Question

Suppose your gross monthly income is $5,600 and your current monthly payments are $475. If the bank will allow you to pay up to 36% of gross monthly income (less current monthly payments) for a monthly house payment, what is the maximum loan you can obtain if the rate for a 30-year mortgage is 4.65%? (Round your answer to the nearest cent.)

Answer 1

9514 1404 393

Answer:

$298,853.76

Explanation:

36% of your gross monthly income is ...

0.36 × $5600 = $2016

If you're already spending $475 on monthly payments, the amount the bank says you can afford for a mortgage loan is ...

$2016 -475 = $1541

__

The amortization formula can be used to find the corresponding loan value. That formula is ...

A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment on a loan of P at interest rate r for t years.

Filling in the known values, we have ...

1541 = P(.0465/12)/(1 -(1 +.0465/12)^(-12·30)) ≈ 0.00515636808·P

Then the maximum loan you can obtain is ...

P = $1541/0.00515636808 ≈ $298,853.76