An engineering graduate plans to buy a home. She has been advised that her monthly house and property tax payment should not exceed 35% of her disposable monthly income. After researching the market, she determines she can obtain a 30 year home loan for 6.95% annual interest per year, compounded monthly. Her monthly property tax payment will be approximately $150.What is the max amount she can par for a house if her disposable monthly income is $2000?

$83,107.20

Explanation:

Amount available for monthly house payment = [$ 2000 * 35% ] - $ 150

= $700 - $150

= $550

Effective rate per month = 6.95% / 12 months = 0.00579 = 0.579%

No of periods = 30 years * 12 months = 360 months

Present Value = Amount available for monthly house payments * [P/A,0.579%,360]

[P/A,0.579%,360] =[(1 + i)^n - 1] / [( 1 + i)^n * I]= [(1 + 0.00579)^360 - 1] / [( 1 + 0.00579)^360 * 0.00579]

P/A,0.579%,360 = [7.99158 - 1] / [ 7.99158 * 0.00579]

P/A,0.579%,360 = 6.99158 / 0.04627

P/A,0.579%,360 = 151.104

Present Value = Amount available for monthly house payments * [P/A,0.579%,360]

Present Value = $550 * 151.104

Present Value = $83,107.20

Thus, the max amount she can par for the house is $83,107.20

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