Question

Sebastian has just graduated after four years of university. He took out an unsubsidized Stafford loan worth $8,180 to help pay for his tuition. The loan has a duration of ten years. If the loan has an interest rate of 5.3%, compounded monthly, how much interest capitalization has occurred by the time he graduated? Round all dollar values to the nearest cent.
a.
$721.93
b.
$842.25
c.
$1,926.97
d.
$1,734.24

Answer 1

Interest accrues monthly for 4 years (48 months) at monthly rate r = 0.053/12.

Capitalized interest = 8180[(1 + r)^48 − 1]
= 8180[(1 + 0.053/12)^48 − 1]
≈ 8180(1.2355712887 − 1)
≈ 8180(0.2355712887)
≈ $1,926.97

Answer: c. $1,926.97