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 calculates the principal and interest payment for a fixed-rate loan over its entire term. This calculation helps you determine how much you'll pay each month, excluding potential additional costs like property taxes, homeowner's insurance, and private mortgage insurance (PMI), which are often included in an 'escrow' payment.
The formula used to calculate the monthly payment (M) for a mortgage is as follows:
$M = P \left[ \frac{r(1+r)^n}{(1+r)^n – 1} \right]$
Where:
M = Your total monthly mortgage payment (principal and interest).
P = The principal loan amount (the total amount borrowed).
r = Your monthly interest rate. This is calculated by dividing your annual interest rate by 12. For example, a 3.5% annual rate becomes 0.035 / 12 = 0.00291667.
n = The total number of payments over the loan's lifetime. This is calculated by multiplying the number of years in the loan term by 12. For a 30-year mortgage, n = 30 * 12 = 360.
How the Calculator Works:
This calculator takes your input for the loan amount, the annual interest rate, and the loan term in years. It then converts the annual interest rate to a monthly rate and the loan term in years to the total number of monthly payments. Finally, it applies the mortgage payment formula to compute your estimated monthly principal and interest payment.
Example:
Let's say you are taking out a mortgage for $300,000 (P = 300,000) with an annual interest rate of 3.5% (annual r = 0.035) and a loan term of 30 years (loan term = 30).
So, the estimated monthly principal and interest payment would be approximately $1,349.84. Remember, this figure does not include property taxes, homeowners insurance, or potential PMI, which would increase your total monthly housing expense.
Use this calculator to estimate your monthly mortgage payments for different loan scenarios and to better understand the financial implications of your home purchase.
function calculateMortgage() {
var loanAmount = parseFloat(document.getElementById("loanAmount").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var loanTermYears = parseInt(document.getElementById("loanTermYears").value);
var monthlyPaymentSpan = document.getElementById("monthlyPayment");
if (isNaN(loanAmount) || loanAmount <= 0 ||
isNaN(annualInterestRate) || annualInterestRate < 0 ||
isNaN(loanTermYears) || loanTermYears 0) {
monthlyPayment = loanAmount * (monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments)) / (Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1);
} else {
// Handle zero interest rate case
monthlyPayment = loanAmount / numberOfPayments;
}
if (isNaN(monthlyPayment) || !isFinite(monthlyPayment)) {
monthlyPaymentSpan.textContent = "Calculation error.";
monthlyPaymentSpan.style.color = "red";
} else {
monthlyPaymentSpan.textContent = "$" + monthlyPayment.toFixed(2);
monthlyPaymentSpan.style.color = "#004a99"; // Reset color to default
}
}