You are ready to buy a house, and you have $25,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $48,000 (monthly income $4000) , and the bank is willing to allow your monthly mortgage payment to be equal to 25% of your monthly income. The interest rate on the loan is 7.2% per year with monthly compounding (.6% per month) for a 30-year fixed rate loan. How much money will the bank loan you

The bank will loan you $147,321.36.

Explanation:

The amount the ban will loan can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value of the of loan or the amount the bank will loan you =?

P = Monthly mortgage payment = Monthly salary * 25% = $4,000 * 25% = $1,000

r = Monthly interest rate = 7.2% / 12 = 0.072 / 12 = 0.006

n = number of months = 30 years * 12 months = 360

Substitute the values into equation (1) to have:

PV = $1,000 * ((1 - (1 / (1 + 0.006))^360) / 0.006)

PV = $1,000 * ((1 - (1 / 1.006)^360) / 0.006)

PV = $1,000 * ((1 - 0.99403578528827^360) / 0.006)

PV = $1,000 * ((1 - 0.116071859187515) / 0.006)

PV = $1,000 * (0.883928140812485 / 0.006)

PV = $1,000 * 147.321356802081

PV = $147,321.36

Therefore, the bank will loan you $147,321.36.

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