Lenders cap the share of your gross monthly income that can go to debt payments — the DTI ratio, commonly around 36% (up to 43–50% for some programs). Subtracting your existing monthly debts from that cap gives the largest housing payment you can carry.

The amortization formula is then run in reverse to find the biggest loan that payment supports, and your down payment is added on top to get the maximum home price.

Given: Income $96,000/yr, debts $500/mo, DTI 36%, rate 6.5%, 30 years, down payment $40,000

Max payment M = 8,000 × 0.36 − 500 = $2,380

r = 0.005417  ·  (1+r)³⁶⁰ = 6.993  ·  P_max = 2,380 × 5.993 / (0.005417 × 6.993) ≈ $376,500

Max home price ≈ 376,500 + 40,000 = $416,500

• The DTI limit varies by lender and loan program; 36% is a conservative benchmark, while some programs allow up to 43–50%.
• The max payment computed here must also cover property tax, insurance and PMI in practice, so the realistic price is somewhat lower.
• Use gross (pre-tax) income; include all recurring debts — car loans, student loans, card minimums.
• Actual approval depends on credit score, employment history, reserves and appraisal.

What DTI should I use?
36% is a safe, widely used ceiling; check your lender's specific limit if you know it.

Front-end vs back-end DTI?
This calculator uses the back-end ratio: all debts including the new housing payment vs gross income.

Is this a pre-approval?
No — it's a planning estimate. Lenders verify income, credit and assets before approving.