Question

A family has a \( \$ 126,626,30 \)-year mortgage at \( 7.2 \% \) compounded monthly. Find the monthly payment. Also find the unpaid balance after the following periods of time. (A) 10 years (B) 20 yea

Answer 1

Answer: The monthly payment is $859.52

(A) The unpaid balance after 10 years is $109,166.29

(B) The unpaid balance after 20 years is $73,374.27

Explanation:

The answer provided below has been developed in a clear step by step manner.Step: 1

PV = Mortgage balance = $126,626

n = 30*12 = 360 months

r = Monthly interest rate = 7.2%/12 = 0.6%

Monthly payment = [r*PV] / [1 - (1+r)^-n]

`Monthly payment = (0.6*126,626)/(1-(1+0.6)-360)`

`=859.522`

P = Monthly payment = $859.52

n = 30*12 = 360 months

r = Monthly interest rate = 7.2%/12 = 0.6%

x1 = Payments made = 10*12 = 120 months

x2 = Payments made = 20*12 = 240 months

x3 = Payments made = 25*12 = 300 months

Unpaid Balance after 10 years = P * [1 - (1+r)^-(n-x1)] / r

`Unpaid balance = 859.522 *(1-(1+0.6)-(360-120))/(0.6)%`

`=109,166.288`

Unpaid Balance after 20 years = P * [1 - (1+r)^-(n-x2)] / r

`Unpaid balance = 859.522 *(1-(1+0.6)-(360-240))/(0.6)%`

`=73,374.274`

Unpaid Balance is the present value of the remaining payments