Question

Antonio 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. Antonio will pay each of them back by making monthly payments, starting as he graduates. Antonio’s loans are detailed in the table below.
Year
Loan Amount ($)
Interest Rate (%)
Subsidized?
Junior
5,894
6.9
Y
Senior
5,258
7.5
N

Once all of his loans are paid off, what will Antonio’s total lifetime cost be? Round all dollar values to the nearest cent.
a.
$16,246.80
b.
$17,804.40
c.
$7,593.16
d.
$9,874.76

Answer 1

Answer: a. $16,246.80

Work (sketch):
- Junior loan: P1 = $5,894, annual rate 6.9% → monthly r1 = 0.069/12 = 0.00575. Ten years → n = 120 months. Monthly payment
m1 = P1 * [r1 / (1 − (1+r1)^−120)] ≈ $68.16, total paid = 120·m1 ≈ $8,179.20.
- Senior loan is unsubsidized so interest accrues while in school for one year; principal at repayment equals
P2' = 5,258·(1 + 0.075/12)^12 ≈ $5,665.91.
With monthly r2 = 0.075/12 = 0.00625 and n = 120,
monthly payment m2 = P2' * [r2 / (1 − (1+r2)^−120)] ≈ $67.23, total paid = 120·m2 ≈ $8,067.60.
- Total lifetime cost ≈ $8,179.20 + $8,067.60 = $16,246.80.

Thus choice (a) is correct.