Question

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?

Answer 1

By calculating 35% of the graduate's disposable income, we find a figure of $700. Subtracting monthly property tax payment from that, we have $550 as the maximum monthly loan payment she can afford. Using the loan payment formula with her interest rate and loan term, we can determine the maximum loan amount she can take.

Step-by-step explanation:

To determine the maximum amount the engineering graduate can pay for a house based on her disposable monthly income, we must first calculate 35% of her disposable monthly income, which will be the maximum monthly payment for house and property tax she can afford. Then, we subtract the monthly property tax amount to find the maximum monthly loan payment she can make.

Calculation:
35% of $2000 = 0.35 × $2000 = $700
Maximum monthly loan payment = $700 - $150 (property tax) = $550

Now, we use the loan payment calculation formula to determine the maximum loan amount. Assuming n = number of monthly payments (30 years × 12 months = 360) and r = monthly interest rate (6.95% annual interest ÷ 12 months = approximately 0.00579), the formula for the monthly payment for a fixed-rate loan is:
PMT = P × r / (1 - (1 + r)^-n), where P = principal loan amount and PMT = monthly loan payment. Solving the equation for P gives us the maximum loan amount the graduate can afford.

Answer 2

$83,107.20

Step-by-step 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