This is an estimate for preapproval purposes only and does not guarantee loan approval.
Understanding Mortgage Preapproval and This Calculator
Obtaining mortgage preapproval is a crucial first step in the home-buying process. It provides a clear indication of how much a lender is willing to lend you, based on your financial profile. This helps you narrow down your home search to properties within your budget and strengthens your offer to sellers.
How This Calculator Works:
This calculator provides an estimated maximum loan amount based on common lending guidelines. It uses your provided financial information to estimate how much you might be able to borrow. The core of the calculation involves assessing your debt-to-income ratio (DTI) and then determining the loan amount that fits within those parameters, considering your down payment.
Annual Income: Your total yearly earnings before taxes.
Lenders use this to gauge your ability to repay a loan.
Total Monthly Debt Payments: This includes payments for credit cards, auto loans, student loans, personal loans, and other recurring debts. It specifically excludes your potential new mortgage payment and existing rent/mortgage, as the calculator aims to determine the maximum mortgage you can afford.
Available Down Payment: The cash you have ready to put towards the purchase of the home. A larger down payment can reduce the loan amount needed and potentially improve your loan terms.
Estimated Mortgage Interest Rate: The anticipated interest rate for your mortgage. This significantly impacts your monthly payment and the total interest paid over the life of the loan.
Loan Term: The duration of the mortgage, typically 15, 20, or 30 years. Longer terms result in lower monthly payments but higher total interest paid.
The Calculation Logic (Simplified):
Lenders often use a maximum Gross Debt Service (GDS) ratio (also known as a front-end DTI) and a Total Debt Service (TDS) ratio (also known as a back-end DTI). For simplicity, this calculator focuses on approximating your maximum affordable housing payment based on a common DTI limit (e.g., 28-36% of gross monthly income) and then derives the maximum loan amount.
1. Calculate Gross Monthly Income: `Annual Income / 12`
2. Calculate Maximum Allowable Monthly Housing Payment: `Gross Monthly Income * (Target DTI %)` (A common target DTI for housing is around 28-30%, but this can vary. We use a benchmark to estimate.)
3. Estimate Maximum Affordable P&I (Principal & Interest): `Maximum Allowable Monthly Housing Payment – Property Taxes – Homeowners Insurance – HOA Dues (if applicable)`
*Note: For this calculator, we simplify by assuming a maximum total housing payment (including PITI – Principal, Interest, Taxes, Insurance) and then subtract your existing monthly debts to see how much is left for the P&I payment.*
A more robust approach involves calculating the maximum acceptable *total* debt payment (including the potential mortgage PITI and existing debts) against your gross income (e.g., a back-end DTI of 36-45%).
4. Calculate Maximum Loan Amount: This is derived from the maximum affordable P&I payment, using the loan term and interest rate. The formula for the maximum loan amount (P) is derived from the mortgage payment formula: `M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]`. Rearranging for P, considering the P&I portion of the payment:
`P = M * [ (1 + i)^n – 1 ] / i(1 + i)^n`
where:
* `M` is your maximum affordable P&I payment.
* `i` is the monthly interest rate (`Annual Interest Rate / 12 / 100`).
* `n` is the total number of payments (`Loan Term in Years * 12`).
Important Considerations:
Lender Variances: Different lenders have different DTI thresholds, credit score requirements, and underwriting standards.
Closing Costs: This calculator does not include closing costs, which can be substantial.
Property Taxes and Insurance: These vary significantly by location and property type.
Credit Score: Your credit score is a major factor in loan approval and interest rates.
Pre-Qualification vs. Preapproval: Preapproval involves a more thorough review of your finances by a lender than a simple pre-qualification.
Disclaimer: This tool is for estimation purposes only. For an accurate preapproval amount, please consult with a qualified mortgage lender.
function calculatePreapproval() {
var annualIncome = parseFloat(document.getElementById("annualIncome").value);
var monthlyDebt = parseFloat(document.getElementById("monthlyDebt").value);
var downPayment = parseFloat(document.getElementById("downPayment").value);
var interestRate = parseFloat(document.getElementById("interestRate").value);
var loanTerm = parseFloat(document.getElementById("loanTerm").value);
var maxLoanAmountElement = document.getElementById("maxLoanAmount");
// Clear previous results and errors
maxLoanAmountElement.textContent = "$0";
maxLoanAmountElement.style.color = "#28a745"; // Reset to success green
// Input validation
if (isNaN(annualIncome) || annualIncome <= 0 ||
isNaN(monthlyDebt) || monthlyDebt < 0 ||
isNaN(downPayment) || downPayment < 0 ||
isNaN(interestRate) || interestRate 20 || // Realistic rate range
isNaN(loanTerm) || loanTerm <= 0) {
maxLoanAmountElement.textContent = "Please enter valid numbers.";
maxLoanAmountElement.style.color = "red";
return;
}
var grossMonthlyIncome = annualIncome / 12;
// Using a common benchmark for total debt-to-income ratio (back-end DTI)
// Lenders typically look at a ratio of PITI + other debts / gross income.
// A common maximum is around 43-45%, but this varies.
// We'll estimate based on a slightly more conservative approach here for pre-approval idea.
// Let's assume a target of max 36% for total housing payment (PITI) + other debts,
// after accounting for other debts.
// A more direct approach: Estimate maximum P&I payment.
// Max Housing Payment (PITI) often capped around 28-30% of gross monthly income.
// Let's use 30% as a benchmark for maximum PITI.
var maxPitiPayment = grossMonthlyIncome * 0.30;
// Then, subtract estimated taxes, insurance, etc.
// This is a simplification. A real lender calculates these more precisely.
// Let's estimate Property Tax and Insurance as a percentage of the *potential* loan amount.
// This iterative process is complex. For a simple estimator, we can approximate.
// Alternative Simplified Logic:
// 1. Calculate maximum total debt allowed (e.g., 43% of gross monthly income)
// 2. Subtract existing monthly debts from this maximum total debt.
// 3. The remainder is the maximum monthly mortgage payment (PITI) you can afford.
// 4. From max PITI, estimate P&I by subtracting property taxes and insurance.
// 5. Calculate loan amount based on max P&I.
// Let's try a simpler benchmark: Maximum P&I based on income and existing debt.
// Estimate maximum monthly P&I payment based on income and existing debt.
// Max Housing Payment (PITI) = Gross Monthly Income * (Front-end DTI Target, e.g., 0.28)
// Max Total Debt Payment (PITI + Other Debts) = Gross Monthly Income * (Back-end DTI Target, e.g., 0.43)
// Let's use the back-end DTI as it's more comprehensive.
var maxTotalDebtAllowed = grossMonthlyIncome * 0.43; // Target back-end DTI of 43%
var maxMonthlyMortgagePayment = maxTotalDebtAllowed – monthlyDebt;
if (maxMonthlyMortgagePayment <= 0) {
maxLoanAmountElement.textContent = "Cannot afford mortgage based on inputs.";
maxLoanAmountElement.style.color = "red";
return;
}
// Now, we need to estimate the loan amount that results in maxMonthlyMortgagePayment.
// This payment includes P&I, Taxes, and Insurance.
// We need to back out Taxes and Insurance to get P&I.
// Estimating Taxes and Insurance is tricky without property details.
// A common rule of thumb is ~1% of property value annually for T&I.
// Property Value = Loan Amount + Down Payment.
// So, Annual T&I = (Loan Amount + Down Payment) * 0.01
// Monthly T&I = (Loan Amount + Down Payment) * 0.01 / 12
// This creates a circular dependency (Loan Amount depends on Loan Amount).
// We need to make an assumption or use an iterative approach.
// SIMPLIFICATION FOR ESTIMATOR:
// Assume monthly T&I is a fixed percentage of the GROSS MONTHLY INCOME or a simpler estimate.
// Let's assume monthly taxes and insurance combined are roughly 1% of the *estimated*
// annual property value, or a percentage of gross income.
// A common estimate for monthly PITI can be around 10-15% of gross income, but this varies hugely.
// Let's try to work backwards from the maximum *total* debt allowed more directly.
// If maxTotalDebtAllowed is 43% of gross income, and `monthlyDebt` is fixed,
// then `maxMonthlyMortgagePayment` (PITI) is what's left.
// Let's assume PITI is approx. 1.2% of the total home value (Loan + Down Payment) per month.
// Home Value = Loan Amount + Down Payment.
// Monthly PITI = (Loan Amount + Down Payment) * 0.012
// So, we have: maxMonthlyMortgagePayment = (Loan Amount + Down Payment) * 0.012
// Rearranging for Loan Amount:
// Loan Amount = (maxMonthlyMortgagePayment / 0.012) – Down Payment
// This is still a simplification as it bundles P&I with T&I in the percentage.
// The correct way is to calculate the loan amount for a given P&I payment.
// Let's revert to calculating P&I from maxMonthlyMortgagePayment.
// Estimate Monthly Taxes & Insurance as a placeholder.
// Let's assume monthly taxes and insurance are approximately 0.15% of the *loan amount* per month.
// This is a rough estimate.
var estimatedMonthlyTaxesAndInsurance = 0;
var loanAmount = 0;
var monthlyInterestRate = interestRate / 100 / 12;
var numberOfPayments = loanTerm * 12;
// We need to find a Loan Amount (P) such that P + T&I <= maxMonthlyMortgagePayment
// And the P&I portion calculated from P is affordable.
// A pragmatic approach for a pre-approval ESTIMATOR:
// Assume the maxMonthlyMortgagePayment IS the P&I payment. This is an OVERESTIMATE
// of affordability as it ignores taxes/insurance.
// Or, assume a percentage for T&I. Let's assume T&I is ~20% of the PITI payment.
// This means P&I is ~80% of PITI.
var estimatedMonthlyPI = maxMonthlyMortgagePayment * 0.80; // P&I portion
if (estimatedMonthlyPI <= 0) {
maxLoanAmountElement.textContent = "Cannot afford mortgage payment.";
maxLoanAmountElement.style.color = "red";
return;
}
// Now, use the mortgage payment formula to find the principal (loan amount)
// M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
// P = M * [ (1 + i)^n – 1 ] / [ i(1 + i)^n ]
// Check for zero interest rate to avoid division by zero
if (monthlyInterestRate === 0) {
// If interest rate is 0, loan amount is simply monthly payment * number of payments
loanAmount = estimatedMonthlyPI * numberOfPayments;
} else {
var factor = Math.pow(1 + monthlyInterestRate, numberOfPayments);
loanAmount = estimatedMonthlyPI * (factor – 1) / (monthlyInterestRate * factor);
}
// The calculated loanAmount is the maximum Principal & Interest loan we can afford.
// However, the initial `maxMonthlyMortgagePayment` was for PITI.
// The `estimatedMonthlyPI` calculation was to derive a P&I payment that FEELS affordable
// within the overall DTI.
// Let's refine the logic slightly. The target `maxMonthlyMortgagePayment` is for PITI.
// We need to find a loan amount `P` such that:
// `P` (Principal) + `Taxes` + `Insurance` <= `maxMonthlyMortgagePayment`.
// And the P&I for `P` is calculated using the mortgage formula.
// The estimation of Taxes and Insurance is the hard part without property specifics.
// Let's use a direct approach based on loan amount affordability:
// Consider the maxTotalDebtAllowed = Gross Monthly Income * 0.43
// Subtract `monthlyDebt` to get the maximum allowed PITI payment.
// Let's assume a ratio for Property Tax + Insurance. For example, 0.15% of the
// total home value per month.
// Home Value = P + Down Payment.
// Monthly T&I = (P + Down Payment) * 0.0015
// P&I Payment = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1]
// So, P * [ i(1 + i)^n ] / [ (1 + i)^n – 1] + (P + Down Payment) * 0.0015 <= maxMonthlyMortgagePayment
// This is an equation difficult to solve directly for P without iteration.
// For a practical calculator, we approximate.
// Let's use the previously calculated `estimatedMonthlyPI` (which was 80% of max PITI).
// This `estimatedMonthlyPI` is what we can afford for Principal & Interest.
// The loan amount derived from this is our best estimate.
// Ensure the loan amount is not negative due to calculation errors or extreme inputs
loanAmount = Math.max(0, loanAmount);
// Format the output
var formattedLoanAmount = loanAmount.toLocaleString('en-US', { style: 'currency', currency: 'USD', minimumFractionDigits: 0, maximumFractionDigits: 0 });
maxLoanAmountElement.textContent = formattedLoanAmount;
maxLoanAmountElement.style.color = "#28a745"; // Success green for calculated result
}