Interest capitalization refers to the addition of interest earned to the principal amount, Roderigo will pay $7353.80 in interest to finish the amount of the loan.
<h3>What is interest capitalization?</h3>
Interest capitalization passes when owed interest is added to the principal amount of the loan. Interest is then charged on that advanced principal balance.
<u>Computation </u><u>of the amount of interest:</u>
Given,
Principal(P) = $8,575,
Rate(i) = 7.1%
Compounded Monthly:
![\dfrac{\frac{7.1}{12}}{1000} = 0.0059](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7B7.1%7D%7B12%7D%7D%7B1000%7D%20%3D%20%200.0059)
Time period (n):
![\text{12 Months} \times \text{4 Years} = 48 \text{Months}](https://tex.z-dn.net/?f=%5Ctext%7B12%20Months%7D%20%5Ctimes%20%5Ctext%7B4%20Years%7D%20%3D%2048%20%5Ctext%7BMonths%7D)
Now, apply the given values in the formula of compound interest(CI):
![\text{A} = \text{P}\times{(1+i)^n}-1\\\\\\\text{A} =\$8,575\times(1+7.1\%)^4^8-1\\\\\\ \text{A} = \$11,381.94](https://tex.z-dn.net/?f=%5Ctext%7BA%7D%20%3D%20%5Ctext%7BP%7D%5Ctimes%7B%281%2Bi%29%5En%7D-1%5C%5C%5C%5C%5C%5C%5Ctext%7BA%7D%20%3D%5C%248%2C575%5Ctimes%281%2B7.1%5C%25%29%5E4%5E8-1%5C%5C%5C%5C%5C%5C%20%5Ctext%7BA%7D%20%3D%20%5C%2411%2C381.94)
Then apply the formula of EMI by taking $11,381.94 as a principal, we have,
Here,
![\text{n} = 12\text{Months}\times\text{10Years} = 120\text{Months}](https://tex.z-dn.net/?f=%5Ctext%7Bn%7D%20%3D%2012%5Ctext%7BMonths%7D%5Ctimes%5Ctext%7B10Years%7D%20%3D%20120%5Ctext%7BMonths%7D)
![\dfrac{\text{p}\times i \times(1+i)^n}{(1+i)^n-1}\\\\\\\\\dfrac{\$11,381.94\times 0.0059\times(1+0.0059)^1^2^0}{(1+0.0059)^1^2^0-1}\\\\\\=\$132.74](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7Bp%7D%5Ctimes%20i%20%5Ctimes%281%2Bi%29%5En%7D%7B%281%2Bi%29%5En-1%7D%5C%5C%5C%5C%5C%5C%5C%5C%5Cdfrac%7B%5C%2411%2C381.94%5Ctimes%200.0059%5Ctimes%281%2B0.0059%29%5E1%5E2%5E0%7D%7B%281%2B0.0059%29%5E1%5E2%5E0-1%7D%5C%5C%5C%5C%5C%5C%3D%5C%24132.74)
Now, the total payment made in 120 months would be:
![\$132.74\times120=\$15,928.80](https://tex.z-dn.net/?f=%5C%24132.74%5Ctimes120%3D%5C%2415%2C928.80)
Hence, Interest paid will be:
![\$15,928.80-\$8,575 = \$7,353.80](https://tex.z-dn.net/?f=%5C%2415%2C928.80-%5C%248%2C575%20%3D%20%5C%247%2C353.80)
Therefore, the total amount of interest that would be paid by Roderigo is $7,353.80.
Learn more about interest capitalization, refer to:
brainly.com/question/417585