House Affordability Calculator
Quickly estimate how much house you can afford using a rigorous, lender-style approach. This tool is designed for first‑time and seasoned homebuyers who want a realistic price target that accounts for DTI limits, interest rate, property taxes, insurance, HOA dues, and PMI.
Your Inputs
If you only know monthly, multiply by 12 and enter the yearly amount.
Results
Monthly Cost Breakdown
Data Source and Methodology
Authoritative Data Source: Fannie Mae — Single-Family Selling Guide, Section B3-6 (Liability Assessment), specifically B3-6-05: Monthly Debt Obligations. Latest updates are published on Fannie Mae’s official site.
Reference: https://selling-guide.fanniemae.com/Selling-Guide/Origination-thru-Closing/Subpart-B3-Underwriting-Borrowers/Chapter-B3-6-Liability-Assessment/Section-B3-6-05-Monthly-Debt-Obligations/
Date accessed: 2025-09-13.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The calculator implements the standard amortization formula and applies adjustable front-end/back-end DTI guidelines commonly used for conventional underwriting. Actual approvals vary by lender, credit profile, loan program, and compensating factors.
The Formula Explained
Mortgage payment (principal and interest), with monthly rate r and n payments:
$$ M = \begin{cases} \dfrac{r \cdot L}{1 - (1 + r)^{-n}}, & r > 0 \\ \dfrac{L}{n}, & r = 0 \end{cases} $$
Total monthly housing cost:
$$ H = M + \frac{\tau \cdot P}{12} + \frac{I_{annual}}{12} + HOA + PMI $$
DTI constraints:
$$ H \le \min\!\left( \alpha \cdot \frac{Y}{12},\ \beta \cdot \frac{Y}{12} - D \right) $$
where L is loan amount, P is purchase price, Y is annual gross income, D is other monthly debt, τ is property tax rate (annual, as a decimal), Iannual is annual insurance, α is the front-end DTI limit, and β is the back-end DTI limit. The calculator numerically solves for the highest P that satisfies the constraint.
Glossary of Variables
- Y — Annual gross income (USD).
- D — Other monthly debts (USD).
- α — Front-end DTI limit (e.g., 0.28).
- β — Back-end DTI limit (e.g., 0.36).
- P — Home purchase price (USD).
- L — Loan amount = P − Down Payment (USD).
- r — Monthly interest rate = APR / 12 (decimal).
- n — Total number of payments = years × 12.
- M — Monthly principal and interest payment (USD).
- τ — Annual property tax rate (decimal of price).
- Iannual — Annual homeowners insurance (USD).
- HOA — Monthly homeowners association dues (USD).
- PMI — Monthly private mortgage insurance (USD) for down payments below 20% (approx. PMIrate × L / 12).
- H — Total monthly housing cost = M + taxes + insurance + HOA + PMI (USD).
Come Funziona: Un Esempio Passo-Passo
Inputs: Y = $120,000; D = $500; APR = 6.5%; term = 30y; down = 20%; τ = 1.2%; Iannual = $1,200; HOA = $0; PMI rate = 0.5%; α = 28%; β = 36%.
- Monthly income = $120,000 / 12 = $10,000.
- Front-end cap = 0.28 × $10,000 = $2,800.
- Back-end cap = 0.36 × $10,000 − $500 = $3,100.
- Allowed housing spend = min($2,800, $3,100) = $2,800.
- Given r = 0.065 / 12 and n = 360, we solve for P so that H ≤ $2,800, where H = M + τP/12 + $1,200/12 + 0 + PMI.
- With 20% down, PMI ≈ $0. Using numerical search, the maximum P that keeps H ≤ $2,800 is returned by the calculator in the Results above.
Note: Local taxes and insurance can change the result materially. Always validate with a lender for a pre-approval.
Frequently Asked Questions (FAQ)
What percentage of my income should housing cost?
Many lenders use 28% (front-end DTI) for total housing costs and 36% (back-end DTI) for all debts. You can customize these limits in the calculator.
Does this include taxes, insurance, HOA, and PMI?
Yes. Property taxes are modeled as a percent of price; insurance is annual; HOA is monthly; PMI appears when down payment < 20%.
How does the interest rate affect affordability?
Higher rates increase the monthly principal and interest payment M, reducing the maximum affordable price P for the same DTI limits.
Can I change the loan term?
Yes. Shorter terms (e.g., 15 years) increase M and typically reduce the affordable price compared to a 30-year term.
When will PMI be removed?
Conventional loans generally remove PMI when loan-to-value reaches 80% via scheduled amortization or a new appraisal. This tool includes PMI only if down payment is under 20% at purchase.
Is this a pre-approval?
No. This is an educational estimate. For binding terms, you need a lender’s pre-approval that considers credit, assets, reserves, and specific program rules.
What if I have irregular income?
Lenders typically average qualifying income over a period (e.g., 24 months for self-employed). Enter a conservative annual figure or consult your loan officer.