Determining how much house you can afford is a crucial step in the home-buying process. It's not just about qualifying for a loan; it's about finding a home that fits comfortably within your budget, both now and in the future. This calculator helps you estimate your maximum affordable home price by considering your income, existing debts, savings, and estimated homeownership costs.
The Math Behind the Affordability Calculation
This calculator uses common financial guidelines and formulas to provide an estimate. The core idea is to ensure your total housing expenses, plus existing debts, don't exceed a certain percentage of your gross monthly income, while also accounting for your available savings.
1. Maximum Monthly Housing Payment (PITI + Other):
Lenders and financial advisors often suggest that your total monthly housing costs (Principal, Interest, Taxes, Insurance, and sometimes HOA fees or PMI) should not exceed 28% to 36% of your gross monthly income. We'll use a common benchmark and adjust for your existing debts.
Front-End Ratio (or Housing Ratio): This ratio considers only housing costs. A common guideline is to keep this below 28% of gross monthly income.
Back-End Ratio (or Debt-to-Income Ratio – DTI): This includes all monthly debt payments (housing + other debts). A common guideline is to keep this below 36% of gross monthly income, though some lenders go up to 43% or higher.
For this calculator, we'll first determine your available funds for housing by subtracting your existing debts from a percentage of your income (e.g., 36% of gross income). This gives us a target for your maximum PITI payment.
Maximum PITI = (Gross Monthly Income * Target DTI Percentage) – Existing Monthly Debts
Note: We use a combined approach to ensure both ratios are implicitly considered.
2. Estimating Principal and Interest (P&I):
Once we have a target for your maximum PITI, we need to determine the maximum Principal & Interest (P&I) payment you can afford. This requires estimating the monthly costs for Property Taxes, Homeowners Insurance, and Private Mortgage Insurance (PMI).
Estimated Monthly Property Tax = (Estimated Home Value * Annual Property Tax Rate %) / 12
Maximum P&I Payment = Maximum PITI – Monthly Property Tax – Monthly Homeowners Insurance – Monthly PMI
3. Calculating Maximum Loan Amount:
With the maximum P&I payment, interest rate, and loan term, we can calculate the maximum loan amount you can afford using the mortgage payment formula, rearranged to solve for the loan amount (Present Value):
n = Total number of payments (Loan Term in Years * 12)
4. Determining Maximum Affordable Home Price:
The maximum affordable home price is the sum of the maximum loan amount you can qualify for and the down payment you have saved.
Maximum Affordable Home Price = Maximum Loan Amount + Down Payment
Key Inputs Explained:
Gross Monthly Income: Your total income before taxes and deductions.
Existing Monthly Debt Payments: All recurring monthly payments for loans (car, student, personal) and credit cards. This helps calculate your Debt-to-Income (DTI) ratio.
Total Savings for Down Payment & Closing Costs: The funds you have available to put towards the purchase price and associated fees.
Estimated Annual Mortgage Interest Rate: The current average interest rate you anticipate for a mortgage. Rates significantly impact your monthly payment.
Mortgage Loan Term (Years): Typically 15 or 30 years. Longer terms result in lower monthly payments but higher total interest paid.
Estimated Annual Property Tax (% of Home Value): An estimate of the annual taxes you'll pay based on the home's value. Varies by location.
Estimated Annual Homeowners Insurance: The yearly cost for protecting your home against damage or loss.
Estimated Annual PMI: Private Mortgage Insurance is usually required if your down payment is less than 20%. This is an annual cost estimate.
Disclaimer:
This calculator provides an estimate for informational purposes only. It does not constitute a loan approval or financial advice. Your actual borrowing capacity will depend on lender underwriting, credit score, loan programs, and specific property details. Always consult with a qualified mortgage lender and financial advisor.
function calculateAffordableHome() {
var monthlyIncome = parseFloat(document.getElementById("monthlyIncome").value);
var existingDebts = parseFloat(document.getElementById("existingDebts").value);
var downPayment = parseFloat(document.getElementById("downPayment").value);
var interestRate = parseFloat(document.getElementById("interestRate").value);
var loanTerm = parseFloat(document.getElementById("loanTerm").value);
var propertyTaxRate = parseFloat(document.getElementById("propertyTaxRate").value);
var homeownersInsurance = parseFloat(document.getElementById("homeownersInsurance").value);
var privateMortgageInsurance = parseFloat(document.getElementById("privateMortgageInsurance").value);
var resultDiv = document.getElementById("result");
// Input validation
if (isNaN(monthlyIncome) || monthlyIncome <= 0 ||
isNaN(existingDebts) || existingDebts < 0 ||
isNaN(downPayment) || downPayment < 0 ||
isNaN(interestRate) || interestRate <= 0 ||
isNaN(loanTerm) || loanTerm <= 0 ||
isNaN(propertyTaxRate) || propertyTaxRate < 0 ||
isNaN(homeownersInsurance) || homeownersInsurance < 0 ||
isNaN(privateMortgageInsurance) || privateMortgageInsurance < 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
// — Calculations —
// Target DTI Percentage (common guideline)
var targetDtiPercentage = 0.36; // 36%
// 1. Calculate Maximum PITI (Principal, Interest, Taxes, Insurance)
var maxPiti = (monthlyIncome * targetDtiPercentage) – existingDebts;
// Ensure maxPiti is not negative
if (maxPiti < 0) {
maxPiti = 0;
}
// 2. Estimate Monthly Costs for Taxes, Insurance, and PMI
// We need an estimated home value to calculate property tax. This is a bit of a circular dependency.
// A common approach is to iterate or make an initial guess.
// For simplicity here, we'll assume a starting point for property tax calculation, or handle it differently.
// Let's re-evaluate: Instead of property tax based on *estimated* home value, we can estimate the *maximum* monthly taxes.
// A simpler approach is to calculate the max P&I first, then work backwards.
// Let's calculate the maximum allowed for Principal & Interest (P&I)
// Maximum P&I = Max PITI – Monthly Taxes – Monthly Insurance – Monthly PMI
// Since property tax depends on the home value, which we are trying to find,
// we need to make an assumption or use an iterative approach.
// A pragmatic approach is to assume property tax as a *percentage of the calculated affordable home price*.
// This leads to a more complex formula.
// Simpler method: Estimate monthly costs for Insurance and PMI first.
var monthlyInsurance = homeownersInsurance / 12;
var monthlyPMI = privateMortgageInsurance / 12;
// Now, let's consider the property tax. A common rule of thumb is that property taxes,
// homeowners insurance, and PMI combined might represent a certain percentage of the P&I payment,
// or are added *on top* of the P&I.
// The 28% front-end ratio is for PITI.
// So, we need to find a home price (HP) such that:
// (HP * PropertyTaxRate / 12) + (Insurance / 12) + (PMI / 12) + P&I <= Max PITI
// Let's try to estimate the max P&I payment first.
// The max P&I will be a portion of the max PITI.
// If we assume the property tax, insurance, and PMI are fixed costs relative to the loan amount,
// this becomes easier. But property tax is based on home value.
// Alternative approach: Use a target DTI for total housing costs (PITI) and derive the maximum loan amount.
// The total monthly housing cost (PITI) should be within the target DTI, minus existing debts.
// Maximum PITI = (monthlyIncome * targetDtiPercentage) – existingDebts
// Let's use a common lender guideline: Total housing expenses (PITI) should not exceed 28% of gross monthly income.
// And total debt (DTI) should not exceed 36%.
// We used the 36% DTI to calculate maxPITI, which accounts for existing debts.
// So, the PITI portion of that maxPITI needs to be calculated.
// Let's simplify by assuming property tax, insurance, and PMI are a *percentage of the loan amount*.
// This is not perfectly accurate for property tax but common in simplified models.
// However, the prompt requires accurate math.
// A more accurate approach involves solving for the Home Price iteratively or through a complex formula.
// Let's use a simplified, commonly accepted method that approximates this:
// Assume the property tax rate is applied to the *final affordable home price* we are trying to find.
// var 'HP' be the affordable home price.
// Loan Amount (LA) = HP – Down Payment
// Monthly P&I is based on LA, interest rate, and loan term.
// Monthly Taxes = (HP * propertyTaxRate / 100) / 12
// Monthly Insurance = homeownersInsurance / 12
// Monthly PMI = privateMortgageInsurance / 12
// Total Housing Cost = P&I + Monthly Taxes + Monthly Insurance + Monthly PMI
// Total Housing Cost <= (monthlyIncome * targetDtiPercentage) – existingDebts
// Let's solve for the maximum P&I payment first.
// If we assume property tax is roughly 1.2% annually, homeowners insurance is $1200/yr, PMI is $0/yr,
// and the interest rate is 6.5% on a 30-year loan.
// We need to find the maximum loan amount (LA) such that:
// P&I(LA, rate, term) + (HP * taxRate/12) + Ins/12 + PMI/12 <= Max PITI
// P&I(LA, rate, term) + ((LA + DP) * taxRate/12) + Ins/12 + PMI/12 Front-end ratio
// Maximum total debt payments (DTI) = (Gross Monthly Income * 0.36) – Existing Debts -> Back-end ratio
// We'll use the more restrictive of these two for the *total* housing payment (PITI).
// For this calculator, we used 36% DTI minus existing debts to determine available funds for *all* debt,
// including housing. This implies the total housing payment (PITI) must fit within that remainder.
var maxMonthlyHousingPayment = (monthlyIncome * targetDtiPercentage) – existingDebts;
if (maxMonthlyHousingPayment < 0) maxMonthlyHousingPayment = 0;
// Now, we need to allocate this maxMonthlyHousingPayment between P&I, Taxes, Insurance, and PMI.
// Monthly Taxes = (AffordableHomePrice * propertyTaxRate / 100) / 12
// Monthly Insurance = homeownersInsurance / 12
// Monthly PMI = privateMortgageInsurance / 12
// So, P&I = maxMonthlyHousingPayment – Monthly Taxes – Monthly Insurance – Monthly PMI
// This is still dependent on AffordableHomePrice.
// Let's rearrange the P&I formula to solve for the loan amount (P).
// P = M * [ (1 + r)^n – 1 ] / r * (1 + r)^n (This is wrong, this is for future value of annuity)
// Correct formula for loan amount (PV):
// PV = M * [1 – (1 + r)^-n] / r
// Where M = monthly payment (our P&I)
// The challenge is that M (P&I) itself depends on the home price because of property taxes.
// Let's use an iterative approach or a common assumption.
// Assumption: Property tax, insurance, and PMI are roughly X% of the P&I payment or a fixed amount.
// Let's use the common structure: Max PITI is capped.
// And we need to find the Home Price (HP) that satisfies this.
// Let's use a simplified calculation that is common for these calculators:
// First, estimate the maximum loan amount based on P&I only, ignoring taxes/insurance for a moment,
// using the maxMonthlyHousingPayment as a proxy for P&I. This will give an upper bound.
// Then, we refine.
// Calculate monthly interest rate and number of payments
var monthlyInterestRate = interestRate / 100 / 12;
var numberOfPayments = loanTerm * 12;
// Let's try to find the maximum P&I payment.
// We know: P&I + MonthlyTaxes + MonthlyInsurance + MonthlyPMI <= maxMonthlyHousingPayment
// P&I = maxMonthlyHousingPayment – MonthlyTaxes – MonthlyInsurance – MonthlyPMI
// Let's assume the property tax rate is applied to the *loan amount* for a simpler calculation,
// OR, assume property tax, insurance, PMI are a *fixed portion* of the P&I payment.
// This is often done by saying PITI 0) {
roughMaxPI = maxMonthlyHousingPayment – (homeownersInsurance / 12) – (privateMortgageInsurance / 12);
if (roughMaxPI < 0) roughMaxPI = 0;
var maxLoanAmountApprox = roughMaxPI * (1 – Math.pow(1 + monthlyInterestRate, -numberOfPayments)) / monthlyInterestRate;
} else { // Handle 0 interest rate case
maxLoanAmountApprox = roughMaxPI * numberOfPayments;
}
// Now, we need to incorporate property tax.
// Let's use an iterative approach or a formula solver for this.
// A common simplification: Assume property tax is X% of the loan amount. This is inaccurate.
// Let's use the property tax rate based on home value.
// We need to find HP such that:
// PV(HP – DP, rate, term) + (HP * propertyTaxRate/100)/12 + Ins/12 + PMI/12 = Max PITI
// This equation can be solved for HP. Let's derive it.
// var M = Max PITI – Ins/12 – PMI/12 (Maximum available for P&I and Taxes)
// P&I(HP-DP) + HP * (propertyTaxRate/100)/12 = M
// This requires solving a non-linear equation.
// A common way calculators handle this is by making an assumption about the ratio of P&I to Taxes/Insurance.
// Or, they iterate.
// Let's use a direct formula derivation by approximation or a standard financial function.
// A commonly used formula, derived from financial principles and approximations:
// Maximum Affordable Home Price = ( (Max PITI – Monthly Fixed Costs) * Loan Factor + Down Payment ) / (1 + Tax Rate Factor)
// Where:
// Monthly Fixed Costs = (Homeowners Insurance / 12) + (PMI / 12)
// Loan Factor = [1 – (1 + r)^-n] / r (This is the PV factor for an ordinary annuity)
// Tax Rate Factor = propertyTaxRate / 100 / 12
var monthlyFixedCosts = (homeownersInsurance / 12) + (privateMortgageInsurance / 12);
var maxPIandTaxes = maxMonthlyHousingPayment – monthlyFixedCosts;
if (maxPIandTaxes 0) {
pvFactor = (1 – Math.pow(1 + monthlyInterestRate, -numberOfPayments)) / monthlyInterestRate;
} else { // Handle 0 interest rate case
pvFactor = numberOfPayments;
}
var taxRateFactor = propertyTaxRate / 100 / 12;
// The equation to solve is approximately:
// (HP – DP) * [r * (1+r)^n] / [(1+r)^n – 1] + HP * taxRateFactor = maxPIandTaxes
// This is hard to solve directly for HP in plain JS without iteration.
// Let's use a more direct estimation based on common calculator logic:
// Calculate the max loan amount IF property taxes were ZERO.
// Max Loan (no tax) = maxPIandTaxes * pvFactor
// Then, adjust for property tax.
// A simplified, common approach:
// Calculate the maximum mortgage amount the P&I portion can support.
// Let's assume a portion of maxMonthlyHousingPayment goes to P&I.
// For example, if taxes/insurance are 20% of PITI, then 80% is P&I.
// This requires an assumption.
// Let's use a standard formula found in financial calculators online:
// Affordable Home Price = ( (Max PITI – Monthly Ins – Monthly PMI) * PV_Factor + Down Payment ) / (1 + (Property Tax Rate / 1200) * PV_Factor)
// This formula seems incorrect or overly simplified.
// Correct approach: Solve for Loan Amount (LA)
// LA * [r * (1+r)^n] / [(1+r)^n – 1] + (LA + DP) * (taxRate/12) = M
// LA * P&I_factor + LA * taxRate_factor + DP * taxRate_factor = M
// LA * (P&I_factor + taxRate_factor) = M – DP * taxRate_factor
// LA = (M – DP * taxRate_factor) / (P&I_factor + taxRate_factor)
var pAndIFactor = (monthlyInterestRate > 0) ? (monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments)) / (Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1) : 0;
// Handle case where interest rate is 0
if (monthlyInterestRate === 0) {
pAndIFactor = 1 / numberOfPayments; // This is incorrect, for 0 rate, P&I = Loan / Term
// For 0 interest rate, P&I = Loan / numberOfPayments
// So, Loan / numberOfPayments + (Loan + DP) * taxRateFactor = M
// Loan * (1/numberOfPayments + taxRateFactor) + DP * taxRateFactor = M
// Loan * (1/numberOfPayments + taxRateFactor) = M – DP * taxRateFactor
// Loan = (M – DP * taxRateFactor) / (1/numberOfPayments + taxRateFactor)
if (numberOfPayments > 0) {
var loanAmount = (maxPIandTaxes – downPayment * taxRateFactor) / (1 / numberOfPayments + taxRateFactor);
} else {
loanAmount = 0; // Avoid division by zero if loanTerm is 0
}
} else {
// Standard calculation for interest rate > 0
var loanAmount = (maxPIandTaxes – downPayment * taxRateFactor) / (pAndIFactor + taxRateFactor);
}
// Ensure loan amount is not negative
if (loanAmount 0 && monthlyInterestRate > 0) {
formattedMonthlyPI = (loanAmount * pAndIFactor).toLocaleString(undefined, { style: 'currency', currency: 'USD', minimumFractionDigits: 0, maximumFractionDigits: 0 });
} else if (loanAmount > 0 && monthlyInterestRate === 0) {
formattedMonthlyPI = (loanAmount / numberOfPayments).toLocaleString(undefined, { style: 'currency', currency: 'USD', minimumFractionDigits: 0, maximumFractionDigits: 0 });
}
var formattedMonthlyTaxes = (affordableHomePrice * propertyTaxRate / 100 / 12).toLocaleString(undefined, { style: 'currency', currency: 'USD', minimumFractionDigits: 0, maximumFractionDigits: 0 });
var formattedMonthlyInsurance = (homeownersInsurance / 12).toLocaleString(undefined, { style: 'currency', currency: 'USD', minimumFractionDigits: 0, maximumFractionDigits: 0 });
var formattedMonthlyPMI = (privateMortgageInsurance / 12).toLocaleString(undefined, { style: 'currency', currency: 'USD', minimumFractionDigits: 0, maximumFractionDigits: 0 });
resultDiv.innerHTML =
`Your Estimated Affordable Home Price: ${formattedHomePrice}` +
`Based on your inputs, your maximum estimated loan amount is ${formattedLoanAmount}.` +
`
Estimated Total Monthly Housing Payment (PITI): ${formattedMonthlyHousingPayment}
` +
`
Estimated Monthly Principal & Interest: ${formattedMonthlyPI}