Question

Jessica took out a Stafford loan worth $7,175 at the beginning of her six-year college career. The loan has a duration of ten years and an interest rate of 6.3%, compounded monthly. How much greater will Jessica’s monthly payment be if the loan is unsubsidized than if the loan is subsidized? Round all dollar values to the nearest cent.
a.
$36.98
b.
$23.07
c.
$37.67
d.
$166.37

Answer 1

Monthly rate r = 0.063/12 = 0.00525. Repayment period n = 10 years = 120 months. Principal P = $7,175.

If subsidized, balance at repayment start = P, so monthly payment
M_s = P * r / (1 - (1+r)^(-120)).

If unsubsidized, interest accrues for 6 years = 72 months, so balance at repayment start
P' = P*(1+r)^{72},
and monthly payment
M_u = P' * r / (1 - (1+r)^(-120)).

Compute (1+r)^{72} ≈ (1.00525)^{72} ≈ 1.4579185, so P' ≈ 7175(1.4579185) ≈ 10460.57.
Also 1 - (1+r)^{-120} ≈ 1 - (1.00525)^{-120} ≈ 0.466379, so the common factor r/(1 - (1+r)^{-120}) ≈ 0.011256.

Thus
M_s ≈ 7175(0.011256) ≈ $80.77,
M_u ≈ 10460.57(0.011256) ≈ $117.75.

Difference M_u - M_s ≈ $117.75 - $80.77 = $36.98.

Answer: (a) $36.98.