The 28/36 Rule and How Lenders Use DTI
Mortgage lenders use two debt-to-income (DTI) ratios to cap the maximum loan amount:
- Front-end DTI (housing ratio): Monthly PITI ÷ gross monthly income. Most conventional lenders cap this at 28%.
- Back-end DTI (total debt ratio): (PITI + all other monthly debts) ÷ gross monthly income. Most cap this at 36%.
The binding constraint is whichever produces the lower maximum PITI. For a borrower with $8,333 gross monthly income and $500/month in other debts: front-end cap = $2,333; back-end cap = $2,500. Front-end is lower, so $2,333 is the maximum PITI.
Borrowers with heavy existing debt (car loans, student loans) are typically constrained by the back-end ratio. FHA loans allow higher ratios (31%/43% by default). VA and USDA loans focus mainly on back-end DTI — adjust the DTI caps in the advanced section for these programs.
How the Maximum Home Price Is Calculated
Property taxes scale with the home price, creating a circular dependency. The calculator resolves this algebraically:
Max price = (maxPITI − fixedCosts + downPayment × lf) ÷ (lf + scalingRate)
Where lf is the monthly P&I per dollar of loan, fixedCosts are monthly insurance and HOA (do not scale with price), and scalingRate is the monthly property tax rate as a fraction of home price.
Example: $100k income, $500/mo debts, $60k down, 7% rate, 30-year term, 1.1% tax, $1,500/year insurance → max PITI = $2,333 → max home price ≈ $344,400.
Down Payment, PMI, and the 20% Threshold
Down payment affects affordability in two ways: it directly reduces the loan amount (lower monthly P&I, higher price ceiling), and it determines whether PMI applies.
When down payment is below 20%, most conventional lenders require private mortgage insurance (PMI), typically 0.5%–1.5% of the loan amount annually. This calculator estimates PMI at 0.8% (a common midpoint). PMI is shown as an informational estimate — to conservatively account for PMI, reduce the front-end DTI cap slightly in the advanced settings.
The Rate Stress Test
The stress test recalculates your maximum home price at a rate 2 percentage points higher than your input — a realistic scenario if rates move between pre-approval and closing, or if you are evaluating an adjustable-rate mortgage.
On the $100k income example (7% → 9%), the maximum affordable price drops from ~$344,400 to ~$300,400 — about $44,000 less (13%). A rough rule: each 1% increase in rate reduces the affordable price by roughly 7%–10%.
What This Calculator Does Not Include
This is a pre-qualification estimate, not a lender approval. Not included: closing costs (2%–5% of the loan), cash reserves, moving expenses, or immediate repair costs. Actual approval depends on credit score, loan type, and lender-specific requirements. Get a formal pre-approval from a lender before making an offer.