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

Monthly rate r = 0.076/12 = 0.0063333333333.

If she pays nothing while in school (48 months), the balance after 48 months is 13100(1+r)^48, so interest capitalized = 13100[(1+r)^48 − 1].
(1+r)^48 ≈ 1.3539704832, so interest capitalized ≈ 13100(0.3539704832) = $4,637.01.

The minimum to prevent capitalization is paying the interest each month: total = 48·(13100·r) = 13100·0.304 = $3,982.40.

Difference = 4,637.01 − 3,982.40 = $654.61.

Closest answer choice: a. $654.45.