Quick Answer
Quick Answer: The maximum home price is found from two debt-to-income limits. The front-end ratio keeps your housing payment at or under 28% of gross monthly income; the back-end ratio keeps your housing payment plus other monthly debts at or under 36%. Each limit leaves a monthly budget for principal and interest, the smaller budget sets the limit, and the method solves for the loan whose payment equals that budget. Maximum price = maximum loan + down payment. On $120,000 of income with $600 of other debts, $500 a month of taxes and insurance, $60,000 down and a 6.5% 30-year rate, that is $423,884.88.
Key Takeaways
- Both ratios divide by gross (pre-tax) monthly income: annual income divided by 12
- The front-end budget is 28% of monthly income minus fixed housing costs; the back-end budget also subtracts your other monthly debts
- The smaller budget binds — with little other debt that is usually the front-end ratio, and with more debt it becomes the back-end ratio
- Fixed housing costs (property tax, insurance, HOA and PMI) count inside the housing payment for both ratios, so every dollar of them lowers the loan you can carry
- The maximum loan comes from the same amortization formula as our mortgage calculator methodology, solved for the loan amount instead of the payment
- The result is an estimate of what the ratios allow, not a lender approval: lenders apply their own limits and look at credit, reserves and the property
The Two Debt-to-Income Ratios
A debt-to-income ratio compares a monthly obligation with gross monthly income. The Consumer Financial Protection Bureau(opens in new tab) describes it as your monthly debt payments divided by your gross monthly income. Mortgage affordability uses two versions of it:
Front-end ratio = Housing payment / Gross monthly income
Back-end ratio = (Housing payment + Other monthly debts) / Gross monthly income
The housing payment is monthly principal and interest plus the fixed monthly housing costs described in Section 4. Other monthly debts are the required payments on existing obligations: car loans, student loans, credit card minimums and similar payments. Both ratios are shown as whole-number percents rounded to two decimals, so 28 means 28%.
The 28/36 rule sets the default targets: 28% for the front-end ratio and 36% for the back-end ratio. It is a common guideline rather than a single legal limit; the loan programs described in Fannie Mae's underwriting guidelines(opens in new tab) and by other agencies set their own maximums. The evaluate_affordability tool lets a caller change both targets; the calculator page uses 28 and 36.
Which Ratio Sets the Limit
Each target ratio, turned around, says how much of your monthly income is left for principal and interest once the other costs are paid:
Front-end P&I budget = 28% x Gross monthly income - Fixed housing costs
Back-end P&I budget = 36% x Gross monthly income - Fixed housing costs - Other monthly debts
The smaller of the two budgets binds. A payment that fits the smaller budget keeps both ratios at or under their targets; a payment above it breaks at least one. When the two budgets are exactly equal, the result names the front-end ratio. The tool's result names the ratio that set the limit in its binding_constraint field.
Because the back-end budget subtracts your other debts and the front-end budget does not, the switch point is easy to find: with the default targets the back-end ratio binds once your other monthly debts exceed 8% of gross monthly income (36% minus 28%). At $10,000 of monthly income that threshold is $800 a month of other debts.
| Other Monthly Debts | Front-End Budget | Back-End Budget | Ratio That Binds |
|---|---|---|---|
| $600 | $2,300 | $2,500 | Front-end |
| $800 | $2,300 | $2,300 | Front-end (tie) |
| $1,200 | $2,300 | $1,900 | Back-end |
Based on $10,000 of gross monthly income ($120,000 a year), $500 a month of fixed housing costs and the default 28% and 36% targets.
The Housing Costs Counted
The housing payment in both ratios is principal and interest plus every fixed monthly housing cost that is included. Those costs come off both budgets before any money is left for the loan, so they lower the maximum price dollar for dollar of payment.
| Cost | Calculator Page | evaluate_affordability Tool |
|---|---|---|
| Principal and interest | From home price, down payment, rate and term | Solved from the binding budget |
| Property tax | Annual field, divided by 12; defaults to 1.1% of the home price a year | One fixed monthly_property_costs amount you supply; defaults to $0 (principal and interest only) |
| Homeowners insurance | Annual field, divided by 12; defaults to 0.40% of the home price a year | |
| HOA dues | Monthly field; defaults to $0 | |
| Private mortgage insurance (PMI) | 0.7% of the loan a year, divided by 12, while the down payment is under 20% of the price |
The 1.1% property tax default is the national median effective rate from the U.S. Census Bureau's American Housing Survey(opens in new tab), the same default our mortgage calculator uses; your own tax bill can be far higher or lower. The 0.7% PMI estimate sits inside the 0.5% to 1.5% range the CFPB(opens in new tab) describes; a quote from an insurer replaces it. The tool does not estimate any of these costs for you: if you know them, fold them into monthly_property_costs, or the result is principal and interest only and its note says so.
Solving for the Maximum Loan and Price
A fixed-rate payment comes from the standard amortization formula, the one documented step by step on our mortgage calculator methodology page:
M = L [ r(1 + r)n ] / [ (1 + r)n - 1 ]
Here M is the monthly principal and interest, L is the loan amount, r is the annual rate divided by 12, and n is the term in years times 12. Affordability asks the question the other way round: which L makes M equal the binding budget B? Solved for L, the same formula reads:
L = B [ (1 + r)n - 1 ] / [ r(1 + r)n ]
Our engine does not keep a second copy of that algebra. It searches for the loan amount directly, running the mortgage payment formula itself, until the payment matches the budget to within a millionth of a dollar. The search uses the regula falsi method with the Illinois modification, kept inside its bracket by bisection. It looks between a $0 loan and a loan of 20 times annual income, it records how many steps it took, and the result's note says so if the search did not converge. On every case in this page's examples the search and the closed form above agree to the cent.
Then:
- Maximum loan is the solved loan amount, rounded to the cent
- Maximum home price = maximum loan + down payment
- Monthly payment at the maximum is the principal and interest on that loan
- Both ratios are then re-measured at the maximum and reported, so you can see how close the non-binding ratio sits to its target
At a 0% rate the payment is simply L divided by n, and the same search applies.
Worked Example: The Front-End Ratio Binds
Inputs: $120,000 gross annual income, $600 a month of other debts, $500 a month of property tax and insurance, $60,000 down, 6.5% for 30 years, default 28% and 36% targets.
Step 1: Monthly Income
- Gross monthly income = $120,000 / 12 = $10,000
Step 2: The Two Budgets
- Front-end budget = 0.28 x $10,000 - $500 = $2,300
- Back-end budget = 0.36 x $10,000 - $500 - $600 = $2,500
- The smaller is $2,300, so the front-end ratio binds
Step 3: The Loan That Payment Supports
- r = 0.065 / 12 = 0.00541667; n = 30 x 12 = 360
- (1 + r)n = 1.00541667360 = 6.99180
- L = $2,300 x (6.99180 - 1) / (0.00541667 x 6.99180) = $2,300 x 5.99180 / 0.0378722
- Maximum loan = $363,884.88
Step 4: The Maximum Price and the Ratios at It
- Maximum home price = $363,884.88 + $60,000 = $423,884.88
- Front-end ratio = ($2,300 + $500) / $10,000 = 28% (at its target)
- Back-end ratio = ($2,300 + $500 + $600) / $10,000 = 34% (2 points of room under 36%)
These are the figures evaluate_affordability returns for the same inputs. Its note adds that monthly_payment_at_max is principal and interest only, because the $500 of monthly property costs is counted separately inside the ratios.
When the Back-End Ratio Binds, and the Edge Cases
Raising Other Debts to $1,200 a Month
Keep every input from Section 6 but raise other monthly debts from $600 to $1,200:
- Front-end budget = 0.28 x $10,000 - $500 = $2,300
- Back-end budget = 0.36 x $10,000 - $500 - $1,200 = $1,900
- The smaller is $1,900, so the back-end ratio binds
- Maximum loan = $1,900 x 5.99180 / 0.0378722 = $300,600.56
- Maximum home price = $300,600.56 + $60,000 = $360,600.56
- Ratios at the maximum: front-end 24%, back-end 36%
An extra $600 a month of other debt lowered the maximum price by $63,284.32, because on this loan every dollar of monthly payment supports about $158 of principal.
No Room for a Loan
If fixed housing costs and other debts already reach the binding target, the budget is zero or negative. With $3,500 of other debts in the same example, the back-end budget is 0.36 x $10,000 - $500 - $3,500 = -$400. Rather than a negative loan, the maximum loan is reported as $0, the maximum price is the down payment alone ($60,000), and the result's note says that fixed obligations leave no room for principal and interest.
The Search Ceiling
The search stops at a loan of 20 times annual income. If even that loan keeps both ratios under target, which can only happen at a very low rate with generous targets, the result returns the ceiling, says in its note that the search was capped, and reports that nothing was solved.
How the Calculator Page Uses the Same Rules
The Mortgage Affordability Calculator starts from a home price rather than from an income, and it offers two views of the same rules.
Price First: Income Needed at 28%
You enter a price, down payment, rate, term, property tax, insurance and HOA. The page computes the full monthly payment (principal and interest, tax, insurance, HOA and PMI when the down payment is under 20%) and the gross annual income at which that payment is exactly 28% of monthly income:
Income needed = Total monthly housing payment / 0.28 x 12, rounded up to the dollar
With the page's default inputs ($300,000 price, $60,000 down, 6.5% for 30 years, $3,300 a year of property tax, $1,200 a year of insurance, no HOA):
- Loan = $300,000 - $60,000 = $240,000 (20% down, so no PMI)
- Principal and interest = $1,516.96; tax = $3,300 / 12 = $275.00; insurance = $1,200 / 12 = $100.00
- Total monthly payment = $1,891.96
- Income needed = $1,891.96 / 0.28 x 12 = $81,085 a year
With 10% down instead, the $270,000 loan adds $157.50 a month of PMI (0.7% of the loan, divided by 12), the principal and interest rises to $1,706.58, the total payment is $2,239.08, and the income needed rises to $95,961. This view applies the front-end ratio only; it does not ask about your other debts.
What Would It Take?
The calculator's "What would it take?" panel applies both ratios. You name a target price, your income and your other monthly debts, and pick one thing to change: income, down payment or rate. The panel then searches for the value of that one input at which the target price is exactly the maximum price under the 28% and 36% targets, using the same engine as evaluate_affordability. It folds the page's property tax, insurance, HOA and PMI into the fixed housing costs, so its answer and the price-first view above count PMI the same way.
Data Sources and Methodology Notes
Calculation Engine and API Access
The ratio search on this page is exposed programmatically through our public calculator API / MCP server as the tool evaluate_affordability (full input and output schema in the API reference). The tool takes annual income, monthly debt payments, down payment, rate and term, with optional monthly property costs and optional targets, and returns the maximum price, the maximum loan, the payment at the maximum, both ratios, the binding ratio and a note. The calculator page's "What would it take?" panel runs the same engine.
Interest Rate Data
The 6.5% rate in the worked examples is illustrative, not a live market quote. Freddie Mac's Primary Mortgage Market Survey(opens in new tab) publishes the weekly benchmark for 30-year and 15-year fixed rates.
Assumptions and Limitations
- Income is gross (before tax) income, the basis lenders use for debt-to-income ratios. Take-home pay is lower, so a payment that fits the ratios can still feel tight
- The rate is fixed for the whole term; adjustable-rate loans are not modeled
- Closing costs, cash reserves, credit score and the property itself are outside the ratios, but lenders weigh them
- Property tax, insurance and PMI defaults on the calculator page are estimates; your own figures replace them
- The default 28% and 36% targets are a guideline; a lender's maximum for your loan program can be higher or lower
- Rounding: money results are rounded to the cent and ratios to two decimals only at the end; the calculator's income needed is rounded up to the whole dollar
Frequently Asked Questions
The 28/36 rule is a common lender guideline with two debt-to-income limits. The front-end ratio keeps the monthly housing payment at or under 28% of gross monthly income. The back-end ratio keeps the housing payment plus every other monthly debt payment at or under 36%. Our affordability math uses 28 and 36 as its default targets; actual lender limits vary by loan program.
Whichever leaves the smaller monthly budget for principal and interest. The front-end budget is 28% of gross monthly income minus the fixed housing costs; the back-end budget is 36% of gross monthly income minus the fixed housing costs and your other monthly debts. With $10,000 of monthly income, $500 of housing costs and $600 of other debts, the front-end budget is $2,300 and the back-end budget is $2,500, so the front-end ratio sets the limit.
Principal and interest, plus the fixed monthly housing costs you include: property tax, homeowners insurance, HOA dues, and private mortgage insurance (PMI) when the down payment is under 20%. On the calculator page these are separate fields; for the evaluate_affordability tool they are one monthly_property_costs amount, and they are counted inside the housing payment for both ratios.
The binding ratio gives a monthly principal and interest budget. The method then finds the loan amount whose fixed-rate payment equals that budget, using the same amortization formula as our mortgage calculator, and adds your down payment. With a $2,300 budget at 6.5% for 30 years, the loan is $363,884.88; with $60,000 down, the maximum price is $423,884.88.
When your fixed housing costs and other debts already reach the binding target, there is no room left for a principal and interest payment, so the loan comes out at $0 and the maximum price equals the down payment. The result says so in its note rather than showing a negative loan.
Sources
- Consumer Financial Protection Bureau -- What Is a Debt-to-Income Ratio?(opens in new tab)
- Fannie Mae -- Originating & Underwriting Guidelines(opens in new tab)
- Consumer Financial Protection Bureau -- Owning a Home(opens in new tab)
- CFPB -- What Is Private Mortgage Insurance (PMI)?(opens in new tab)
- U.S. Census Bureau -- American Housing Survey(opens in new tab)
- Freddie Mac -- Primary Mortgage Market Survey (PMMS)(opens in new tab)
Important Disclaimer
Disclaimer: This content is for educational and informational purposes only and does not constitute financial, tax, or legal advice. An affordability estimate is not a loan approval: lenders set their own debt-to-income limits and weigh credit, savings and the property. Individual circumstances vary, and you should consult a qualified mortgage professional before making home buying decisions. The examples on this page use illustrative inputs and simplified assumptions.