Mortgage Payment Calculator
Understanding Your Mortgage Payment
A mortgage is a significant financial commitment, and understanding how your monthly payment is calculated is crucial.
The primary components of your monthly mortgage payment, often referred to as P&I (Principal and Interest), are determined by
three key factors: the loan amount (principal), the annual interest rate, and the loan term (the length of time you have to repay the loan).
The Mortgage Payment Formula
The standard formula used to calculate the fixed monthly payment for a mortgage is:
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 borrow)
- i = Your monthly interest rate. This is your annual interest rate divided by 12. For example, if your annual rate is 6%, your monthly rate is 0.06 / 12 = 0.005.
- n = The total number of payments over the loan's lifetime. This is your loan term in years multiplied by 12. For a 30-year mortgage, n = 30 * 12 = 360.
It's important to note that this calculation typically only covers the principal and interest portion of your payment.
Many mortgage payments also include escrow for property taxes and homeowner's insurance, which would be added to this P&I amount to get your total monthly housing expense.
Example Calculation
Let's say you are taking out a mortgage with the following terms:
- Loan Amount (P): $250,000
- Annual Interest Rate: 4.5%
- Loan Term: 30 years
First, we need to calculate the monthly interest rate (i) and the total number of payments (n):
- Monthly Interest Rate (i) = 4.5% / 12 = 0.045 / 12 = 0.00375
- Total Number of Payments (n) = 30 years * 12 months/year = 360
Now, plugging these values into the formula:
M = 250,000 [ 0.00375(1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1]
M = 250,000 [ 0.00375(1.00375)^360 ] / [ (1.00375)^360 – 1]
M = 250,000 [ 0.00375 * 3.82832 ] / [ 3.82832 – 1]
M = 250,000 [ 0.014356 ] / [ 2.82832 ]
M = 3589 / 2.82832
M ≈ $1,269.15
So, the estimated monthly principal and interest payment for this mortgage would be approximately $1,269.15.
Using a mortgage calculator like the one above can quickly provide this figure and help you compare different loan scenarios.
function calculateMortgage() {
var principal = parseFloat(document.getElementById("principal").value);
var interestRate = parseFloat(document.getElementById("interestRate").value);
var loanTerm = parseFloat(document.getElementById("loanTerm").value);
var resultDiv = document.getElementById("result");
if (isNaN(principal) || principal <= 0) {
resultDiv.innerHTML = "Please enter a valid loan amount.";
return;
}
if (isNaN(interestRate) || interestRate <= 0) {
resultDiv.innerHTML = "Please enter a valid annual interest rate.";
return;
}
if (isNaN(loanTerm) || loanTerm <= 0) {
resultDiv.innerHTML = "Please enter a valid loan term in years.";
return;
}
var monthlyInterestRate = interestRate / 100 / 12;
var numberOfPayments = loanTerm * 12;
var monthlyPayment = principal * (monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments)) / (Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1);
if (isNaN(monthlyPayment) || !isFinite(monthlyPayment)) {
resultDiv.innerHTML = "Calculation resulted in an error. Please check your inputs.";
} else {
resultDiv.innerHTML = "
Your Estimated Monthly Payment (P&I):
$" + monthlyPayment.toFixed(2) + "";
}
}
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