Question

Gertrude takes out a $5,500 subsidized Stafford loan, which must be paid back in ten years. Gertrude will graduate four years after taking out the loan. If the loan has an interest rate of 6.8%, compounded monthly, and Gertrude makes monthly payments, how much interest will she pay by the time the loan is repaid? Round all dollar values to the nearest cent.

Answer 1

Interest to be paid = $2904

Explanation:

As we know the formula of per month installments

`E.M.I.=(P* r* (1+r)^(n))/((1+r)^(n)-1)`

By putting the value of P (loan applied for)=$5500

r (Monthly rate of interest)
`=(6.8)/(12* 100)`

n = number of monthly installments = 10×12 = 120

`E.M.I.=(5500* ((6.8)/(12* 100))(1+(6.8)/(1200))^(120))/((1+(6.8)/(1200))^(120)-1)`

`=(5500* .00567* (1+.00567)^(120))/((1+.00567)^(120)-1)`

`=(5500* .00567* 1.971)/(1.971-1)`

`=(61.461)/(0.971)=$63.29`

E.M.I.=$63.29

Total Installments of loan =120

Therefore total amount paid against loan = $63.39×120=7594.28

So interest paid = 7594.28-5500= $2094.28

Answer 2

Interest paid = $2,095.30

Explanation:

Gertrude takes out a $5,500 subsidized Stafford loan.

The loan has an interest rate of 6.8%, compounded monthly.

Present Value = $5,500.

Time period = 10 years. So N = 10 x 12 = 120 months.

Interest rate, R = 6.8/1200 = 0.005666667

Then PV = Pmt * [1 - (1+R)^(-N)]/(R)

5500 = Pmt * [1 - (1+0.005666667)^(-120)]/(0.005666667)

Pmt = $63.29418157

She made total repayment = 63.29418157 x 120 = $7,595.30

Interest paid = Total repayment - Loan Principal = $7,595.30 - $5,500 = $2,095.30

Interest paid = $2,095.30