Question

Hal has just graduated from four years of college. For the last two years, he took out a Stafford loan to pay for his tuition. Each loan had a duration of ten years and interest compounded monthly, and Hal will pay each of them back by making monthly payments, starting as he graduates. Hal’s loans are detailed in the table below.

Year
Loan Amount ($)
Interest Rate (%)
Subsidized?
Junior
4,048
5.9
N
Senior
5,295
7.6
Y

Once all of his loans are paid off, what will Hal’s total lifetime cost be? Round all dollar values to the nearest cent.
a.
$9,023.28
b.
$8,467.20
c.
$11,498.40
d.
$13,615.20


Please select the best answer from the choices provided

A
B
C
D

Answer 1

D

Work (summary):
- Junior loan accrues interest for 2 years before repayment (unsubsidized): P1 = 4048*(1+0.059/12)^(24) ≈ $4,550.95.
- Senior loan is subsidized, so P2 = $5,295 at repayment start.
- Monthly rates: i1 = 0.059/12, i2 = 0.076/12. Repayment term = 120 months.
- Monthly payments:
- M1 = P1 * i1 / (1-(1+i1)^-120) ≈ $50.32 → total ≈ $6,037.80
- M2 = P2 * i2 / (1-(1+i2)^-120) ≈ $63.15 → total ≈ $7,577.40
- Total lifetime cost ≈ $6,037.80 + $7,577.40 ≈ $13,615.20

Therefore the best choice is D.