Carlos pays <u>service charges</u> of $1,721. 31 while paying off the loan amount.
The <u>principle amount</u> is given as $22,375 at 5.49% <u>interest </u>or 0.0549. It needs to be <em>compounded quarterly</em>, which is in <u>4 months for 7 years.</u>
The interest amount would be:
![\frac{ 0.0549}{4} \\=0.013725](https://tex.z-dn.net/?f=%5Cfrac%7B%200.0549%7D%7B4%7D%20%5C%5C%3D0.013725)
The<u> value of n </u>is computed as:
![n=T*4\\=7*4\\=28](https://tex.z-dn.net/?f=n%3DT%2A4%5C%5C%3D7%2A4%5C%5C%3D28)
Therefore, the discount factor is derived as follows:
![D=\frac{1-(1+i)^{n} }{i} \\=\frac{1-(1+0.013725)^{28} )}{0.013725} \\=23.1177](https://tex.z-dn.net/?f=D%3D%5Cfrac%7B1-%281%2Bi%29%5E%7Bn%7D%20%7D%7Bi%7D%20%5C%5C%3D%5Cfrac%7B1-%281%2B0.013725%29%5E%7B28%7D%20%29%7D%7B0.013725%7D%20%5C%5C%3D23.1177)
Here, the monthly payment is calculated by:
![M=\frac{Amount}{D}\\=\frac{22375}{23.1177} \\=967.87](https://tex.z-dn.net/?f=M%3D%5Cfrac%7BAmount%7D%7BD%7D%5C%5C%3D%5Cfrac%7B22375%7D%7B23.1177%7D%20%20%5C%5C%3D967.87)
Thus, the final payment for 7 years that is compounded quarterly would be:
![967.871*28\\=27100.39](https://tex.z-dn.net/?f=967.871%2A28%5C%5C%3D27100.39)
The service charge here would be:
![28,821.67-27100.39\\=1721.27](https://tex.z-dn.net/?f=28%2C821.67-27100.39%5C%5C%3D1721.27)
Hence, the<em> service charge is 1721.27</em> by deducting the <u>final payment from the total payment. </u>
Learn more about interest payment calculations here:
brainly.com/question/9739031