Tamora has just graduated from college. When she entered college four years ago, she took out a $9,100 subsidized Stafford loan, which has a duration of ten years. The loan has an interest rate of 5.4%, compounded monthly. If Tamora makes monthly payments, how much interest will she have paid in total by the time the loan is paid off? Round all dollar values to the nearest cent.

a.

$2,697.20

b.

$1,574.00

c.

$5,534.00

d.

$3,888.08

I really don't understand how to do this.

  a.  $2,697.20

Step-by-step explanation:

First, you use the amortization formula to determine Tamora's monthly payment. Then you figure the total amount repaid, and subtract the principal to find the amount of interest.

The amortization formula for monthly payment A on a loan of P at interest rate r compounded monthly for t years is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

For P=9100, r=0.054, t=10, we find the monthly payment to be ...

  A = $9100(0.054/12)/(1 -(1 +0.054/12)^(-12·10)) = $98.31

The total of the 120 monthly payments Tamora makes over the period of 10 years will be ...

  ($98.31)(120) = $11,797.20

This amount is the total of the principal Tamora borrowed along with the interest on that loan. So, the amount of interest Tamora will have paid is ...

  $11,797.20 -9,100 = $2,697.20

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