Question

Roderigo has just finished paying back his $8,575 unsubsidized Stafford loan, which he took out to fund his four-year degree. The loan had a duration of ten years and an interest rate of 7. 1%, compounded monthly. Roderigo will allow interest capitalization. If Roderigo made monthly payments to pay off his loan, how much interest did he pay in total? Round all dollar values to the nearest cent. A. $4,547. 02 b. $3,426. 20 c. $7,353. 80 d. $5,436. 20.

Answer 1

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.

What is interest capitalization?

Interest capitalization passes when owed interest is added to the principal amount of the loan. Interest is then charged on that advanced principal balance.

Computation of the amount of interest:

Given,

Principal(P) = $8,575,

Rate(i) = 7.1%  

Compounded Monthly:

$\dfrac{\frac{7.1}{12}}{1000} = 0.0059$

Time period (n):

$\text{12 Months} \times \text{4 Years} = 48 \text{Months}$

Now, apply the given values in the formula of compound interest(CI):

$\text{A} = \text{P}\times{(1+i)^n}-1\\\\\\\text{A} =\ 8,575\times(1+7.1\%)^4^8-1\\\\\\ \text{A} = \ 11,381.94$

Then apply the formula of EMI by taking $11,381.94 as a principal, we have,

Here,

$\text{n} = 12\text{Months}\times\text{10Years} = 120\text{Months}$

$\dfrac{\text{p}\times i \times(1+i)^n}{(1+i)^n-1}\\\\\\\\\dfrac{\ 11,381.94\times 0.0059\times(1+0.0059)^1^2^0}{(1+0.0059)^1^2^0-1}\\\\\\=\ 132.74$

Now, the total payment made in 120 months would be:

$\ 132.74\times120=\ 15,928.80$

Hence, Interest paid will be:

$\ 15,928.80-\ 8,575 = \ 7,353.80$

Therefore, the total amount of interest that would be paid by Roderigo is $7,353.80.

Learn more about interest capitalization, refer to:

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