Question

Barb is a freshman attending a 4-year college. She has been approved for a $12000

subsidized federal loan at 4.29% for 10 years. How much will the U.S. Department of
Education pick up in interest costs during her 4.5-year non-payment period?

Answer 1

The amount in interest accruable to the U.S. Department of Education after 4.5 years is $2,882.33

Explanation:

The given parameters are;

The amount, P of subsidized federal loan Barb has been approved for = $12,000

The interest rate at which the loan was approved, r = 4.29%

The duration of the loan = 10 years

The interest after 4.5 years is given as follows;

`A = P * \left (1 + (r)/(n) \right ) ^(n \cdot t)`

Where;

A = The total amount of the loan plus interest after a given time period

n = The number of compounding of the interest per annum

Plugging in the values, we get;

`A = 12,000 * \left (1 + 0.049 \right ) ^(4.5) \approx 14,882.33`

The interest, i, is therefore given as follows;

i = A - P = 14,882.33 - 12,000 = 2,882.33

The interest, i after 4.5 years = $2,882.33

The amount in interest accruable to the U.S. Department of Education after 4.5 years = $2,882.33.