You are ready to buy a house, and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $48000 (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 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan. How much can you offer for the house

So we can offer for the house $180119.95

Explanation:

Monthly income = $4000

Monthly mortgage payment allowed (P) = 25% of 4000 = $1000

Interest rate per month (i) = 0.5%

Number of months in total (n) = 30*12 = 360

Maximum loan affordable = P * (1 - (1 / (1+i) ^n)) / i

=1000 * (1 - (1 / (1+0.5%) ^360)) / 0.5%

=$166791.61

Closing cost is 4% of loan value = 166791.61*4% = $6671.66

Balance Amount left for down payment = 20000-6671.66

=$13328.34

It means we can pay $6671.66 for closing cost of Loan and $13328.34 for down payment.

Cost of house paid maximum = Down payment + Affordable loan

=13328.34+166791.61

=$180119.95

So we can offer for the house $180119.95