Question

Assume the following items regarding your purchase of a home:

You have saved up $20,000 toward the purchase of your home.

Your salary is $36,000 per year.

The bank will lend you up to a total amount where your monthly home loan payment will equal 28% of your monthly salary. The bank is offering you a 30 year loan (360 payments) with an APR of 6%.

Closing costs are expected to be 4% of the total loan amount.

In light of the above factors, answer the following questions:

1. What is the maximum amount the bank will lend you?

2. If you borrow this entire amount, how much house can you buy?

(Remember, closing costs are expected to be 4% of the value of the home and that you have saved $20,000 toward your home purchase.)

Answer 1

1.

Monthly income = 36,000/12 = 3,000

Maximum monthly payment,PMT = 28% * 3000 = .28 x 3000 = 840

Number of Period, n = 30 *12 = 360

Interest Rate per month, i = 6%/12 = 0.5%

This 840 monthly amount is an annuity, which needs to be paid every month to the bank. So to calculate the loan bank will lend, we need to calculate the PV of annuity

PV= PMT [(1 - (1 / (1 + i)ⁿ)) / i] = 840 [(1 - (1 / (1 + 0.005)^360)) / 0.005]

= 840 [(1 - (1 / (1.005)^360)) / 0.005] = 168000( 1 - 0.16604) = 168,000* 0.8339 = 140,104.96

2. Closing costs includes cost such as attorney fee, application fee, brokerage fees etc. and is given as 4% of the total loan amount.

Closing costs = 0.04 x 140,104.96 = 5604.20

You saved 20,000 for the home purchase and after removing the closing fee, remaining will be down payment towards the house

Down payment = 20, 000 - 5604.20 = 14,395.80

Therefore, total Price = 140,104.96 + 14,395.80 = 154,500.76