Question

Donna took out a 25-year loan for $115,000 at an APR of 7.2%, compounded monthly, and she is making monthly payments of $827.53. What will her balance be with 15 years left on the loan?

Answer 1

the answer would be. $90,932.36

Answer 2

Her balance would be $ 90,931.84.

Explanation:

The future value of a loan is,

`F.V.=P.V.(1+i)^n-(Pmt)/(i)[((1+i)^n-1]`

Where, P.V. is the present value of the loan,

i is the rate per period,

Pmt is Payment per period,

n is the number of periods,

Here, P.V. = $ 115000,

Also the payment is paid per month,

And, annual rate of interest = 7.2 % = 0.072,

So, the rate per period ( per month ) =
`(0.072)/(12)=0.006`

( 1 year = 12 months )

Pmt = $827.53

Number of years = 25 - 15 = 10 years ( 25-year loan and we have to find her balance when 15 years left )

So, the number of periods, n = 12 × 10 = 120 months

Hence, by the above formula her balance when 15 years left is,

`F.V.=115000(1+0.006)^(120)-(827.53)/(0.006)[(1+0.006)^(120)-1]`

`=\$ 90931.8361081\approx \$ 90931.84`