How Much House Can You Afford? The Payment Math Lenders Use, and the Math They Don't
Lenders size your loan with debt-to-income ratios. That tells you the most you can borrow, not what you can comfortably carry. Here is how the numbers work, and how much a half-point of rate changes your price range.
"How much house can I afford?" has two very different answers. One is what a lender will approve. The other is what you can pay every month without feeling squeezed, while still saving, fixing the furnace, and living your life. The first number is usually higher.
This guide shows how lenders calculate the first number, works through an example at several interest rates, and then lists the costs that a lender's math leaves out.
The short version
- Lenders look at debt-to-income (DTI) ratios: your monthly debt payments divided by your gross monthly income.
- A common guideline is that housing costs stay around 28% of gross income and total debts around 36%, though many loan programs allow higher ratios.
- Housing cost here means PITI: principal, interest, property taxes, and homeowners insurance, plus mortgage insurance and HOA dues where they apply.
- In our example, a household earning $120,000 can afford about a $441,000 home at 6.5% under the 28% guideline. Each half-point change in the rate moves that by roughly $18,000–$21,000.
- Lender approval is a ceiling, not a target. Maintenance, utilities, savings goals, and other costs are not in the ratio.
How lenders calculate it
Front-end ratio (housing ratio):
Back-end ratio (total DTI):
Other debts include car loans, student loans, minimum credit card payments, personal loans, and child support. They usually don't include utilities, insurance other than homeowners, groceries, or childcare.
The 28%/36% guideline is traditional and widely quoted. Actual limits depend on the loan program, credit score, down payment, and cash reserves. Many lenders approve back-end ratios well above 36%. That doesn't mean it's comfortable.
The worked example
A hypothetical household:
- Gross income: $120,000 a year, or $10,000 a month
- Other debt payments: $600 a month (a car loan)
- Down payment: 20%, so no private mortgage insurance
- Property tax: 1.1% of the price per year
- Homeowners insurance: $2,000 a year
- Loan: 30-year fixed
Now work backward from $2,800 to find the price. At 6.5%:
How the rate changes the answer
Running the same calculation at different mortgage rates:
| Mortgage rate | Approximate home price | Principal and interest |
|---|---|---|
| 5.5% | $482,000 | $2,191 |
| 6.0% | $461,000 | $2,211 |
| 6.5% | $441,000 | $2,229 |
| 7.0% | $422,000 | $2,246 |
| 7.5% | $404,000 | $2,263 |
Show the numbers behind this chart
| 30-year fixed rate | Approximate home price |
|---|---|
| 5.5% | $482,000 |
| 6.0% | $461,000 |
| 6.5% | $441,000 |
| 7.0% | $422,000 |
| 7.5% | $404,000 |
Going from 5.5% to 7.5% cuts the affordable price by about $78,000, with the same income and the same monthly budget. That's why rate changes move housing markets so strongly.
What the lender math leaves out
Maintenance and repairs. A common rule of thumb is budgeting around 1% of the home's value per year, more for older homes. On a $441,000 home, that's about $370 a month that isn't in PITI.
Utilities. Owning a larger home usually means higher heating, cooling, water, and electricity costs than renting.
HOA dues and special assessments. Dues are counted by lenders. Future special assessments are not.
Rising taxes and insurance. Property taxes are often reassessed, and insurance premiums can rise significantly. Fixed-rate principal and interest stays the same, but the total payment usually doesn't. See our article on why premiums rise without claims.
Net income, not gross. DTI uses income before taxes. Your actual budget runs on take-home pay, after taxes, retirement contributions, and health insurance.
Savings goals. Retirement contributions, college savings, and an emergency fund aren't in the ratio. A house that maxes out your DTI can crowd them out.
Childcare and other large expenses. These aren't debt payments, so lenders don't count them, but they're real.
Closing costs and moving costs. Paid upfront, separate from the down payment.
A more personal way to set your budget
- Start with take-home pay. Subtract retirement savings and other goals you won't give up.
- List your real monthly costs other than housing.
- What's left is what housing can absorb, including maintenance and utilities.
- Compare that to the lender's number. If the lender approves more, that's a ceiling, not an instruction.
- Stress-test it. Could you still make the payment if insurance rose sharply, or if one income stopped for a few months?
- Keep reserves after closing. Draining savings for a larger down payment or a bigger house leaves no cushion for the first surprise repair.
Pre-approval vs. comfort
A pre-approval letter tells you what a lender is willing to lend under its rules. It doesn't know about your childcare costs, your plans to travel, or how much you want to save. Treat it as an upper bound and decide your real budget yourself.
Other ways to reach a price range
- Larger down payment reduces the loan and may remove mortgage insurance.
- Paying down other debts frees up back-end DTI.
- Buying points lowers the rate; see our guide on mortgage points.
- Adjustable-rate mortgages start lower but add risk; see fixed vs. adjustable.
- Lower-tax areas or lower-insurance-cost areas change PITI considerably.
The takeaway
Lenders measure affordability with debt-to-income ratios on gross income, which sets a ceiling on what you can borrow. Your comfortable number depends on take-home pay, maintenance, savings goals, and everything else a ratio ignores. Run both numbers, and let the lower one decide.
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