Question

At the beginning of each of her four years in college, Miranda took out a new Stafford loan. Each loan had a principal of $5,500, an interest rate of 7.5% compounded monthly, and a duration of ten years. Miranda paid off each loan by making constant monthly payments, starting with when she graduated. All of the loans were subsidized. What is the total lifetime cost for Miranda to pay off her 4 loans? Round each loan's calculation to the nearest cent.
a.
$23,650.00
b.
$29,481.08
c.
$7,834.32
d.
$31,337.27

Answer 1

Compute one loan's amortized payment, then multiply by 4.

Monthly rate r = 0.075/12 = 0.00625, n = 10·12 = 120 months.
Monthly payment for one loan:
A = 5500 · [r / (1 − (1 + r)^(−120))] ≈ 5500 · 0.011869 = $65.286 (rounded).
Total paid on one loan = 120 · A ≈ $7,834.32 (rounded to the nearest cent).
Total for four loans = 4 · 7,834.32 = $31,337.27.

Answer: d. $31,337.27