Loan Affordability Calculator: How Much Can You Borrow?

How loan affordability is worked out

On the defaults — $7,500.00 a month, $400.00 of debts, a 36% debt-to-income target, 6.5% APR, 30 years, and $40,000.00 down — the max total monthly debt payment is $2,700.00, the max new loan payment is $2,300.00, the annuity factor is 158.2108, the max loan is $363,884.88, and the max price is $403,884.88. The whole calculation is four moves: multiply the income by the DTI target for the max total, subtract the debts for the max new payment, multiply the payment by the annuity factor for the max loan, and add the down payment for the max price.

Five things about the model are worth stating plainly. First, the max total monthly debt payment is the gross monthly income times the debt-to-income target — $7,500.00 × 36% = $2,700.00. Second, the max new loan payment is that total minus the existing monthly debts — $2,700.00 − $400.00 = $2,300.00 — and it is clamped at $0.00: debts that eat the whole total leave no payment at all. Third, the annuity factor is F = (1 − (1 + r)⁻ⁿ) / r, where r = APR ÷ 12 and n = the term in months — 158.2108 at 6.5% over 30 years. Fourth, the max loan is the max payment times the factor — $2,300.00 × 158.2108 = $363,884.88. And fifth, the max price is the max loan plus the down payment — $363,884.88 + $40,000.00 = $403,884.88. This is the standard DTI sizing rule, not an approval — lenders also check credit score, employment history, reserves, and the front-end (housing-only) ratio; a 36% total DTI is the common conventional ceiling and 43% is the common FHA ceiling, but some lenders allow more with compensating factors; the calculator assumes a fixed rate and the same payment every month.

The worked example, line by line

Setup: $7,500.00 a month, $400.00 of debts, 36% DTI, 6.5% APR, 30 years, $40,000.00 down.

Line 1 — multiply the income by the DTI target. The max total monthly debt payment is $7,500.00 × 36% = $2,700.00.

Line 2 — subtract the debts. The max new loan payment is $2,700.00 − $400.00 = $2,300.00.

Line 3 — work out the annuity factor. The monthly rate is 6.5% ÷ 12 = 0.541667% and the term is 360 months, so the factor is (1 − (1 + 0.00541667)⁻³⁶⁰) / 0.00541667 = 158.2108.

Line 4 — multiply the payment by the factor, then add the down payment. The max loan is $2,300.00 × 158.2108 = $363,884.88, and the max price is $363,884.88 + $40,000.00 = $403,884.88. Rounding convention: totals are computed from unrounded values, so rounded parts may differ by a cent from their rounded sum.

Every branch, checked

Income $10,000/mo: Income $10,000.00/mo, debts $400.00, DTI 36.00%, APR 6.50%, 30 years, down $40,000.00: max total $3,600.00, max payment $3,200.00, factor 158.2108, max loan $506,274.62, max price $546,274.62 — more income, more loan: $10,000.00 a month lifts the max payment to $3,200.00 and the max loan to $506,274.62.

DTI 43%: Income $7,500.00/mo, debts $400.00, DTI 43.00%, APR 6.50%, 30 years, down $40,000.00: max total $3,225.00, max payment $2,825.00, factor 158.2108, max loan $446,945.57, max price $486,945.57 — a higher ceiling lifts everything: 43% lifts the max total to $3,225.00 and the max loan to $446,945.57.

APR 5.0%: Income $7,500.00/mo, debts $400.00, DTI 36.00%, APR 5.00%, 30 years, down $40,000.00: max total $2,700.00, max payment $2,300.00, factor 186.2816, max loan $428,447.72, max price $468,447.72 — a cheaper rate stretches the same payment further: 5.0% lifts the factor to 186.2816 and the max loan to $428,447.72.

Term 15 years: Income $7,500.00/mo, debts $400.00, DTI 36.00%, APR 6.50%, 15 years, down $40,000.00: max total $2,700.00, max payment $2,300.00, factor 114.7964, max loan $264,031.75, max price $304,031.75 — a shorter term shrinks the factor: 15 years gives a factor of 114.7964 and a max loan of $264,031.75 — the same $2,300.00 a month buys less house, but the loan is paid off in half the time.

Debts $0: Income $7,500.00/mo, debts $0.00, DTI 36.00%, APR 6.50%, 30 years, down $40,000.00: max total $2,700.00, max payment $2,700.00, factor 158.2108, max loan $427,169.21, max price $467,169.21 — no other debts means the whole total is yours: the max payment is $2,700.00 and the max loan is $427,169.21.

Down payment $0: Income $7,500.00/mo, debts $400.00, DTI 36.00%, APR 6.50%, 30 years, down $0.00: max total $2,700.00, max payment $2,300.00, factor 158.2108, max loan $363,884.88, max price $363,884.88 — the down payment moves the price, not the loan: with $0 down the max loan is still $363,884.88, and the max price is $363,884.88.

Income $5,000/mo, debts $800/mo: Income $5,000.00/mo, debts $800.00, DTI 36.00%, APR 6.50%, 30 years, down $40,000.00: max total $1,800.00, max payment $1,000.00, factor 158.2108, max loan $158,210.82, max price $198,210.82 — less income and more debts squeeze both ends: $5,000.00 a month at 36% gives a $1,800.00 total, $800.00 of debts leaves a $1,000.00 payment, and the max loan is $158,210.82.

The reverses, worked backwards

Income for a $3,000.00 max payment: $9,444.44 — the exact income is 9444.4444. At the displayed $9,444.44 the max payment is $3,000.00 (exact to the cent). $9,443.44 gives $2,999.64; $9,445.44 gives $3,000.36. The star is DOLLARS.

DTI for a $2,500.00 max payment: 38.67% — the exact DTI is 38.6667%. At the displayed 38.67% the max payment is $2,500.25, $0.25 over the $2,500.00 target — rounding. 38.66% gives $2,499.50; 38.68% gives $2,501.00. The star is a PERCENT.

APR for a $400,000.00 max loan: 5.61% — the exact APR is 5.6146%. At the displayed 5.61% the max loan is $400,202.04, $202.04 over the $400,000.00 target — rounding. 5.60% gives $400,641.74. The star is a PERCENT.

Term for max loan to reach $375,000: 34 years — the smallest whole number of years that clears $375,000 of max loan. At 34 years the max loan is $377,756.17; 33 years gives $374,617.92. This is a step reverse: the term comes in whole years here, so there is no exact in-between. The star is YEARS.

Debts for a $2,000.00 max payment: $700.00 — the exact debts are 700.0000. At $700.00 the max payment is $2,000.00 (exact). $699 gives $2,001.00; $701 gives $1,999.00. The star is DOLLARS.

Down payment for a $450,000.00 max price: $86,115.12 — the exact down payment is 86115.1200. At $86,115.12 the max price is $450,000.00 (exact). $86,115.11 gives $449,999.99; $86,115.13 gives $450,000.01. The star is DOLLARS.

What the defaults assume

The defaults are $7,500.00 a month, $400.00 of debts, 36% DTI, 6.5% APR, 30 years, $40,000.00 down — max total $2,700.00, max payment $2,300.00, max loan $363,884.88, max price $403,884.88. With a DTI of 0%, Income $7,500.00/mo, debts $400.00, DTI 0.00%, APR 6.50%, 30 years, down $40,000.00: max total $0.00, max payment $0.00, factor 158.2108, max loan $0.00, max price $40,000.00 — no payment is allowed at all, and the price is the down payment alone. With an APR of 0%, Income $7,500.00/mo, debts $400.00, DTI 36.00%, APR 0.00%, 30 years, down $40,000.00: max total $2,700.00, max payment $2,300.00, factor 360.0000, max loan $828,000.00, max price $868,000.00 — the factor is 360.0000, the number of months, because no interest accrues. With a term of 1 year, Income $7,500.00/mo, debts $400.00, DTI 36.00%, APR 6.50%, 1 years, down $40,000.00: max total $2,700.00, max payment $2,300.00, factor 11.5880, max loan $26,652.32, max price $66,652.32 — a factor of 11.5880. With an income of $20,000.00 a month, Income $20,000.00/mo, debts $400.00, DTI 36.00%, APR 6.50%, 30 years, down $40,000.00: max total $7,200.00, max payment $6,800.00, factor 158.2108, max loan $1,075,833.57, max price $1,115,833.57. With debts of $2,700.00, equal to the max total, Income $7,500.00/mo, debts $2,700.00, DTI 36.00%, APR 6.50%, 30 years, down $40,000.00: max total $2,700.00, max payment $0.00, factor 158.2108, max loan $0.00, max price $40,000.00 — the payment is clamped at $0.00, and the price is the down payment alone. With a DTI of 50%, Income $7,500.00/mo, debts $400.00, DTI 50.00%, APR 6.50%, 30 years, down $40,000.00: max total $3,750.00, max payment $3,350.00, factor 158.2108, max loan $530,006.25, max price $570,006.25. Rounding convention: totals are computed from unrounded values, so rounded parts may differ by a cent from their rounded sum.

Output · formula · meaning

Who uses this

• The first-time buyer on $7,500 a month: they learn the max payment is $2,300.00 and the max loan is $363,884.88 — and they check the $9,444.44 reverse to see the income it takes to carry a $3,000.00 payment.
• The buyer weighing a higher DTI: they learn 43% lifts the max loan to $446,945.57 — and they check the 38.67% reverse to see the target that gives a $2,500.00 payment.
• The buyer comparing 30 years with 15: they learn 15 years cuts the max loan to $264,031.75 — and they check the 34-year step to see when the max loan first reaches $375,000.
• The buyer with no other debts: they learn $0 of debts lifts the max loan to $427,169.21 — and they check the $700.00 reverse to see the debts that leave a $2,000.00 payment.

Accuracy & limitations

The math is first-principles: the max total monthly debt payment is the gross monthly income times the debt-to-income target; the max new loan payment is that total minus the existing monthly debts, clamped at $0.00; the annuity factor is (1 − (1 + r)⁻ⁿ) / r with r = APR ÷ 12 and n = the term in months; the max loan is the max payment times the factor; the max price is the max loan plus the down payment. Every figure is rounded to cents half-up, and the totals are computed from unrounded values, so rounded parts may differ by a cent from their rounded sum. What the model cannot do is tell you what YOUR lender will approve: it is the standard DTI sizing rule only — it does NOT check credit score, employment history, or reserves; it does NOT model the front-end (housing-only) ratio, which is a separate ceiling; it does NOT add property taxes, homeowner's insurance, HOA dues, or PMI to the payment; it does NOT model closing costs or a rate that changes part-way through; and it assumes a fixed rate and the same payment every month. A 36% total DTI is the common conventional ceiling and 43% is the common FHA ceiling, but some lenders allow more with compensating factors. Use it to size the loan before you shop, then check the real terms with a lender before you make an offer.

Frequently asked questions