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.

$1,926.97

Explanation:

Given the following :

Loan amount (L) = 8,180

Interest rate (I) = 5.3%

Period (n) = 4 years

Using the formula:

A = L(1 + I/t)^nt

Where A = final amount

t = number of compounding periods per year

A = 8180( 1 + 0.053/12)^(4 * 12)

A = 8180 ( 1 + 0.0044166)^48

A = 8180 * ( 1.0044166)^48

A = 8180 * 1.2355709

A = 10106.970

Final amount after 4 years = 10,106.970

Hence amount Paid as interest over that period will be :

Final amount - Loan amount

10,106.970 - 8,180

= $1,926.97

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