Understanding Your Mortgage Pre-Approval Potential
Obtaining mortgage pre-approval is a crucial step in the home-buying process. It provides a strong indication of how much a lender is willing to lend you, allowing you to shop for homes within a specific budget and giving you a competitive edge over other buyers. This calculator helps you estimate your potential mortgage borrowing power based on key financial factors.
How Pre-Approval is Determined (The Math Behind the Calculator)
Lenders typically use debt-to-income (DTI) ratios to assess your ability to repay a mortgage. There are two main DTI ratios they consider:
Front-End Ratio (Housing Ratio): This compares your estimated total monthly housing costs (principal, interest, property taxes, homeowners insurance – PITI) to your gross monthly income. While not directly calculated here, it influences the maximum loan amount.
Back-End Ratio (Total Debt Ratio): This compares your total monthly debt obligations (including the estimated PITI for the new mortgage) to your gross monthly income. Most lenders have a maximum acceptable back-end DTI, commonly around 43%, though this can vary.
This calculator focuses on the back-end ratio to estimate your borrowing capacity. It works by:
Calculating Maximum Allowable Total Monthly Debt:
Your gross annual income is converted to gross monthly income. This is then multiplied by the maximum DTI ratio (we use 43% as a common benchmark).
Gross Monthly Income = Annual Income / 12 Max Allowable Total Monthly Debt = Gross Monthly Income * 0.43
Determining Maximum Allowable P&I Payment:
The maximum total monthly debt is reduced by your existing total monthly debt payments.
Max Allowable P&I Payment = Max Allowable Total Monthly Debt - Total Monthly Debt Payments
Calculating Maximum Loan Amount:
Using the maximum allowable Principal & Interest (P&I) payment, the loan term, and the estimated interest rate, we calculate the maximum loan amount you can afford. This uses the standard loan payment formula (amortization formula) rearranged to solve for the principal.
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Maximum P&I Payment
P = Principal Loan Amount (what we're solving for)
n = Total number of payments (Loan Term in Years * 12)
Rearranging for P:
P = M * [ (1 + i)^n – 1] / [ i(1 + i)^n ]
Calculating Estimated Mortgage Amount:
The maximum loan amount is then adjusted by your down payment to give you an idea of the total home price you might be able to afford.
Estimated Mortgage Amount = Maximum Loan Amount (P) Estimated Affordable Home Price = Maximum Loan Amount (P) + Down Payment
Important Considerations:
This is an estimate for pre-approval purposes. Actual loan offers may vary.
Lenders will also consider your credit score, employment history, assets, and other factors.
Property taxes and homeowners insurance (PITI components beyond Principal & Interest) are not fully factored into the loan amount calculation but are crucial for your overall housing affordability.
The 43% DTI ratio is a guideline; your specific lender may have different thresholds.
Use this calculator as a starting point to understand your borrowing potential and prepare for discussions with mortgage lenders.
function calculateMortgagePreApproval() {
var annualIncome = parseFloat(document.getElementById("annualIncome").value);
var monthlyDebt = parseFloat(document.getElementById("monthlyDebt").value);
var downPayment = parseFloat(document.getElementById("downPayment").value);
var estimatedInterestRate = parseFloat(document.getElementById("estimatedInterestRate").value);
var loanTermYears = parseFloat(document.getElementById("loanTermYears").value);
var resultDiv = document.getElementById("result");
// Clear previous result and styling
resultDiv.innerHTML = "";
resultDiv.classList.remove('negative');
// Input validation
if (isNaN(annualIncome) || annualIncome <= 0 ||
isNaN(monthlyDebt) || monthlyDebt < 0 ||
isNaN(downPayment) || downPayment < 0 ||
isNaN(estimatedInterestRate) || estimatedInterestRate <= 0 ||
isNaN(loanTermYears) || loanTermYears <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
// — Calculations —
// DTI Ratio Assumption (commonly used max back-end DTI)
var maxDtiRatio = 0.43;
// Gross Monthly Income
var grossMonthlyIncome = annualIncome / 12;
// Max Allowable Total Monthly Debt (including PITI)
var maxAllowableTotalMonthlyDebt = grossMonthlyIncome * maxDtiRatio;
// Max Allowable Principal & Interest (P&I) Payment
var maxAllowablePI = maxAllowableTotalMonthlyDebt – monthlyDebt;
// Check if maxAllowablePI is positive. If not, the user likely can't afford any mortgage based on DTI.
if (maxAllowablePI 0) {
var numerator = Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1;
var denominator = monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments);
maxLoanAmount = maxAllowablePI * (numerator / denominator);
} else {
// Handle case of 0% interest rate (though unlikely for mortgages)
maxLoanAmount = maxAllowablePI * numberOfPayments;
}
// Ensure loan amount is not negative due to rounding or edge cases
maxLoanAmount = Math.max(0, maxLoanAmount);
// Estimated Affordable Home Price
var estimatedAffordableHomePrice = maxLoanAmount + downPayment;
// Format results for display
var formattedMaxLoanAmount = maxLoanAmount.toLocaleString('en-US', { style: 'currency', currency: 'USD' });
var formattedDownPayment = downPayment.toLocaleString('en-US', { style: 'currency', currency: 'USD' });
var formattedEstimatedAffordableHomePrice = estimatedAffordableHomePrice.toLocaleString('en-US', { style: 'currency', currency: 'USD' });
var formattedMaxAllowablePI = maxAllowablePI.toLocaleString('en-US', { style: 'currency', currency: 'USD' });
// Display results
resultDiv.innerHTML = `
Estimated Max Loan Amount:
${formattedMaxLoanAmount}
(This is the maximum Principal & Interest you can afford monthly: ${formattedMaxAllowablePI}/month)
With your ${formattedDownPayment} down payment, your estimated affordable home price is:
${formattedEstimatedAffordableHomePrice}
`;
}