Respuesta :
The amount of interest capitalized be than the minimum amount that Olivia could pay to prevent interest capitalization is $654.45.
Given that
Olivia has taken out a $13,100 unsubsidized Stafford loan to pay for her college education.
She plans to graduate in four years.
The loan has a duration of ten years and an interest rate of 7. 6%, compounded monthly.
We have to determine
By the time Olivia graduates, how much greater will the amount of interest capitalized be than the minimum amount that Olivia could pay to prevent interest capitalization?
According to the question
Olivia wants to prevent interest capitalization, she must pay the accrued interest each month.
Then,
The amount is,
[tex]\rm Interset = Principal \times Rate \times Time\\ \\ Interest = 13,100 \times 0.076\times \dfrac{1}{12}\\ \\ Interest=82.97[/tex]
If no payments are made, the loan balance grows by the multiplier (1 +r/12) each month.
Therefore,
The amount of interest that will be capitalized at the end of 48 months is,
[tex]\rm Amount = 13,100\times 1 +\left( \dfrac{0.076}{12}\right)^{12\times 4}\\ \\ Amount = 13,100\times 1 +\left( \dfrac{0.076}{12}\right)^{48}\\ \\ Amount = 13,100\times 1 +\left( 0.00633}\right)^{48 }\\ \\ Amount = 3982.40 [/tex]
Then,
The amount of interest capitalized be than the minimum amount that Olivia could pay to prevent interest capitalization is,
4636.85 - 3982.40 = 654.45
Hence, the amount of interest capitalized be than the minimum amount that Olivia could pay to prevent interest capitalization is $654.45.
To know more about Interest capitalization click the link given below.
https://brainly.com/question/1132884
