Question

Viola took out a $8,470 Stafford loan at the beginning of her four-year college career. The loan has a duration of ten years and an interest rate of 7.5%, compounded monthly. How much more will Viola’s monthly payment be if the loan is unsubsidized than if the loan is subsidized? Round all dollar values to the nearest cent.
a.
$35.05
b.
$45.94
c.
$96.96
d.
$63.52

Answer 1

Unsubsidized: interest accrues during 4 years (48 months), so principal at repayment start
P_unsub = 8470(1 + 0.075/12)^{48} ≈ 11422.93.

Monthly rate r = 0.075/12 = 0.00625, n = 120. Payment formula M = P * r / (1 − (1+r)^{-n}).

Compute the factor: r/(1−(1+r)^{-120}) ≈ 0.01187085.

Subsidized monthly payment: M_sub = 8470(0.01187085) ≈ $100.55.
Unsubsidized monthly payment: M_unsub = 11422.93(0.01187085) ≈ $135.60.

Difference = 135.60 − 100.55 = $35.05.

Answer: (a) $35.05.