Mortgage Affordability Calculator
Estimate the maximum home price you can afford based on your gross income, monthly debts, down payment, and current interest rates using standard lending guidelines.
Formulas Used
1. Maximum Housing Payment (PITI + HOA):
Front-End Limit = Gross Monthly Income × 0.28
Back-End Limit = Gross Monthly Income × 0.36 − Monthly Debts
Max Housing Payment = min(Front-End Limit, Back-End Limit)
2. Maximum Loan Amount (P):
Solving: P × MF + (P + D) × (t/1200) + Imo + HOA = Max Housing Payment
⇒ P = [Max Housing Payment − D × (t/1200) − Imo − HOA] / [MF + (t/1200)]
Where:
- MF (Mortgage Factor) = r(1+r)n / [(1+r)n − 1]
- r = Monthly interest rate = Annual Rate / 1200
- n = Total number of payments = Years × 12
- D = Down payment
- t = Annual property tax rate (%)
- Imo = Monthly home insurance = Annual Insurance / 12
3. Maximum Home Price: Home Price = Max Loan Amount + Down Payment
4. DTI Ratios:
Front-End DTI = Total Housing Payment / Gross Monthly Income
Back-End DTI = (Total Housing Payment + Monthly Debts) / Gross Monthly Income
Assumptions & References
- 28/36 Rule: Standard conventional lending guideline — housing costs should not exceed 28% of gross monthly income (front-end), and total debt payments should not exceed 36% (back-end). Some lenders allow up to 43% back-end DTI for qualified mortgages (CFPB).
- Property Tax: Default rate of 1.2% is a U.S. national average; actual rates vary significantly by state and county (source: Tax Foundation).
- Home Insurance: Default of $1,200/year is a U.S. national average estimate; actual premiums vary by location, home value, and coverage (source: Insurance Information Institute).
- PMI: Private Mortgage Insurance is typically required when the down payment is less than 20% of the home price. Estimated at 0.75% of the loan amount annually; actual rates range from 0.5%–1.5% depending on credit score and LTV ratio (source: Urban Institute).
- Fixed-Rate Mortgage: This calculator assumes a conventional fixed-rate mortgage. ARM (adjustable-rate) products will have different payment structures.
- Gross Income: Calculations use pre-tax (gross) income, consistent with standard underwriting practices.
- References: Consumer Financial Protection Bureau (CFPB) — Debt-to-Income Calculator; Fannie Mae Selling Guide; HUD Homebuyer Education Guidelines.