Question

A lakefront house in Kingston, Ontario, is for sale with an asking price of $457,700. The real estate market has been quite active, so the house will almost certainly attract several offers, and may sell for more than the asking price. Charlie is very eager to purchase this house, but is concerned that he may not be able to afford it. He has $126,000 available for a down payment, and can pay up to $1,790 per month on a mortgage loan. As Charlie is a long-time customer, his bank has offered him a great mortgage rate of 4.1 percent on a one-year term. If the loan will be amortized over 25 years.

What is the most that Charlie can afford to pay for the house? (Round effective monthly rate to 4 decimal places, e.g. 5.1235% and final answer to 2 decimal places, e.g. 125.12. Do not round your intermediate calculations.)

Answer 1

Sol:

House cost = $457,700

Down payment = $126,000

Monthly payment (PMT) =$1790

Loan period = 25 years, Monthly = 25 x 12 = 300

Interest rate = 4.1% per year, Monthly rate = 4.1/12 = 0.3417%

The most that Charlie can afford to pay for the house is by finding present value of annuity:

Present value (PV) = PMT x (1-(1/(1+r)^n)/r

PV = 1790 x (1-(1/(1+0.3417%)^300) / 0.3417%

PV = 1790 x (1-(1/(1.003417%)^300) / 0.003417

PV = 1790 x 0.640576 / 0.003417

PV = 1790 x 187.4857

PV = $335,599.41

The most Charlie can afford to pay for the house will be:

PV of annuity + Down payment

$335,599.41 + $126,000 = $461,599.41

Therefore most Charlie can afford to pay for the house will be $461,599.41