How it works
This calculator answers a question most mortgage tools never touch: given what you earn and what you already owe, what is the ceiling on a home purchase before a lender says no? Every other mortgage calculator on this site starts with a house price and works outward to a monthly payment. This one runs the opposite direction — it takes your gross annual income, your recurring monthly debts, the cash you have for a down payment, and a debt-to-income (DTI) ceiling you are willing to live within, then solves for the maximum home price that fits.
The engine treats your income as a monthly gross figure, applies the DTI cap to find the total monthly debt you are allowed to carry, subtracts the debts you already have, and treats the remainder as the monthly payment available for a new mortgage. That payment capacity is then converted into a loan principal using the interest rate and term you enter. Add your down payment on top and you get the maximum affordable home price.
The formula
MaxHomePrice = DownPayment + (PMT_Capacity × (1 − (1 + r)^−n) / r)
Where:
- PMT_Capacity = (Monthly Gross Income × Max DTI) − Monthly Debts
- r = monthly interest rate = annual rate ÷ 12
- n = total number of monthly payments = term in years × 12
Worked example
A household earns $95,000 per year. They carry $400 in monthly debts (a car loan plus minimum credit card payments). They have $30,000 saved for a down payment. Mortgage rates are 6.5% per annum on a 30-year term, and they want to cap their total debt-to-income ratio at 36%.
| Input | Value |
|---|---|
| Annual income | $95,000 |
| Monthly gross income | $95,000 ÷ 12 = $7,916.67 |
| Monthly debts | $400 |
| Down payment | $30,000 |
| Interest rate | 6.5% p.a. (0.5417% monthly) |
| Term | 30 years (360 months) |
| Max DTI | 36% |
Step 1 — Total monthly debt allowed at 36% DTI:
$7,916.67 × 0.36 = $2,850.00
Step 2 — Payment capacity for the new mortgage:
$2,850.00 − $400 = $2,450.00
Step 3 — Convert that payment into a loan principal. With r = 0.005417 and n = 360:
Loan = $2,450 × (1 − (1.005417)^−360) / 0.005417
(1.005417)^−360 ≈ 0.14298
Loan = $2,450 × (1 − 0.14298) / 0.005417
Loan = $2,450 × 0.85702 / 0.005417
Loan = $2,450 × 158.18 ≈ $387,541
Step 4 — Add the down payment:
Max home price = $387,541 + $30,000 = $417,541
Things to watch
This is an estimate, not professional advice or a loan approval. Three real-world factors will shrink the number above in practice. First, the calculation assumes the entire payment capacity goes toward principal and interest only. In reality, property taxes, homeowners insurance, and — for down payments below 20% — private mortgage insurance are escrowed into your monthly payment. A lender's 36% DTI cap applies to the full PITI figure, so every dollar of taxes and insurance reduces the principal-and-interest portion and therefore the loan size. Second, front-end ratios (housing payment alone versus income) may impose a tighter limit than your back-end ratio if your existing debts are low. Third, lenders verify income with tax documents, not the annual figure you type in — bonuses, overtime, and self-employment income are often averaged over two years or discounted, which can lower the gross income the underwriter actually uses.