Question

Olivia has taken out a $13,100 unsubsidized Stafford loan to pay for her college education. She plans to graduate in four years. The loan has a duration of ten years and an interest rate of 7.6%, compounded monthly. By the time Olivia graduates, how much greater will the amount of interest capitalized be than the minimum amount that Olivia could pay to prevent interest capitalization? Round all dollar values to the nearest cent.
a. $654.45
b. $477.27
c. $995.60
d. $354.22

Answer 1

If Olivia wants to prevent interest capitalization, she must pay the accrued interest each month. That amount is

... I = Prt = $13,100×0.076×(1/12) = $82.97

Over 4 years (48 months), these payments total $82.97×48 = $3982.56.

_____

If no payments are made, the loan balance grows by the multiplier (1 +r/12) each month. Then the amount of interest that will be capitalized at the end of 48 months is ...

... $13,100×((1 +0.076/12)^48 -1) = $4637.01

The difference in these amounts is ...

... $4637.01 -3982.56 = $654.45 . . . . . matches selection a.