Home Affordability Calculator

How home affordability is worked out

One of the main things lenders check is your debt-to-income ratio (DTI): monthly debt payments divided by gross monthly income. Two versions are common:

• Front-end (housing) ratio — the full housing payment (principal, interest, property tax, insurance, HOA and any mortgage insurance) divided by income.
• Back-end (total) ratio — the housing payment plus every other monthly debt payment divided by income.

A widely used rule of thumb is 28/36: housing up to 28% of gross income and all debts up to 36%. The calculator works out the most you could pay for housing under each limit, takes the smaller, and then finds the highest home price whose payment fits — with your down payment fixed, so a higher price means a bigger loan. The result tells you which limit decided the price: with few other debts the housing limit usually binds; with a car loan or student loans the total limit takes over.

These percentages are guidelines, not law. Actual limits depend on the loan program and the lender’s underwriting. Fannie Mae, for example, sets no separate housing ratio: its maximum total DTI is 36% for manually underwritten loans, up to 45% with qualifying credit scores and reserves, and 50% for loans run through its automated Desktop Underwriter. FHA, VA and USDA loans have their own rules. The table under the calculator shows prices at the stretch ratios so you can see how much of your budget they would use.

The affordability formula

First the housing payment you can carry:

Then the highest price whose total payment is at most H:

I

gross monthly income (annual income ÷ 12)

F

front-end (housing) limit, e.g. 28%

B

back-end (total debt) limit, e.g. 36%

D

other monthly debt payments

M

principal-and-interest payment on the loan L = P − down: L × r ÷ (1 − (1 + r)⁻ⁿ), r = rate ÷ 12

PMI

loan × PMI rate ÷ 12 when the down payment is under 20% of the price, otherwise 0

Because property tax and PMI depend on the price, there is no neat formula to solve for P. The calculator searches for it instead: the payment only goes up as the price goes up, so it narrows the range until it finds the highest price, to the cent, whose payment is still within the limit. One cent more and the payment would break it.

Worked example

You earn $100,000 a year, pay $500 a month on a car loan and have $40,000 for a down payment. Rates are 6.5% on a 30-year loan, property tax is 1.1% a year, insurance $1,800 a year and PMI 0.5%.

1. Monthly income: $100,000 ÷ 12 = $8,333.33
2. Housing limit: $8,333.33 × 28% = $2,333.33
3. Total limit: $8,333.33 × 36% − $500 = $2,500.00
4. The housing limit is lower, so it decides the price.
5. Highest price with a payment of $2,333.33 or less: $320,462, a loan of $280,462.69

At that price the payment is $1,772.71 principal and interest + $293.76 property tax + $150.00 insurance + $116.86 PMI (the down payment is 12.5%, under 20%) = $2,333.33.

At Fannie Mae’s 45% total ceiling the same buyer could reach about $440,226, with a $3,250 housing payment — about 37% more house, with more than a third of gross income going to housing.

Before you rely on the number

• The maximum is not a target. DTI uses gross income; your take-home pay after tax and retirement contributions is lower. Check the payment against your real budget — the income tax calculator and salary calculator help.
• Cash beyond the down payment. Closing costs, moving and early repairs need money too, and lenders may want reserves left after closing.
• Rates move the answer a lot. Every rise in the rate raises the payment on the same loan, so the affordable price falls. Try a rate a point higher to see how much room you have.
• Count every debt. Lenders include minimum card payments, student loans, car loans, and child support or alimony.