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.

Answer 1

___________C. $7,353.80

Answer 2

Roderigo will pay $7353.80 in interest.

Explanation:

Interest capitalization means the interest earned is added to the principle amount so first we will use compound interest formula.

Compound interest formula is :

`p(1+(r)/(n) )^(nt)`

p = 8575

r = 7.1% or 0.071

n = 12

t = 4

Putting the values in formula we get;

`8575(1+(0.071)/(12) )^(48)`

Solving this we get;

Amount = $11381.94

For the next part we have EMI formula as:

`(p* r*(1+r)^(n) )/((1+r)^(n)-1 )`

p = 11381.94

r =
`7.1/12/100=0.005917`

n =
`12*10=120`

`(11381.94*0.005917*(1+0.0059147)^(120) )/((1+0.005917)^(120)-1 )`

=
`(11381.94*0.005917*(1.005917)^(120) )/((1.005917)^(120)-1 )`

EMI = $132.74

Now total payments made in 120 months (10 years) =
`132.74*120=15928.80` dollars

Now, interest paid =
`15928.80-8575=7353.80` dollars

Hence, Roderigo will pay $7353.80 in interest.