In order to pay off a debt that he took out today, Roger will have to make a payment of $3,500 in 15 months and $5,500 in 36 months. The interest rate is 8% compounded quarterly. What is the total amount of interest that is included in these payments?
A) $1,016.39
B) $1,493.23
C) $2,287.88
D) $7,506.77
E) $1,839.61

Question

Quizplus · Accepted Answer

To find the total amount of interest included in the payments, we first need to calculate the present value of each payment using the given interest rate and then compare it to the total payments. The formula for present value with compound interest is PV = FV / (1 + r/n)^(nt), where FV is the future value, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. After calculating the present values of both payments and summing them, subtract this sum from the total future payments ($3,500 + $5,500) to find the total interest. The correct calculation results in $1,493.23 as the total interest.

In Order to Pay Off a Debt That He Took