Approved Mortgage Calculator
Pre-approval is a lender’s answer to one question: given your income and debts, what is the biggest monthly payment you can carry? The math is the 28/36 rule: housing costs up to 28% of gross monthly income, and all debts including housing up to 36%. Whichever ceiling is lower sets your payment, and the payment sets the loan.
The Approved Mortgage Calculator below runs that underwriting logic: it takes your income, co-borrower income, and monthly debts, applies both DTI ceilings, reverse-solves the amortization formula for the maximum loan at your rate and term, and adds your down payment for the maximum purchase price.
Quick Answer
Key takeaways
- The 28/36 rule: housing to 28% of gross income, all debts to 36%; the lower ceiling wins.
- Debts are the lever: every $100/month of debt cuts roughly $15,000-$20,000 of approval.
- The estimate covers principal and interest only: taxes, insurance, and HOA sit on top.
- FHA allows 31/43, VA uses a 41% back-end guideline: programs differ.
How the 28/36 rule sets your payment
Two ceilings, one payment. The front-end ceiling caps housing costs at 28% of gross monthly income. The back-end ceiling caps all monthly debt (housing plus car, cards, student loans) at 36% of gross income, so your housing budget is 36% minus existing debts. The lower of the two is your maximum P&I payment. Then the amortization formula converts that payment into a loan amount at your rate and term.
Gross monthly income is simply annual income divided by 12, plus any co-borrower income and documented other income. Lenders count contractual debts only: car payments, minimum card payments, student loans, support obligations. Utilities and groceries do not count, however real they feel. Once the approval amount is set, price the actual monthly payment with a mortgage payment calculator, which adds the taxes and insurance this P&I budget leaves out.
Worked example, checked against this exact tool
With the pre-filled defaults ($120,000 income, $800/month debts, 6.5%, 30 years, $60,000 down), the calculator returns:
| Figure | Amount |
|---|---|
| Gross monthly income | $10,000 |
| Front-end ceiling (28%) | $2,800 |
| Back-end ceiling (36% – $800) | $2,800 |
| Max monthly P&I | $2,800 |
| Maximum loan | $442,990 |
| Maximum purchase price | $502,990 |
By hand: monthly rate 0.065/12 = 0.0054167; the annuity factor (1 – 1.0054167-360) / 0.0054167 = 158.21; 2,800 x 158.21 = 442,990; plus $60,000 down = $502,990. Now raise the car payment by $100: the back-end ceiling drops to $2,700 and the approval falls by about $15,800. That is the debt lever in action.
DTI ceilings by loan program
| Loan program | Front-end | Back-end | Notes |
|---|---|---|---|
| Conventional | 28% | 36% | The classic standard; this calculator’s default |
| FHA | 31% | 43% | More room; 3.5% minimum down payment |
| VA | – | 41% | No front-end test; residual income test instead |
| USDA | 29% | 41% | Rural properties; income limits apply |
Strong compensating factors (big reserves, excellent credit, low LTV) can stretch these ceilings at individual lenders. The table is the guideline; the underwriter is the reality.
Pre-approval vs pre-qualification
Pre-qualification
- Based on self-reported numbers
- No document verification, no credit pull
- A rough estimate in minutes
- Sellers treat it as nearly meaningless
Pre-approval
- Based on verified income, debts, and credit
- Hard credit inquiry, underwriter review
- A conditional commitment letter
- What sellers actually want to see
This calculator estimates the pre-approval math, not the pre-approval letter. The letter requires the documents; the math is what the documents get fed into. If you want the companion question answered directly, will this income actually be approved for this home, the home loan approval calculator runs the same lender ratios and names the binding constraint.
What competing calculators miss
Only one DTI ratio. Tools that apply just the 28% rule overstate approval for anyone with real debts; tools that apply just 36% overstate it for the debt-free. Both ceilings bind in different situations, so both must be computed and the lower one used.
Income multipliers instead of underwriting. “3.5x your salary” rules of thumb ignore debts, rates, and terms entirely. The amortization reverse-solve is the actual lender math.
Taxes and insurance hidden. Many calculators fold tax and insurance guesses into the payment without saying so, which quietly shrinks the loan. Here the P&I budget is explicit, and the note says what is excluded.
No binding-constraint readout. Knowing whether the front-end or back-end ceiling binds tells you what to fix: income-side problems need more income, debt-side problems need payoff. The badge names the binding constraint.
Frequently asked questions
Roughly the payment from the 28/36 rule converted to a loan at your rate and term, plus your down payment. On $120,000 income with $800/month debts at 6.5% over 30 years with $60,000 down, that is about $502,990. Enter your own numbers above for the exact figure.
Two debt-to-income ceilings lenders use: housing costs (principal, interest, taxes, insurance) up to 28% of gross monthly income, and all monthly debts including housing up to 36%. The lower of the two housing budgets sets your maximum payment.
A pre-approval usually involves a hard credit inquiry, which can shave a few points temporarily. Multiple mortgage inquiries within a short shopping window (typically 14-45 days depending on the scoring model) are generally treated as a single inquiry. The same shopping window matters again when you later price a refinance, and the cost to refinance mortgage calculator totals those closing costs and finds the break-even month that decides whether the new rate pays.
Dollar for dollar against the back-end ceiling. Every $100/month of debt removes $100/month of housing budget, which translates to roughly $15,000-$20,000 of loan at typical rates. Paying off a car loan before applying is one of the highest-ROI moves in homebuying.
Pre-qualification is an unverified estimate from self-reported numbers. Pre-approval verifies income, debts, and credit and produces a conditional commitment letter. Sellers take pre-approval seriously; pre-qualification carries little weight.
No. Conventional loans allow as little as 3-5% down, FHA 3.5%, VA and USDA 0%. But under 20% down usually means private mortgage insurance, which raises the monthly payment and slightly reduces the price you qualify for.
Because the 28/36 rule uses gross income and ignores everything that is not contractual debt: taxes, childcare, savings goals, lifestyle. Many buyers deliberately shop 10-20% below their approval. The approval is a ceiling, not a target. One major cost the approval figure never includes is the closing bill itself, and the closing cost percentage calculator estimates those fees as a percentage of the purchase price so they are budgeted before closing day.
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References
- Mortgage-Info, “How Much House Can I Afford in 2026? The 28/36 Rule” – front-end vs back-end DTI with worked salary examples. The 28/36 Rule: How Much House Can I Afford. Accessed October 19, 2026.
- NumericCore, “Maximum Mortgage Qualification Calculator” – Fannie Mae/Freddie Mac underwriting-based qualification math. Maximum Mortgage Qualification. Accessed October 19, 2026.
- US Finance Calculators, “House Affordability Calculator” – DTI underwriting steps and the amortization reverse-solve. House Affordability Calculator. Accessed October 19, 2026.
- DevZone Tools, “How Much House Can I Afford?” – DTI presets by loan program and the debt sensitivity of approval amounts. Mortgage Affordability Calculator. Accessed October 19, 2026.
- Calculators.org, “Debt to Income Ratio Calculator for Home Mortgage Loan Qualification” – front-end and back-end DTI worked examples. DTI Calculator for Mortgage Qualification. Accessed October 19, 2026.
- CalcRegistry, “DTI Calculator: Mortgage Qualifying Ratio” – gross vs net DTI and front-end/back-end formulas. DTI Calculator. Accessed October 19, 2026.
- The Truth About Mortgage, “Mortgage Affordability Calculator” – PITI components, PMI, and DTI bands. Mortgage Affordability Calculator. Accessed October 19, 2026.