A mortgage is a significant financial commitment, and understanding how your monthly payment is calculated is crucial. The standard mortgage payment formula determines the fixed amount you'll pay each month for the life of the loan, covering both principal and interest.
The Mortgage Payment Formula
The most common formula used to calculate a fixed-rate mortgage payment is the annuity formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Your total monthly mortgage payment (principal and interest)
P = The principal loan amount (the total amount you borrow)
i = Your monthly interest rate. This is calculated by dividing your annual interest rate by 12 (e.g., if your annual rate is 4.5%, your monthly rate is 0.045 / 12 = 0.00375).
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 (e.g., for a 30-year mortgage, n = 30 * 12 = 360).
How the Calculator Works
This calculator takes the inputs you provide:
Loan Amount (P): The total sum you are borrowing to purchase your home.
Annual Interest Rate: The yearly percentage charged by the lender. This is converted to a monthly rate (i) for the calculation.
Loan Term (Years): The duration of the loan, typically 15, 20, or 30 years. This is converted into the total number of monthly payments (n).
It then applies the annuity formula to compute your estimated fixed monthly principal and interest payment.
Important Considerations
Please note that this calculator provides an estimate for the principal and interest portion of your mortgage payment only. Your actual total monthly housing expense will likely be higher and may include:
Property Taxes: Annual taxes assessed by your local government, often paid monthly as part of your mortgage payment (escrow).
Homeowner's Insurance: Insurance to protect against damage to your home, also often paid monthly via escrow.
Private Mortgage Insurance (PMI): If your down payment is less than 20% of the home's value, lenders typically require PMI.
Homeowner Association (HOA) Fees: If applicable, these are regular fees for community amenities and maintenance.
This calculator is a valuable tool for budgeting and comparing different loan scenarios. For precise figures and personalized advice, always consult with a mortgage lender or financial advisor.
function calculateMortgage() {
var loanAmount = parseFloat(document.getElementById("loanAmount").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var loanTermYears = parseFloat(document.getElementById("loanTermYears").value);
var monthlyPaymentElement = document.getElementById("monthlyPayment");
if (isNaN(loanAmount) || isNaN(annualInterestRate) || isNaN(loanTermYears) || loanAmount <= 0 || annualInterestRate < 0 || loanTermYears 0) {
monthlyPayment = loanAmount * (monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments)) / (Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1);
} else {
// Handle zero interest rate case to avoid division by zero
monthlyPayment = loanAmount / numberOfPayments;
}
monthlyPaymentElement.textContent = "$" + monthlyPayment.toFixed(2);
}