Viola took out a $8,470 Stafford loan at the beginning of her four-year college career. The loan has a duration of ten years and an interest rate of 7.5%, compounded monthly. How much more will Viola’s monthly payment be if the loan is unsubsidized than if the loan is subsidized? Round all dollar values to the nearest cent.

 P=R(1-(1+i)^-n/i)            

Explanation:

Where P=8,470

R=Monthly installment

I=7.5%

N=10*12=120

By using above data we get R=$100.54 per month

Since the interest varies every month, it will be too long to write down how much she will save, but on the attached spreadsheet you can find the amount saved during the first 54 months.  

Viola will save $2,382.84 during the 54 months that the government will subsidize her loan.

Explanation:

The current rate for direct subsidized or direct unsubsidized undergraduate loans (4 years) is 4.53%.

The advantage of a subsidized loan is that the government pays the interest during the first 4 and a half years, so Viola will pay only principal. Since the question gave us a 7.5% rate, I will use that rate to calculate the monthly payment on an excel spreadsheet.

The monthly payment for both loans is $100.54, but Viola will have a discount during the first 54 months. The interest varies monthly, but the total amount of interest that she will save during the first 54 months (4 1/2 years) is $2,382.84.

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