Max home price from income and down payment.
Home Price = { min(0.28×GMI, 0.36×GMI − MD) − T } × [(1 − (1 + r)^(−n)) / r] + DPLenders typically use two debt-to-income (DTI) ratio limits to determine how much you can borrow:
Front-end ratio (housing ratio): Your monthly housing payment (principal + interest + taxes + insurance, or PITI) should not exceed 28% of your gross monthly income.
Back-end ratio (total DTI): All monthly debt payments (housing + car loans + student loans + credit cards, etc.) should not exceed 36% of your gross monthly income.
The more restrictive of the two limits determines your maximum monthly mortgage payment. From that payment, we back-calculate the maximum loan amount using the standard fixed-rate mortgage payment formula, then add your down payment to arrive at the maximum affordable home price.
Step 1 – Maximum monthly payment (P&I only, excluding taxes & insurance):
Let T = estimated monthly taxes + insurance (often approximated as 0.14% of home price per month, or a fixed input).
Max PITI from front-end = 0.28 × GMI Max PITI from back-end = 0.36 × GMI − MD
Max monthly P&I = min(0.28 × GMI, 0.36 × GMI − MD) − T
Step 2 – Maximum loan amount from P&I:
Loan = P&I × [(1 − (1 + r)^(−n)) / r]
Step 3 – Maximum home price:
Home Price = Loan + Down Payment
Step 1 – Max monthly payment limits:
Front-end cap: 0.28 × $7,500 = $2,100 PITI
Back-end cap: 0.36 × $7,500 − $600 = $2,700 − $600 = $2,100 PITI
Both limits give $2,100; subtract T: $2,100 − $300 = $1,800 available for P&I
Step 2 – Max loan amount:
Annuity factor = (1 − (1 + 0.005833)^(−360)) / 0.005833
= (1 − (1.005833)^(−360)) / 0.005833
(1.005833)^360 ≈ 8.1165, so (1.005833)^(−360) ≈ 0.12320
Annuity factor = (1 − 0.12320) / 0.005833 = 0.87680 / 0.005833 ≈ 150.31
Max Loan = $1,800 × 150.31 ≈ $270,558
Step 3 – Max home price:
$270,558 + $30,000 = $300,558 ≈ $300,600Result: Estimated Maximum Home Price: **~$300,600** Max Loan Amount: ~$270,600 Monthly P&I Payment: ~$1,800 Total Monthly Housing Cost (PITI): ~$2,100
In this example, a household earning $90,000 per year with $600 in monthly debts, a $30,000 down payment, a 7% interest rate, and $300/month in taxes and insurance can afford a home priced at roughly $300,600. Both the front-end and back-end DTI limits converged at the same $2,100/month ceiling, leaving $1,800 for principal and interest after taxes and insurance. Increasing the down payment, reducing existing debts, or securing a lower interest rate would each raise the affordable price. Results are estimates only — actual lender approval depends on credit score, loan type (conventional, FHA, VA), reserves, and other underwriting criteria.
The 28/36 rule is the most widely used guideline in conventional mortgage lending. It states:
FHA loans sometimes allow higher ratios (up to ~31%/43%), and some conventional loans allow a back-end DTI up to 45%–50% with strong compensating factors (excellent credit, large reserves). Our calculator uses the conservative 28/36 standard.
| Factor | Effect on Affordability | |---|---| | Higher income | Increases affordable price | | Lower existing debts | Increases affordable price | | Larger down payment | Directly adds to affordable price | | Lower interest rate | Increases loan amount from same payment | | Shorter loan term | Lowers affordable price (higher monthly P&I) | | Higher property taxes/insurance | Reduces P&I budget |
A down payment of 20% or more eliminates the need for Private Mortgage Insurance (PMI), which typically costs 0.5%–1.5% of the loan per year and is not included in simple affordability estimates. If your down payment is below 20%, add estimated PMI to your monthly costs for a more accurate picture.
Closing costs typically run 2%–5% of the purchase price and are paid at settlement. These are separate from the down payment and reduce the cash available for your down payment if you're working from a fixed savings pool.
This calculator provides an affordability estimate, not a mortgage commitment. A formal lender pre-approval involves a full credit check, income verification, and asset review. Use this calculator to set a realistic search budget, then get pre-approved before making offers.
Disclaimer: Results are estimates for informational purposes only and do not constitute financial advice. Actual loan amounts and terms are determined by your lender based on full underwriting review. Consult a licensed mortgage professional or financial advisor before making a home purchase decision.
On a $75,000 gross annual salary ($6,250/month), the 28% front-end limit gives you $1,750/month for PITI. After subtracting estimated taxes and insurance of ~$250/month, you have ~$1,500 for P&I. At a 7% rate over 30 years, that supports a loan of roughly $225,000. Add a $20,000 down payment and you can afford approximately $245,000 — though existing debts, credit score, and local tax rates will shift this figure.
A 30-year mortgage offers a lower monthly payment for the same loan amount, which increases the loan you can qualify for under a DTI limit and therefore raises your affordable home price. A 15-year mortgage has higher monthly payments but far less total interest paid. For maximum affordability (highest purchase price), a 30-year loan wins; for minimum total cost, a 15-year loan wins.
The minimum depends on loan type: FHA requires 3.5%, conventional loans can go as low as 3%, VA and USDA loans can be 0% for eligible borrowers. However, putting down at least 20% avoids PMI and reduces your monthly payment. From a pure affordability standpoint, a larger down payment directly increases the home price you can target.
Beyond PITI (principal, interest, taxes, insurance), budget for HOA fees (if applicable), PMI (if down payment < 20%), utilities, routine maintenance (commonly estimated at 1% of home value per year), and emergency repair reserves. These costs don't affect mortgage qualification but significantly impact your true monthly budget.
Interest rate directly affects the annuity factor used to convert your monthly P&I allowance into a loan amount. At 5%, a $1,500/month P&I budget supports a loan of ~$279,000; at 7%, the same payment supports only ~$225,500 — a difference of over $53,000 in purchasing power from a 2-percentage-point rate change.
The 28/36 rule is a conventional lending guideline stating that your monthly housing costs (PITI) should not exceed 28% of your gross monthly income, and your total monthly debt payments should not exceed 36% of your gross monthly income. Whichever limit is more restrictive determines your maximum mortgage payment.
Use **gross income** — your income before taxes and deductions. Mortgage lenders always qualify borrowers using gross income, so using net (take-home) pay would understate your true borrowing capacity.
Yes. The calculator lets you input (or estimate) monthly property taxes and homeowner's insurance. These are subtracted from your DTI-based monthly housing allowance before calculating the maximum loan amount, giving you a more accurate home price estimate.
Your down payment is added directly to the maximum loan amount to produce the total home price. For example, increasing your down payment from $20,000 to $40,000 raises your affordable price by exactly $20,000, all else equal. A larger down payment also reduces or eliminates PMI and lowers your monthly payment.
The base calculation does not automatically add PMI. If your down payment is less than 20% of the home price, you should manually add your estimated PMI cost (typically 0.5%–1.5% of the loan per year ÷ 12) to your monthly debt obligations or 'T' input to get a more realistic estimate.
This calculator does not factor in credit score, but lenders do. Conventional loans typically require a minimum 620 score; FHA loans can go as low as 580 (or 500 with a larger down payment). A higher credit score also earns you a lower interest rate, which improves affordability.
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