Mortgage Affordability Calculator: How Much House?
This calculator answers the question lenders ask first: how much of your monthly income can carry a house? It takes your gross income, your existing debt payments, the cash you have for a down payment and the carrying costs of the property, and returns the maximum price you can reasonably afford with the full monthly payment split into principal, interest, taxes, insurance, PMI and HOA.
With $90,000 of gross income, $500 of monthly debts, $40,000 down, a 6.5% rate over 30 years, 1.1% property tax and 0.5% insurance:
- Maximum home price: about $292,290
- Loan amount: about $252,290
- Monthly payment: $2,100 (principal and interest $1,594.65, taxes $267.93, insurance $121.79, PMI $115.63)
- Housing ratio: 28% of gross monthly income; total debt ratio: 34.67%
How the calculator builds the number
The engine follows the way underwriters look at a file, in this order:
- Housing budget. Two limits are computed and the tighter one wins:
- Housing cap (front-end): 28% of gross monthly income.
- Total debt cap (back-end): the debt-to-income limit you choose (36%, 45% or 50%) applied to gross monthly income, minus your existing debt payments.
- Payment factor. From the interest rate and term it derives the principal-and-interest payment per dollar borrowed.
- Price solve. Because property taxes, insurance and PMI grow with the price, the engine solves for the price where the whole payment equals the housing budget, instead of multiplying a payment by a rough factor.
- PMI check. If the resulting loan is above 80% of the price, PMI is added and the price is recalculated, because PMI takes part of the budget. Write the down payment over 20% and PMI disappears from the breakdown.
Formulas
budget = min(28% × gross monthly income, DTI limit × gross monthly income − monthly debts)
gross monthly income = annual gross income ÷ 12
factor = i ÷ (1 − (1 + i)^(−months))
price = (budget + down payment × (factor + pmi factor) − HOA) ÷ (factor + pmi factor + carrying rate)
carrying rate = (property tax % + insurance %) ÷ 1200 pmi factor = PMI % ÷ 1200, applied only while the loan is above 80% of the price
Step-by-step example (calculator defaults)
- Gross monthly income: 90,000 ÷ 12 = $7,500
- Housing cap: 7,500 × 0.28 = $2,100; total debt cap: 7,500 × 0.36 − 500 = $2,200
- Budget applied: $2,100, so housing cost alone is what limits this case
- Carrying rate: (1.1 + 0.5) ÷ 1200 = 0.001333 per dollar of price
- Price solved: $292,290, of which $252,290 is the loan (LTV 86.31%, so PMI applies)
- Payment: $2,100 = principal and interest $1,594.65 + taxes $267.93 + insurance $121.79 + PMI $115.63
Scenario table (same engine, verified outputs)
| Scenario | Maximum price | Monthly payment | What changes |
|---|---|---|---|
| Defaults (90,000 income, 500 debts, 40,000 down, 6.5%, 30 years) | 292,290 | 2,100 | Baseline: the 28% housing cap binds |
| Same, but debt-to-income limit raised to 50% | 292,290 | 2,100 | No change: housing alone already hits 28% |
| 120,000 income, 2,000 debts, 60,000 down, 250 HOA | 225,926 | 1,600 | Debts and HOA eat the budget; total debt ratio reaches 36% |
| 90,000 income, 500 debts, 200,000 down | 439,526 | 2,100 | A larger down payment buys price, not a larger payment |
| Same as default on a 15-year term | 234,870 | 2,100 | A shorter term raises the payment per dollar borrowed |
Reading the result
- The binding constraint is the useful part of the answer. If the housing cap is binding, more income raises the price directly; if the total debt cap is binding, paying down a car loan or a card adds buying power month for month.
- Property tax rates are local. They run from under 0.5% to over 2% of value depending on the county, and they are charged on the whole price, so a 1% difference moves the affordable price by tens of thousands of dollars.
- PMI is a down-payment question, not a price question. Under the Homeowners Protection Act (12 U.S.C. 4902) you can request cancellation at 80% loan-to-value and the servicer must terminate it automatically at 78%, based on the original value and the original schedule.
- A shorter term is not free. Dropping from 30 to 15 years cuts the affordable price by about 20% here because the same budget carries a much larger payment per dollar.
This is an educational estimate, not a pre-approval, a loan offer or tax advice. Lenders also weigh credit score, reserves, employment history, loan type and the property itself, and they use their own debt-to-income rules; automatic underwriting can approve ratios this planning model treats as too high. Property tax and insurance rates are inputs you should replace with your county's numbers. Tax law, rates and guidelines are subject to change.
Frequently asked questions
With the calculator defaults (90,000 of gross income, 500 of monthly debts, 40,000 down, 6.5% over 30 years, 1.1% property tax and 0.5% insurance) the housing budget lands at 2,100 a month under the 28% cap, which supports a price of about 292,290 and a loan of 252,290 with PMI, since the down payment is below 20%.
There is no single legal limit. Fannie Mae allows 36% for manually underwritten loans, up to 45% when the borrower meets its Eligibility Matrix credit score and reserve requirements, and 50% for casefiles run through Desktop Underwriter. The 2020 CFPB general QM rule replaced the 43% debt-to-income limit with price-based thresholds, so 36% here is a conservative planning choice.
Lenders check two ratios: housing alone (front-end) and housing plus all debts (back-end). With few debts the 28% housing cap is the binding one; with larger debts the total debt limit decides. The calculator always applies the tighter of the two and tells you which one set the result.
PMI applies when the loan is above 80% of the home price, which is what happens with a down payment below 20%. Under the Homeowners Protection Act (12 U.S.C. 4902) you can request cancellation once the balance reaches 80% of the original value, and the servicer must terminate it automatically at 78%.
Related calculators
- Mortgage calculator: the payment and amortization side of the same loan
- Debt-to-income ratio: see how lenders score the debts you already carry
- Paycheck calculator: the take-home pay behind your monthly budget
- Mortgage refinance: whether replacing the rate lowers the payment