A mortgage is a significant financial commitment, and understanding how your monthly payment is calculated is crucial for budgeting and financial planning. 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 Explained
The formula used to calculate the monthly mortgage payment (M) is a standard amortization 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). This is the "Loan Amount" in our calculator.
i = Your monthly interest rate. This is calculated by dividing your annual interest rate by 12. For example, if your annual rate is 3.75%, your monthly rate is 3.75 / 100 / 12 = 0.003125.
n = The total number of payments over the loan's lifetime. This is calculated by multiplying the loan term in years by 12. For a 30-year mortgage, n = 30 * 12 = 360.
How the Calculator Works
Our calculator takes the inputs you provide for the Loan Amount, Annual Interest Rate, and Loan Term (in years) and applies the formula above:
It converts the annual interest rate to a monthly interest rate (divides by 12).
It calculates the total number of payments (multiplies loan term by 12).
It plugs these values, along with your loan amount, into the mortgage payment formula.
The result is your estimated fixed monthly payment for principal and interest.
Important Considerations:
This calculator provides an estimate for the principal and interest (P&I) portion of your mortgage payment. It does not include other costs that are typically part of your total monthly housing expense, often referred to as PITI:
Principal & Interest (P&I): The core loan repayment.
Taxes: Property taxes, which vary by location and property value.
Insurance: Homeowners insurance and potentially Private Mortgage Insurance (PMI) if your down payment is less than 20%.
Escrow: Many lenders collect estimated amounts for taxes and insurance with your monthly payment and pay them on your behalf.
Your actual mortgage payment may be higher once these additional costs are factored in. For a precise figure, consult with a mortgage lender.
Example Calculation:
Let's say you're looking to buy a home and need a mortgage with the following details:
Loan Amount (P): $300,000
Annual Interest Rate: 4.5%
Loan Term: 30 Years
First, we calculate the monthly interest rate (i) and the total number of payments (n):
Calculating this yields an estimated monthly payment of approximately $1,520.07 for principal and interest. This calculator automates this process for you instantly.
function calculateMortgage() {
var loanAmount = parseFloat(document.getElementById("loanAmount").value);
var interestRate = parseFloat(document.getElementById("interestRate").value);
var loanTerm = parseFloat(document.getElementById("loanTerm").value);
var errorMessageElement = document.getElementById("errorMessage");
var monthlyPaymentElement = document.getElementById("monthlyPayment");
errorMessageElement.innerText = ""; // Clear previous errors
if (isNaN(loanAmount) || loanAmount <= 0) {
errorMessageElement.innerText = "Please enter a valid loan amount.";
monthlyPaymentElement.innerText = "$0.00";
return;
}
if (isNaN(interestRate) || interestRate <= 0) {
errorMessageElement.innerText = "Please enter a valid annual interest rate (greater than 0).";
monthlyPaymentElement.innerText = "$0.00";
return;
}
if (isNaN(loanTerm) || loanTerm <= 0) {
errorMessageElement.innerText = "Please enter a valid loan term in years (greater than 0).";
monthlyPaymentElement.innerText = "$0.00";
return;
}
// Calculate monthly interest rate
var monthlyInterestRate = interestRate / 100 / 12;
// Calculate total number of payments
var numberOfPayments = loanTerm * 12;
// Calculate monthly payment using the mortgage formula
// M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
var numerator = monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments);
var denominator = Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1;
var monthlyPayment = loanAmount * (numerator / denominator);
// Format the monthly payment to two decimal places
monthlyPaymentElement.innerText = "$" + monthlyPayment.toFixed(2);
}