Question

I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments. Find the value of the mortgage on their house and the value of the monthly payment.

Answer 1

I.             Value of Mortgage

Worth of house = $326,000

Deposit paid = $75,000

J12 = 9% p.a

T = 30 years = $30\times12 = 360months$

Mortgage = House price – Deposit paid

Mortgage = $326,000 - $75,000

Mortgage value = $ 251,000

II.           Value of the monthly payment.

Interest rate per month = $9\% / 12 = 0.75\% per month$

251,000 =$PMT \times (1-(1+0.0075)^{-360}) /0.0075$

PMT = $(251,000 \times 0.0075) / (1-(1.0075)^{-360})$

PMT = $1882.5 / (1-(1.0075)^{-360})$

PMT = $1882.5 / 0.932113993$

PMT = $ 2019.602769