Mortgage Qualification Calculator: How Much House?

What does $336,609.61 mean?

It means the most expensive home you qualify for on $100,000 a year with $500 a month of other debts and a $40,000 down payment: a $296,609.61 loan plus the $40,000 down payment, for a $336,609.61 home. The monthly housing payment at that price is $2,333.33 — $1,874.77 of principal and interest, $308.56 of property tax, $150 of insurance and no HOA — which is exactly 28.00% of the $8,333.33 gross monthly income. The number is a ceiling from the lender's debt-to-income rules, not a recommendation: qualifying for $336,609.61 does not mean spending $336,609.61 is wise.

Three things to check before you trust the number

There are two limits, and the lower one binds. The front-end limit caps housing alone at 28% of gross monthly income — $2,333.33 here — and the back-end limit caps housing plus all other debts at 36% — $2,500.00 here, because 36% of $8,333.33 is $3,000.00 and $500 of debts leaves $2,500.00. The binding cap is the smaller of the two, so the front-end limit binds on these numbers. Change the debts to $1,000 a month and the back-end cap falls to $2,000.00, the back-end limit binds instead, and the max price drops to $290,552.22.

The tax depends on the price, so the loan is solved, not looked up. Property tax is charged on the home's price, and the price depends on the loan, and the loan depends on how much payment is left after tax — a circle. The calculator breaks it by solving the loan from the binding payment in one step: the loan is the binding cap minus insurance and HOA minus the tax on the down payment, divided by the amortization factor plus the monthly tax rate. That is why a higher tax rate shrinks the max price even though the payment cap does not change: at a 2.00% tax rate the same $2,333.33 cap buys only $305,002.47 of home.

This is an estimate, not a lender decision. Lenders use their own underwriting: credit score, employment history, reserves, the loan program, and their own DTI caps, which are often higher than 28% and 36% — some programs allow a back-end ratio into the 40s. PMI is not in this number, closing costs are not in it, and a rate quote is not a rate lock. Use the figure to narrow the search, then get pre-approved for the real number.

Worked example

On the defaults: $100,000 a year, $500 a month of debts, $40,000 down, 6.50% for 30 years, 1.10% tax, $150 insurance, no HOA, front 28%, back 36%.

1. Monthly gross income: $100,000 ÷ 12 is $8,333.33.
2. Front-end cap: 28% of $8,333.33 is $2,333.33 a month.
3. Back-end cap: 36% of $8,333.33 is $3,000.00, minus $500 of debts is $2,500.00 a month.
4. Binding cap: the smaller of the two is the front-end cap, $2,333.33 a month.
5. Tax and insurance first: insurance is $150 a month, and the tax on the price is worked out with the loan below.
6. Solve the loan: the binding payment, less insurance and the tax on the down payment, divided by the amortization factor plus the monthly tax rate, gives a loan of $296,609.61.
7. Add the down payment: $296,609.61 + $40,000 is a max home price of $336,609.61.
8. Principal and interest: $296,609.61 at 6.50% over 30 years is $1,874.77 a month.
9. Property tax: 1.10% of $336,609.61 a year, divided by 12, is $308.56 a month.
10. Add it up: $1,874.77 + $308.56 + $150.00 + $0.00 is $2,333.33 — exactly the binding cap.
11. Check the ratios: $2,333.33 is 28.00% of $8,333.33, and with the $500 of debts the back-end ratio is 34.00% — inside both limits.
12. Check the flip: at a front limit of 36% and a back limit of 28%, the back-end cap is $1,833.33, the back-end limit binds, and the max price is $267,523.52.

Every branch, checked

• Income $120,000: Income $120,000: Max price $401,089.96 (401089.964163 unrounded, binding front-end $2,800.00). Income $120,000 — the binding cap is $2,800.00 a month (front-end), and the max price is $401,089.96.
• Debts $1,000/mo: Debts $1,000/mo: Max price $290,552.22 (290552.220032 unrounded, binding back-end $2,000.00). Debts $1,000/mo — the binding cap is $2,000.00 a month (back-end), and the max price is $290,552.22.
• Down payment $80,000: Down payment $80,000: Max price $371,543.30 (371543.300147 unrounded, binding front-end $2,333.33). Down payment $80,000 — the binding cap is $2,333.33 a month (front-end), and the max price is $371,543.30.
• Rate 5.00%: Rate 5.00%: Max price $381,560.33 (381560.328477 unrounded, binding front-end $2,333.33). Rate 5.00% — the binding cap is $2,333.33 a month (front-end), and the max price is $381,560.33.
• 15-year term: 15-year term: Max price $262,966.82 (262966.822473 unrounded, binding front-end $2,333.33). 15-year term — the binding cap is $2,333.33 a month (front-end), and the max price is $262,966.82.
• Tax 2.00%/yr: Tax 2.00%/yr: Max price $305,002.47 (305002.471126 unrounded, binding front-end $2,333.33). Tax 2.00%/yr — the binding cap is $2,333.33 a month (front-end), and the max price is $305,002.47.
• Insurance $300, HOA $200: Insurance $300, HOA $200: Max price $288,249.35 (288249.350362 unrounded, binding front-end $2,333.33). Insurance $300, HOA $200 — the binding cap is $2,333.33 a month (front-end), and the max price is $288,249.35.
• Front 36%, back 28% (back binds): Front 36%, back 28% (back binds): Max price $267,523.52 (267523.523337 unrounded, binding back-end $1,833.33). Front 36%, back 28% (back binds) — the binding cap is $1,833.33 a month (back-end), and the max price is $267,523.52.
• Income $60,000: Income $60,000: Max price $193,831.69 (193831.693916 unrounded, binding back-end $1,300.00). Income $60,000 — the binding cap is $1,300.00 a month (back-end), and the max price is $193,831.69.
• Rate 0%: Rate 0%: Max price $621,052.63 (621052.631579 unrounded, binding front-end $2,333.33). Rate 0% — the binding cap is $2,333.33 a month (front-end), and the max price is $621,052.63.

The reverses, worked backwards

• Smallest income for a $400,000 max price: 120000 — at 120000 the figures are Max price $401,089.96 (401089.964163 unrounded, binding front-end $2,800.00); at the lower neighbor the figures are Max price $397,865.95 (397865.946626 unrounded, binding front-end $2,776.67); at the upper neighbor the figures are Max price $404,313.98 (404313.981700 unrounded, binding front-end $2,823.33) — verdict: STEP.
• Smallest monthly debts where the back-end limit binds: 667 — at 667 the figures are Max price $336,563.56 (336563.556026 unrounded, binding back-end $2,333.00); at the lower neighbor the figures are Max price $336,609.61 (336609.613420 unrounded, binding front-end $2,333.33); at the upper neighbor the figures are Max price $336,425.38 (336425.383846 unrounded, binding back-end $2,332.00) — verdict: STEP.
• Smallest down payment for a $400,000 max price: 113000 — at 113000 the figures are Max price $400,363.59 (400363.591697 unrounded, binding front-end $2,333.33); at the lower neighbor the figures are Max price $399,490.25 (399490.249529 unrounded, binding front-end $2,333.33); at the upper neighbor the figures are Max price $401,236.93 (401236.933865 unrounded, binding front-end $2,333.33) — verdict: STEP.
• Largest whole-percent rate for a $300,000 max price: 8 — at 8 the figures are Max price $300,066.08 (300066.079550 unrounded, binding front-end $2,333.33); at the lower neighbor the figures are Max price $323,587.07 (323587.069972 unrounded, binding front-end $2,333.33); at the upper neighbor the figures are Max price $279,506.01 (279506.006143 unrounded, binding front-end $2,333.33) — verdict: STEP.
• Smallest front-end limit for a $350,000 max price: 30 — at 30 the figures are Max price $359,638.31 (359638.310114 unrounded, binding front-end $2,500.00); at the lower neighbor the figures are Max price $348,123.96 (348123.961767 unrounded, binding front-end $2,416.67); at the upper neighbor the figures are Max price $359,638.31 (359638.310114 unrounded, binding back-end $2,500.00) — verdict: STEP.
• Largest HOA dues for a $300,000 max price: 250 — at 250 the figures are Max price $302,066.57 (302066.568379 unrounded, binding front-end $2,333.33); at the lower neighbor the figures are Max price $308,975.18 (308975.177387 unrounded, binding front-end $2,333.33); at the upper neighbor the figures are Max price $295,157.96 (295157.959370 unrounded, binding front-end $2,333.33) — verdict: STEP.

What the defaults assume

The defaults are $100,000 a year, $500 a month of debts, a $40,000 down payment, 6.50% for 30 years, a 1.10% tax rate, $150 a month of insurance, no HOA, and DTI limits of 28% front-end and 36% back-end. They are a starting point, not a standard: your income, debts, down payment and rate will differ, and the right answer for you is the one your numbers describe. Change any field and the calculator recomputes instantly. Put your numbers in, read the max price, and check the breakdown before you use it.

These notes repeat in every explainer section because this page is built to be read start to finish: there are two limits and the lower one binds; the tax depends on the price, so the loan is solved; and the figure is an estimate, not a lender decision.

Output · formula · meaning

Who uses this

• A first-time buyer setting a budget — on $100,000 a year the front-end limit binds at $2,333.33 a month, so the search starts at homes up to $336,609.61, not at the price of the nicest listing.
• A buyer weighing a bigger down payment — $80,000 down lifts the max price to $371,543.30, and the calculator shows exactly how much each extra dollar of down payment buys.
• A buyer with heavy debts — $1,000 a month of debts flips the binding limit to the back end and cuts the max price to $290,552.22, which is why paying a car off before applying can matter more than saving a little more.
• A financial planner sanity-checking a client's target — the front-end ratio of 28.00% and the back-end ratio of 34.00% are the two numbers a lender will actually test.

Accuracy & limitations

The calculator uses exact decimal arithmetic on the numbers you enter: the caps, the amortization factor, the loan solve and the ratios are computed to the cent, and the breakdown adds back to the binding cap exactly — $1,874.77 + $308.56 + $150.00 + $0.00 is $2,333.33. What it cannot do is underwrite you: lenders apply their own DTI caps, which are often higher than 28% and 36%, and they weigh credit score, employment history, reserves and the loan program, none of which this tool sees. PMI is not included — with less than 20% down most loans carry it, and it would shrink the max price — closing costs are not included, taxes are assumed to stay at the rate you enter, and the rate is assumed fixed for the whole term. It is an estimate for narrowing a search, not a pre-approval and not financial advice.

Cite this calculator

On $100,000 a year, the front-end limit binds: you qualify for a home up to $336,609.61 with a $40,000 down payment. Front cap $2,333.33 a month; back cap $2,500.00 a month; max loan $296,609.61. Smallest income for a $400,000 max price: 120000. Smallest monthly debts where the back-end limit binds: 667. Smallest down payment for a $400,000 max price: 113000. Largest whole-percent rate for a $300,000 max price: 8. Smallest front-end limit for a $350,000 max price: 30. Largest HOA dues for a $300,000 max price: 250. Source: Bright Side Kit, brightoolbox.com.

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