The total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.
<h3>What is compound interest?</h3>
Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount with the compound interest formula can be given as,
![A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\](https://tex.z-dn.net/?f=A%3DP%5Ctimes%5Cleft%281%2B%5Cdfrac%7Br%7D%7Bn%5Ctimes100%7D%5Cright%29%5E%7Bnt%7D%5C%5C)
Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate<em> r </em>of in the time period of <em>t.</em>
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.
Put the values in the above formula as,
![5500=P_{mt}\times\left(1-\dfrac{6.8}{12\times100}\right)^{-12\times10}\\P_{mt}=63.29](https://tex.z-dn.net/?f=5500%3DP_%7Bmt%7D%5Ctimes%5Cleft%281-%5Cdfrac%7B6.8%7D%7B12%5Ctimes100%7D%5Cright%29%5E%7B-12%5Ctimes10%7D%5C%5CP_%7Bmt%7D%3D63.29)
In the 10 years, the refund she gets,
![A_r=63.29\times12\times100\\A_r=7594.8](https://tex.z-dn.net/?f=A_r%3D63.29%5Ctimes12%5Ctimes100%5C%5CA_r%3D7594.8)
Interest paid by her is,
![I=7594.8-5500\\I=2094.8](https://tex.z-dn.net/?f=I%3D7594.8-5500%5C%5CI%3D2094.8)
Thus, the total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.
Learn more about the compound interest here;
brainly.com/question/24274034