Question

Mr. Smith is purchasing a $ 190000 house. The down payment is 20 % of the price of the house.
He is given the choice of two mortgages:

a) a 25-year mortgage at a rate of 9 %.
Find

(i) the monthly payment: $

(ii) the total amount of interest paid: $

b) a 15-year mortgage at a rate of 9 %.
Find

(i) The monthly payment: $

(ii) the total amount of interest paid: $

Answer 1

Answer:

Given,

Loan = Price*(1-down payment%)

Monthly payment = Loan*(rate/12)/(1-1/(1+rate/12)^(12*t))

a (i)

Monthly payment = Loan*(rate/12)/(1-1/(1+rate/12)^(12*t))

substitute values

Monthly payment = 190000*(1 - 20%)*(9% / 12) / (1 - 1/(1+9%/12)^(12*20))

= 1367.58345289226

= 1367.58

(ii)

Monthly payment = Loan*(rate/12)/(1-1/(1+rate/12)^(12*t))

substitute values

Monthly payment = 190000*(1 - 20%)*(9% / 12) / (1 - 1/(1+9%/12)^(12*20))*12*20 - 190000*(1 - 20%)

= 176220.028694142

= 176220.03

b(i)

Monthly payment = Loan*(rate/12)/(1-1/(1+rate/12)^(12*t))

substitute values

Monthly payment =190000*(1 - 20%)*(9% / 12) / (1 - 1/(1+9%/12)^(12*15))

= 1541.6852079259

= 1541.69

(ii)

Monthly payment = Loan*(rate/12)/(1-1/(1+rate/12)^(12*t))

substitute values

Monthly payment = 190000*(1 - 20%)*(9% / 12) / (1 - 1/(1+9%/12)^(12*15))*12*15 - 190000*(1 - 20%)

= 125503.337426663

= 125503.34