Question

Emma Jones s plain to move this coming summer. She has not yet decided whether she wants to rent or buy a property here in Mississippi. Her monthly budget is $1500 to cover any housing expenses including rent or owners' costs (example: mortgage, hazard insurance, property taxes, and Home Owner Association fees). Estimated the maximum house value she can afford to buy. Assume the mortgage is fixed rate, 30 years maturity, 80% LTV, with no points. The interest rate that she was quoted is 4.8% with monthly payments. The value; the hazard insurance premium is 0.5% per year, and that on average you should consider $50 per month for maintenance.

Determine the required monthly payment for the mortgage and maximum house value she can afford if she buys?

Answer 1

At the outset, let me tell you that, while copying and pasting the question, you have lost at least one sentence. In the middle, your question reads "....The interest rate that she was quoted is 4.8% with monthly payments. The value; the hazard insurance..." There is something amiss. I have seen a similar question in past. To me it seems, you have lost a sentence that gives information about the property tax in the city to be 0.7% of the property value. I have used this information to solve this question below. Please do check at your end. I have assumed the property tax to be 0.7%. If it's anything different, please use the rate given in the question in lieu of 0.7%. Please don't provide a negative rating or thumbs down merely because of this.

Let's say that A be the mortgage amount Emma is able to pay per month to service the mortgage.

Frequency = monthly, Period = month

Interest rate per period, R = Interest rate per month = 4.8% / 12 = 0.40%

Number of periods, N = nos. of months in 30 years = 12 x 30 = 360

Hence, the present value of mortgage payments = Loan amount = PV of annuities, A = A / R x [1 - (1 + R)^-N]

= A / 0.4% x [1 - (1 + 0.4%)^-360] =  190.60A

LTV = 80%

Hence, maximum value of house = Loan amount / LTV = 190.60A / 80% = 238.25A

Property tax rate in the city of Oxford = 0.7% per year of the property value = 0.7% x 238.25A = 1.67A

Monthly property tax = 1.67A / 12 = 0.14A

The hazard insurance premium = 0.5% per year

Hence monthly payment = 0.5% x 238.25A / 12 = 0.10A

$50 per month for maintenance

Monthly budget towards house = $ 1,500

Hence, Monthly mortgage payment + monthly property tax + monthly hazard insurance premium + monthly maintenance expense = 1,500

Hence, A + 0.14A + 0.10A + 50 = 1,500

Or, 1.24A = 1,500 - 50 = 1,450

Hence, A = 1,450 / 1.24 = $ 1,169.35

Hence, the required monthly payment for the mortgage, A = $ 1,169.35

and the maximum house value she can afford if she buys =  238.25A = $ 278,599 (can be rounded off to $ 278,600 as well)