Reviewed & Verified by:
David Chen, CFA
Use this **mortgage approval calculator** to estimate the maximum loan amount you may qualify for based on common Debt-to-Income (DTI) and Housing Expense Ratio limits. This provides a clear, data-driven assessment of your financial readiness.
Mortgage Approval Calculator
Your Estimated Maximum Loan Amount:
$0.00
Based on a 30-year fixed rate.
Detailed Calculation Steps
Mortgage Approval Calculator Formula
The maximum loan amount ($L$) is derived from the maximum affordable monthly Principal & Interest (P\&I) payment ($P$).
Step 1: Determine Max Monthly P&I Payment ($P$)
$$P = \min \left( \frac{AGI}{12} \times 0.28, \left( \frac{AGI}{12} \times 0.36 \right) – D \right)$$
Where:
- $AGI$ = Annual Gross Income
- $D$ = Monthly Non-Mortgage Debts
- $0.28$ = Front-End Ratio (Housing Expense Limit)
- $0.36$ = Back-End Ratio (DTI Limit)
Step 2: Calculate Max Loan Amount ($L$)
$$L = P \times \frac{1 – (1 + r)^{-n}}{r}$$
Where:
- $r$ = Monthly Interest Rate (Annual Rate / 1200)
- $n$ = Total Number of Payments (360 for 30 years)
Formula Source: CFPB DTI Guidelines | Investopedia Housing Ratios
Variables
- Annual Gross Income (AGI): Your total yearly earnings before taxes. This is the foundation of affordability.
- Total Monthly Non-Mortgage Debts (D): Required monthly payments for credit cards, auto loans, student loans, etc.
- Estimated Annual Interest Rate (R): The projected rate for your mortgage. A higher rate reduces the maximum loan amount.
- Desired Down Payment (%): The percentage of the home price you plan to pay upfront, affecting the maximum purchase price.
Related Calculators
- Affordability Limit Calculator
- Debt-to-Income Ratio Estimator
- Monthly P&I Payment Calculator
- Early Loan Payoff Calculator
What is Mortgage Approval Calculator?
A Mortgage Approval Calculator is a financial tool that estimates the maximum principal and interest (P&I) payment and corresponding loan size a lender is likely to approve for a borrower. It primarily relies on the **Debt-to-Income (DTI) ratio** and the **Housing Expense Ratio (HER)**, which are the two critical metrics used by mortgage underwriters to assess risk. This tool helps potential homeowners set realistic expectations before formally applying for a loan.
The calculation is inherently conservative, using standard thresholds (like 28% HER and 36% DTI) to determine the borrowing capacity. If a borrower exceeds these ratios, they may need special approval or qualify for government-backed loans (like FHA), which allow higher ratios. The calculator’s result is an estimate of the maximum **loan amount** (Principal) you could receive, not the maximum home purchase price, which must factor in your down payment.
How to Calculate Mortgage Approval (Example)
- Determine Monthly Income and Debt: A borrower has an Annual Gross Income ($AGI$) of $100,000 and total Monthly Debts ($D$) of $700. Monthly Income is $\$100,000 / 12 = \$8,333.33$.
- Calculate Front-End Limit (28% HER): $\$8,333.33 \times 0.28 = \$2,333.33$. This is the maximum payment allowed by the Housing Expense Ratio.
- Calculate Back-End Limit (36% DTI): $(\$8,333.33 \times 0.36) – \$700 = \$3,000.00 – \$700 = \$2,300.00$. This is the maximum P\&I payment allowed by the DTI ratio.
- Determine Max P&I Payment: The maximum affordable monthly payment ($P$) is the minimum of the two limits: $\min(\$2,333.33, \$2,300.00) = \$2,300.00$.
- Calculate Max Loan Amount: Using $P = \$2,300.00$, a 6.5\% annual rate, and a 30-year term ($n=360$), the maximum loan amount $L$ is calculated using the loan formula, resulting in approximately $\$365,498$.
Frequently Asked Questions (FAQ)
Is the Down Payment percentage used in the approval calculation?
No, the down payment percentage is used to determine the Loan-to-Value (LTV) ratio and the final Max Home Price, but the core **approval limit** (Max P&I) is based on your income and debts (DTI/HER) only.
What DTI ratio do lenders use for approval?
The most common DTI targets are 36% for conventional loans, but many lenders will allow up to 43% or even 50% for qualified borrowers or specific loan types (like FHA or VA loans). This calculator uses 36% as a safe conventional target.
What is the difference between Front-End and Back-End Ratio?
The Front-End Ratio (Housing Expense Ratio) measures only the P&I payment against your gross monthly income (target 28%). The Back-End Ratio (DTI) measures all monthly debts (including the P&I payment) against your gross monthly income (target 36%).
Is the calculated amount a guarantee of approval?
No. The result is a strong estimate based on key ratios. Lenders also evaluate credit score, employment history, assets, and overall debt reserves, which are not included in this simplified calculation.