Question

Mr. Smith is purchasing a $ 130000 house. The down payment is 20 % of the price of the house. He is given the choice of two mortgages:

a) a 30-year mortgage at a rate of 10 %.

Find (i) the monthly payment: $

(ii) the total amount of interest paid: $

b) a 15-year mortgage at a rate of 10 %.

Find (i) The monthly payment: $

ii) the total amount of interest paid: $

Answer 1

a) P = 130000
Monthly interest rate, r = 20%/12 = 1.67%

For a 30-year mortgage rate, n = 30 x 12 = 360
For a 15-year mortgage rate, n = 15 x 12 = 180

(i) The formula for monthly payment is:

M = 130000 x 1.67% x 1.0167360 / (1.0167360-1)

M = $2172.32

Total Interest = Total Paid - Principal
= 2172.32 x 360 - 130000
= $652,036.75

b) For n = 180, r = (5/3)%

Let's input into the formula,

M = $2283.19

Total Interest = Total Paid - Principal
= 2283.19 x 180 - 130000
= $280,973.38