A mortgage is a loan used to purchase real estate, typically a home. The monthly mortgage payment is the amount you pay each month to the lender to repay this loan. This payment usually consists of four main components, often referred to as PITI:
Principal: The actual amount borrowed from the lender.
Interest: The cost of borrowing the money, expressed as an annual percentage rate (APR).
Taxes: Property taxes, which are collected by the lender and paid to local tax authorities on your behalf.
Insurance: Homeowners insurance premiums, and sometimes Private Mortgage Insurance (PMI) if your down payment is less than 20% of the home's value.
This calculator focuses on calculating the Principal and Interest (P&I) portion of your monthly mortgage payment. Property taxes and insurance costs can vary significantly by location and property type, so they are excluded here but are crucial factors when budgeting for your total housing expense.
The Math Behind the Monthly Payment
The formula used to calculate the Principal and Interest (P&I) portion of a fixed-rate mortgage payment is derived from the standard annuity formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Your total monthly mortgage payment (Principal & Interest)
P = The principal loan amount (the amount you borrowed)
i = Your monthly interest rate. This is calculated by dividing your annual interest rate by 12. For example, an annual rate of 4.5% becomes 0.045 / 12 = 0.00375 monthly.
n = The total number of payments over the loan's lifetime. This is calculated by multiplying the number of years in your loan term by 12. For a 30-year mortgage, n = 30 * 12 = 360 payments.
How to Use This Calculator:
Loan Amount: Enter the total amount you plan to borrow for the home.
Annual Interest Rate: Enter the yearly interest rate offered by your lender (as a percentage).
Loan Term (Years): Enter the duration of the loan in years (e.g., 15, 30).
Click "Calculate Monthly Payment". The calculator will display your estimated Principal & Interest payment.
Important Considerations:
This calculator provides an estimate for the P&I portion only. Your actual total monthly housing expense will be higher once property taxes, homeowners insurance, and potential PMI are included. It's also important to remember that interest rates can fluctuate, and loan terms have significant impacts on your monthly payments and the total interest paid over the life of the loan.
function calculateMortgage() {
var loanAmount = parseFloat(document.getElementById("loanAmount").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var loanTermYears = parseFloat(document.getElementById("loanTermYears").value);
var resultValueElement = document.getElementById("result-value");
// Clear previous results and error messages
resultValueElement.textContent = "$0.00";
// Validate inputs
if (isNaN(loanAmount) || loanAmount <= 0) {
alert("Please enter a valid loan amount greater than zero.");
return;
}
if (isNaN(annualInterestRate) || annualInterestRate <= 0) {
alert("Please enter a valid annual interest rate greater than zero.");
return;
}
if (isNaN(loanTermYears) || loanTermYears <= 0) {
alert("Please enter a valid loan term in years greater than zero.");
return;
}
// Calculate monthly interest rate
var monthlyInterestRate = annualInterestRate / 100 / 12;
// Calculate total number of payments
var numberOfPayments = loanTermYears * 12;
// Calculate monthly payment using the mortgage payment formula
var monthlyPayment = 0;
if (monthlyInterestRate === 0) {
// Handle case for 0% interest rate (though unlikely for mortgages)
monthlyPayment = loanAmount / numberOfPayments;
} else {
monthlyPayment = loanAmount * (monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments)) / (Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1);
}
// Format and display the result
resultValueElement.textContent = "$" + monthlyPayment.toFixed(2);
}