# Real Estate Math Problem

Math problems dealing with real estate, debt and income can be a little tricky, but fun and extremely useful in the real world! Check out this real estate math problem to see if you can find the solution!

**This puzzle** is a DTI–Debt-to-Income–problem that banks usually utilize to calculate whether or not a potential borrower will be able to pay back the loan.

**Background Info:** Mr. and Mrs. Abrams have a combined yearly income of $90,000. They would like to purchase a commercial property on which to start a business for $215,000. They have spoken with a potential lender, who indicated they can provide a $200,000, 30 year loan at 7% interest if the Abrams can qualify. In addition to the property payment, the Abrams estimate their taxes and insurance to be $145 per month. Mr. Abrams has a student loan payment of $67 a month and Mrs. Abrams has a car payment of $347 a month. Assume an amortization factor of 6.65.

**Question:** Will the Abrams be able to qualify for this loan?

Do your own calculations, and then check below for the right steps and the correct answer.

**Step One:** Calculate their monthly income by dividing $90,000 by twelve. Their monthly income is then $7,500.

**Step Two:** Calculate their property payment by taking into account the amortization factor for a 30 year long at 7%. Their estimated monthly payment is $200 multiplied by 6.65 amortization factor, leaving them with a $1330 monthly payment.

**Step Three:** Calculate their total PITI and monthly debt. The $1300 a month, added to the $145 month, means their monthly expenses are $1475 per month. Their total monthly expenses then include the $1475, plus their $67 and $347 payments, bringing them to $1889.

**Step Four:** Calculate their Debt to Income Ratios. The first ratio is the $1475 expense versus their $7500 income, meaning that they are under the 28% threshold the bank requires. Their full expenses of $1889 versus their $7500 monthly income is just over 25%, which is still well below the 36% the bank requires.

**Solution:** Their percentage of monthly income to monthly debt is high enough that they do qualify for the loan!

*Danielle is a math whiz with a keen interest in real estate, checking on prices of land for sale in her area and calculating the probability of being approved for loans.*