Mathematical Model: Front-End & Back-End DTI RatiosClient-Side Precision28/36 Rule Based

House Affordability Calculator

Estimate how much house you can afford based on your income, existing debts, down payment, and standard debt-to-income qualification limits — including property tax, insurance and PMI.

Financial Parameters

Adjust inputs to estimate your maximum purchase price

Pre-tax annual base & bonus
$
Liquid reserves & savings
$
Student, auto & credit cards
$/ mo
%
Quick set:
Loan Term
of price / yr
%
$/yr
if under 20% down
% / yr
Estimated Purchasing Power—
Maximum Affordable Home Price
—
Loan Amount: —Down Payment: —
Estimated Monthly Outlay (PITI + PMI)— / mo
Principal & Interest— Property Taxes— Homeowners Ins.— Private Mortg. Ins.—
Debt-to-Income (DTI) Stress Audit—
Front-End DTI (Housing Only)——
Back-End DTI (Housing + Debts)——
Conservative—

25% housing ratio, low financial friction.

Recommended—

28/36 benchmark.

Max Stretch—

High risk: 43% total DTI ceiling.

Multi-Scenario Affordability Matrix

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Underwriting Rule: 28/36 Standard

The 28/36 Underwriting Rule Explained

Lenders commonly use two debt-to-income ratios to decide how large a mortgage payment you can take on:

  • Front-End Ratio (≤ 28%): no more than 28% of gross monthly income should go to housing costs — principal, interest, property taxes and insurance (PITI), plus PMI.
  • Back-End Ratio (≤ 36%): total monthly debt payments — the new housing payment plus student loans, credit cards and auto loans — should stay within 36% of gross income.
Formula
Max PITI = min(Gross × 0.28, Gross × 0.36 − Debts)

The maximum price is the one whose full monthly cost — P&I on the loan, property tax, insurance and any PMI — exactly equals that allowed payment, with P&I from the standard fixed-rate loan formula.

The 28/36 rule explained

Lenders commonly use two ratios to determine affordability: the front-end ratio caps housing costs at 28% of gross monthly income, while the back-end ratio caps total debt payments (housing plus all other debts) at 36%. This calculator uses whichever limit is more restrictive for your situation.

These are guidelines, not hard rules — some lenders allow higher ratios (up to 43-50% back-end) for well-qualified borrowers, particularly with strong credit and stable income, while more conservative buyers may prefer to stay well under these limits.

By Suhaib Hassan · Formula verified 27 Sep 2026 · How CalculatePilot verifies formulas →

What this estimate doesn't include

Property tax is applied as a percentage of the home price and insurance as a yearly amount you enter; PMI is added at your chosen rate whenever the down payment is under 20%. Rates differ significantly by state and even by county, so use your local figures.

It doesn't include HOA fees, closing costs, or your personal comfort level with a given payment — getting pre-approved by an actual lender remains the most accurate way to know your real number.

Read the guide: How much house can you afford on a $75,000 salary?

Frequently asked questions

Why is my back-end ratio lower than my front-end limit?

The back-end ratio subtracts your existing monthly debts (car payments, student loans, credit cards) from your total allowed debt load, which often makes it the more restrictive limit if you carry other debt.

Does this account for property taxes and insurance?

Yes — enter your property tax rate and annual homeowners insurance, and PMI is added automatically when you put down less than 20%. All of them count toward the housing payment used in both ratios.

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