Question

The Tremblays have been preapproved by their bank to enter the housing market with a mortgage interest rate of 8.6%. They have $30,000 set aside for a down payment. They have also calculated that they can afford a monthly payment of $1,350. They have narrowed their search to three houses and are hoping that financial constraints will narrow their choices. The three houses will cost the following amounts: $150,000, $270,000, and $400,000. The bank will add $50 to each mortgage payment if they put less than 20% down and an additional fee of $50 more to each payment if they put less than 10% down.
Which of these houses can they afford with a 30-year mortgage?
Which of these houses can they afford with a 15-year mortgage?

Answer 1

Solution:

Look at the tables below. I have answered the question in the form of a table. You need Microsoft excel or financial calculator to solve this problem. I used excel for this. I have given formulae in the second column of the sheet. I will explain on scenario taking House 2 for 30 year mortgage and I will calculate the monthly payment that need to be done.

The total cost of House 2 is $ 270,000. Tremblays are ready to pay a down payment of $ 30,000. So Tremblays have to take a loan of $ 240,000 to buy the house.

Given that the annual mortgage rate is 8.6%. The monthly mortgage can be calculated by dividing it by 12 for 12 months. So monthly mortgage rate is 0.717%.

Life of the Mortgage is 30 years i.e. 360 months.

The total payment for month can be calculated in excel using the formula

“=PMT(monthly interest rate, No. of months, -Total loan amount)”

By using this formula the monthly mortgage rate comes to $ 1862.43. But it’s stated in the problem that there is additional amount of $ 50 to be paid to the bank if the down payment is less than 20% and an amount $ 100 to be paid if the down payment is less than 10%.

Down payment of $ 30,000 is 11% of $ 270,000 (cost of house). So the additional monthly payment needed is $ 50 per month.

The total monthly payment in this case is $ 1,862.43 + $ 50 = $ 1912.43

Scenario 1: 30 year mortgage

The monthly amount that needed to be paid for House 1, House 2, and House 3 are $ 931.21, 1912.43 and 2971.24 respectively. But, Tremblays can make a monthly payment of $ 1,350 only. So they can afford only House 1 for $ 931 monthly payment.

Scenario 2: 15 year mortgage

Similar to scenario 1, Tremblays can afford only House 1 for monthly payment of $ 1188.73