Question

Helena has taken out a $9,300 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 6.4%, compounded monthly. By the time Helena graduates, how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization? Round all dollar values to the nearest cent.
a.
$238.46
b.
$496.00
c.
$595.20
d.
$324.33

Answer 1

Interest that would be capitalized at graduation (the accrued, compounded interest over 4 years) is
9300[(1 + 0.064/12)^(4·12) − 1].
The minimum she could pay to prevent capitalization is to pay the monthly interest as it accrues, totaling
9300·(0.064/12)·(4·12).

Difference = 9300{(1 + 0.064/12)^48 − 1 − (0.064/12)·48}
= 9300[(1.0053333333)^48 − 1 − 0.256]
≈ $324.33.

Answer: d.