Following his high school graduation, Brandon buys a new laptop for $1,500 through BestSpend's payment program which requires no money down and only a $40/month payment at the end of each month. Interest on purchases through this program accrues at 25% APR compounded monthly.

Instead of the $40/month minimum payment, assume that Brandon decides to pay $100 each month. How long will it take Brandon to pay off his laptop now? (see Practice Problem 4)
A. 20.1 months
B. 17.7 months
C. 18.2 months
D. It will take Brandon just as long to pay off the loan as the $40/month payment would.

Answer 1

C) 18.2 months

Step-by-step explanation:

If Brandon had paid only $40 per month with such a high APR, it would have taken him almost 74 months to pay for the computer. But since he paid $100 per month, then he will need to pay for only 18.2 months.

A 25% APR represents over $362 in interests during the first year, while his total payments would have been only $480. That is why it would have taken so long to pay the debt. By paying 2.5 times more money, the total time needed to pay the debt is only one fourth of the established schedule.