Question

Monica took out a 30-year loan for $130,000 at an APR of 8.4%, compounded monthly, and she is making monthly payments of $990.39. What will her balance be with 12 years left on the loan

Answer 1

$89,668.12

I took the test

Answer 2

Answer: $ 40331.781 (Approx)

Explanation:

Let Monica pay off $ x in 12 years,

Thus, for 12 years, his present value, PV = $ x

Given, APR of the loan = 8.4% = 0.084

Thus, the monthly rate of the loan, r = 0.084/12 = 0.007

The number of period in 12 years, n = 144

And, the monthly payment, P = $ 990.39

Thus, by the formula,

`(r(PV))/(1-(1+r)^(-n))=P`

`(0.007 x)/(1-(1+0.007)^(-144)) = 990.39`

`(0.007 x)/(1-0.36623195919)=990.39`

`(0.007 x)/(0.6337680408  ) = 990.39`

`0.007 x=990.39* 0.6337680408`

`0.007 x=627.677529937`

`x=89668.2185624`

Thus, He pay off $ 89668.2185624 of the original amount of the loan.

⇒The amount of loan left after 12 years

= 130,000 - 89668.2185624

=40331.7814376 ≈ $ 40331.781