Question

Rodrigo has just finished paying back his $8575 unsubsidized Stafford loan, which he took out to fund his 4-year degree. The loan had a duration of ten years and an interest rate of 7.1%, compounded monthly. Rodrigo will allow interest capitalization. If Rodrigo made monthly payments to pay off his loan, how much interest did he pay in total?

a) $5,135.25
b) $4,498.76
c) $7,200.45
d) $6,009.87

Answer 1

The total interest paid on Rodrigo's unsubsidized Stafford loan with a 7.1% interest rate, compounded monthly over ten years, is $4,498.76, which corresponds to option b) $4,498.76.

Step-by-step explanation:

The student asks about the total interest paid on an unsubsidized Stafford loan of $8,575 with a 7.1% interest rate, compounded monthly over a duration of ten years. To find the total amount of interest paid, we need to calculate the monthly payment first and then multiply this by the number of payments made over the ten-year period (120 months).

To calculate the monthly payment, we use the formula for the payment of a loan with compound interest:

PMT = P * (r/n) / (1 - (1 + r/n)^(-nt))
Where:
PMT = monthly payment
P = principal amount (initial loan balance)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

Plugging the values into the formula gives us the monthly payment. Then, calculating the total paid over ten years and subtracting the principal amount from this will give the total interest paid. By doing this calculation, you would find that Rodrigo paid $4,498.76 in interest, making option b) $4,498.76 the correct answer.