Question

Ursula took out an unsubsidized Stafford loan to help pay for her first of her four years at college. The loan had a principal of $6,400, an interest rate of 6.9% compounded monthly. After college, Ursula started making monthly payments over a 10 year period on her loan. What percentage of the total cost of the loan is the finance charge?
a.
45.25%
b.
27.91%
c.
43.50%
d.
82.66%

Answer 1

Answer: a. 45.25%

Work:
- monthly rate r = 0.069/12 = 0.00575.
- balance after 4 years (48 months): 6400(1.00575)^48 ≈ $8,427.74.
- monthly payment for 120 months: PMT = 8427.74·0.00575 / (1 − (1.00575)^−120) ≈ $97.45.
- total paid = 97.45·120 ≈ $11,693.64.
- finance charge = total paid − original principal = 11,693.64 − 6,400 = $5,293.64.
- percent of total cost that is finance charge = 5,293.64 / 11,693.64 ≈ 0.4525 = 45.25%.