Determining your home buying budget is the most critical step in the mortgage process. While a bank might pre-approve you for a high amount, understanding the math behind "home affordability" ensures you don't become "house poor."
The 28/36 Rule Explained
Lenders typically use the 28/36 rule to determine your borrowing capacity:
Front-End Ratio (28%): Your total housing expenses (mortgage, taxes, insurance) should not exceed 28% of your gross monthly income.
Back-End Ratio (36%): Your total debt obligations (housing plus car loans, credit cards, and student loans) should not exceed 36% of your gross monthly income.
Key Factors Influencing Affordability
1. Debt-to-Income (DTI) Ratio: This is the percentage of your gross monthly income that goes toward paying debts. The lower your DTI, the higher your purchasing power.
2. Down Payment: A larger down payment reduces the loan amount, which lowers your monthly interest costs and may eliminate the need for Private Mortgage Insurance (PMI).
3. Interest Rates: Even a 1% difference in interest rates can change your purchasing power by tens of thousands of dollars over the life of the loan.
Example Calculation
If your household earns $100,000 annually, your gross monthly income is $8,333. Using the 36% rule, your total monthly debt (including the new mortgage) should stay under $3,000. If you currently pay $500/month for a car loan, you have $2,500 available for your mortgage, taxes, and insurance.
function calculateAffordability() {
var annualIncome = parseFloat(document.getElementById('annualIncome').value);
var monthlyDebt = parseFloat(document.getElementById('monthlyDebt').value);
var downPayment = parseFloat(document.getElementById('downPayment').value);
var annualInterest = parseFloat(document.getElementById('interestRate').value);
var years = parseFloat(document.getElementById('loanTerm').value);
var taxRate = parseFloat(document.getElementById('propertyTax').value) / 100;
if (isNaN(annualIncome) || isNaN(monthlyDebt) || isNaN(downPayment) || isNaN(annualInterest)) {
alert("Please enter valid numerical values.");
return;
}
// Monthly Gross Income
var monthlyGross = annualIncome / 12;
// Maximum monthly PITI (Principal, Interest, Taxes, Insurance)
// Using 36% DTI rule as a standard conservative benchmark
var maxTotalMonthlyDebt = monthlyGross * 0.36;
var availableForPITI = maxTotalMonthlyDebt – monthlyDebt;
// Estimate monthly insurance and misc (roughly $150/mo)
var monthlyInsurance = 150;
var availableForPIT = availableForPITI – monthlyInsurance;
if (availableForPIT <= 0) {
document.getElementById('maxHomePrice').innerText = "Insufficient Income";
document.getElementById('monthlyPI').innerText = "$0";
document.getElementById('resultsArea').style.display = "block";
return;
}
// Mortgage Math
var monthlyInterest = (annualInterest / 100) / 12;
var numberOfPayments = years * 12;
// Formula to solve for Loan Amount (L) based on Monthly Payment (M)
// M = L * [i(1+i)^n] / [(1+i)^n – 1] + (L+Down)*Tax/12
// Simplified approximation for solving with property taxes included:
// M = L * [AmortizationFactor] + (L + Down)*TaxFactor
var amortFactor = (monthlyInterest * Math.pow(1 + monthlyInterest, numberOfPayments)) / (Math.pow(1 + monthlyInterest, numberOfPayments) – 1);
var monthlyTaxFactor = taxRate / 12;
// Solving: availableForPIT = L * amortFactor + (L + downPayment) * monthlyTaxFactor
// availableForPIT = L * (amortFactor + monthlyTaxFactor) + downPayment * monthlyTaxFactor
// L = (availableForPIT – downPayment * monthlyTaxFactor) / (amortFactor + monthlyTaxFactor)
var loanAmount = (availableForPIT – (downPayment * monthlyTaxFactor)) / (amortFactor + monthlyTaxFactor);
if (loanAmount < 0) loanAmount = 0;
var maxHomePrice = loanAmount + downPayment;
var finalMonthlyPITI = (loanAmount * amortFactor) + (maxHomePrice * monthlyTaxFactor) + monthlyInsurance;
// Formatting
var formatter = new Intl.NumberFormat('en-US', {
style: 'currency',
currency: 'USD',
maximumFractionDigits: 0
});
document.getElementById('maxHomePrice').innerText = formatter.format(maxHomePrice);
document.getElementById('monthlyPI').innerText = formatter.format(finalMonthlyPITI);
document.getElementById('resultsArea').style.display = "block";
}