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

Answer 1

Interpretation: the junior loan (unsubsidized) accrues interest while he’s still in school; the senior loan (subsidized) does not. The junior loan was taken one year earlier than the senior, so it accrues 2 years of monthly-compounded interest before repayment begins; the senior accrues 0 years.

1) Accumulate junior loan to graduation:
Pj = 4048*(1 + 0.059/12)^{24} = 4048*(1.0049166667)^{24} = $4,553.68

2) Senior loan at graduation (subsidized):
Ps = $5,295.00

3) Monthly rates and number of payments:
ij = 0.059/12 = 0.0049166667
is = 0.076/12 = 0.0063333333
n = 120 months

4) Monthly payment formula: M = P * [i / (1 - (1+i)^{-n})]

Junior monthly payment:
Mj = 4553.68 * [0.0049166667 / (1 - (1.0049166667)^{-120})] = $50.35 (approx)
Total paid on junior = 50.35 * 120 = $6,042.00 (approx)

Senior monthly payment:
Ms = 5295.00 * [0.0063333333 / (1 - (1.0063333333)^{-120})] = $63.10 (approx)
Total paid on senior = 63.10 * 120 = $7,573.20 (approx)

5) Total lifetime cost = 6,042.00 + 7,573.20 = $13,615.20

Answer: (d) $13,615.20.