Question

In underwriting a new 30-year, monthly payment mortgage loan at 5% interest for Jackie, the lender requires that Jackie meet three ratios to be approved for the loan.

First, the payment on her loan plus the monthly cost of homeowner's insurance of $200 plus monthly property taxes of $225 plus monthly home owner association fees of $100 can be no more than 28% of her gross monthly income.

Second, the monthly total of the four items above plus her car loan payment of $400 per month plus her student loan payment of $250 per month can be no more than 36% of her gross monthly income.

Third, the maximum Loan to Value is 80%.

Jackie's monthly gross income is $10,800 and she has saved $200,000 for the down payment on a new home.

What is the most expensive home Jackie can purchase?

Answer 1

As per first ratio, maximum monthly mortgage payment is calculated as below :

(monthly mortgage payment + insurance + taxes + fees) = monthly gross income * 28%.

(monthly mortgage payment + 200 + 225 + 100) = 28% * 10800

monthly mortgage payment = 2499.

As per second ratio, maximum monthly mortgage payment is calculated as below :

(monthly mortgage payment + insurance + taxes + fees + car loan + student loan) = monthly gross income * 36%.

(monthly mortgage payment + 200 + 225 + 100 + 400 + 250) = 36% * 10800

monthly mortgage payment = 2713.

Of the two ratios, the first is lower. Hence, $2499 is the maximum monthly mortgage payment.

The loan amount that can be afforded with this monthly mortgage payment is calculated using PV function in Excel :

rate = 5%/12 (converting annual rate into monthly rate)

nper = 30 * 12 (30 year loan with 12 monthly payments each year)

pmt = -2499 (maximum monthly mortgage payment)

PV is calculated to be $465,518.

f =PV(5%/12,30*12,-2499) 1 $465,518

This is the maximum loan amount. This represents 80% of the home value at the maximum. Hence, maximum value of home = $465,518 / 80% = $581,897.

The most expensive home Jackie can purchase is $581,897.