Mortgage affordability calculator

How the formula works

Lenders do not ask what house you want; they ask what payment your income can carry. Two ratios set the ceiling. The front-end (or housing) ratio caps the full monthly housing payment — principal, interest, taxes and insurance, the PITI — at a share \(f\) of gross monthly income. The back-end (or total-debt) ratio caps that same PITI plus your other monthly debt at a larger share \(b\). The payment you are allowed is the smaller of the two ceilings:

That maximum PITI has to cover escrow as well as the loan, so back out the part left for principal and interest by subtracting monthly property tax and insurance. Property tax is charged as a rate \(t\) on the home's value, so the tax depends on the price — the very thing we are solving for:

A P&I budget buys a loan through the amortization formula run backwards — the payment times the present-value factor — and the price is that loan plus the cash you bring:

Notice the price appears on both sides: it sets the tax, which sets the P&I budget, which sets the loan, which sets the price again. There is no tidy closed form, so this is a fixed-point solve. Guess a price, price its tax, back out P&I, size the loan, add the down payment for a new price, and repeat. Each pass moves the estimate a little; because the tax is a small fraction of the payment the guesses close in fast, and after about fifty passes the price has stopped moving to the dollar. That converged price is the answer.

What each input means

Gross annual income

Pay before tax — the figure lenders qualify you on. Both ratios are taken against gross monthly income, so this is divided by twelve.

Monthly debt payments

The minimums that show on your credit report: car loans, student loans, credit-card minimum payments, personal loans. They only enter the back-end ratio, where they eat directly into the payment you have left for housing. Utilities, groceries and insurance premiums are not counted here.

Down payment cash

The money you put in up front. It does not change the loan your income qualifies for, so it adds to the price you can reach almost dollar for dollar — and crossing 20% of the price removes PMI, which frees up still more of the payment for the loan.

Interest rate — \(r\)

The note rate. It sets how much loan a given P&I budget buys: a higher rate means each dollar of payment supports a smaller loan, so affordability falls even though your income has not changed.

Term — \(T\)

How long the loan runs. A longer term lowers the payment per dollar borrowed, so it lifts the price you qualify for — at the cost of far more interest over the life of the loan.

Property tax rate

An annual percentage of the home's assessed value, collected monthly into escrow. Because it scales with the price, it is what makes this a fixed-point solve rather than a one-line formula. Around 1.1% is a common national ballpark; check the county for the property.

Home insurance

Annual premium, also escrowed. Held as a flat dollar figure here rather than scaled to the price.

DTI limit

Which pair of ratios to apply. Conservative (28/36) is the classic rule of thumb and the safer budget. Lenient (36/43) stretches to limits many lenders will still approve — a bigger number on the page, a tighter squeeze in real life.

A worked example

The worksheet's defaults: a $90,000 income, $600 a month of other debt, $60,000 in down-payment cash, a 6.5% rate over 30 years, property tax at 1.1% of value and $1,800 a year of insurance, under the conservative 28/36 limits.

• Gross monthly income: $90,000 / 12 = $7,500.
• Front-end cap: 28% × $7,500 = $2,100 for the whole housing payment.
• Back-end cap: 36% × $7,500 − $600 debt = $2,100 left for housing after the other payments.
• The binding budget is the smaller: $2,100 — here the payment-to-income (28%) limit.
• Back out escrow: at the converged price the tax runs $295 a month and insurance $150, leaving $2,100 − $295 − $150 = $1,655 for principal and interest.
• That P&I budget buys a loan of $1,655 × (6.9918 − 1) / (0.005417 × 6.9918) = $261,836.
• Add the $60,000 down: max home price = $321,836.

The tax figure and the price above are consistent because they were solved together: 1.1% of $321,836 is $3,540 a year, which is the $295 a month used to back out the loan. That mutual consistency is exactly what the iteration delivers.

Assumptions and limits

• Lenders vary. The 28/36 and 36/43 pairs are common guidelines, not law; underwriting also weighs credit score, cash reserves, employment history and loan program, and an automated system may approve more or less than the ratios alone suggest.
• Property tax, insurance and any HOA dues are estimates. Tax is modeled as a flat percentage of value and insurance as a flat annual figure; HOA dues are not modeled at all, and where they exist they count against the same housing budget and lower the price you qualify for.
• No PMI is modeled in the budget. Putting less than 20% down adds private mortgage insurance to the monthly payment, which consumes part of the housing budget and lowers affordability below what is shown here.
• The rate is the note rate held fixed, and taxes and insurance are today's figures held flat.
• This is a pre-qualification estimate, not a pre-approval. Approval depends on documents, credit and reserves a calculator cannot see. This is arithmetic, not advice.

Questions people ask

What is the 28/36 rule?

It is the classic pair of debt-to-income limits lenders use. The first number is the front-end ratio: your total housing payment — principal, interest, taxes and insurance — should stay under 28% of gross monthly income. The second is the back-end ratio: that housing payment plus every other monthly debt should stay under 36%. On the default $90,000 income, 28% of the $7,500 monthly gross is $2,100, and 36% leaves $2,100 for housing after $600 of other debt — the smaller of the two, $2,100, is the budget this calculator works back from.

What is the difference between front-end and back-end DTI?

The front-end ratio looks only at the housing payment; the back-end ratio looks at the housing payment plus all your other required debt — car, student loans, credit-card minimums. The front-end cap protects the roof; the back-end cap protects everything else you already owe. Whichever ratio leaves less room for the mortgage is the one that binds, and the worksheet names it. Carry little other debt and the front-end ratio usually binds; carry a lot and the back-end ratio takes over.

Does a bigger down payment raise how much house I can afford?

Yes — almost dollar for dollar. Your income fixes the loan you qualify for, so extra cash mostly lands straight on top of the price. On the defaults, lifting the down payment from $60,000 to $100,000 raises the max price from $321,836 to $356,770 — about $34,934 more house for $40,000 more cash. It is a touch under dollar-for-dollar here only because a pricier home carries a little more property tax, which trims the loan. And crossing 20% of the price removes PMI, which frees up still more of the monthly budget for the loan itself.

Should I borrow the maximum I qualify for?

Approval is not the same as comfortable. The ratios here are a lender's ceiling, computed on gross pay before tax, retirement saving, childcare, commuting or anything else your budget actually carries. Many buyers deliberately borrow well under the maximum so the payment leaves room to save and absorb a bad month. The calculator shows the ceiling; the right number for you is usually below it.

How do student loans affect how much house I can afford?

They enter the back-end ratio as a monthly payment and push the price down. On the defaults, adding $500 a month of student-loan payment drops the max price from $321,836 to $252,750 — roughly $69,086 less house. What counts is the monthly minimum on your credit report, so an income-driven repayment plan that lowers that payment can raise your affordability, even though the balance is unchanged.