Understanding Loan Amortization and Extra Payments
Loan amortization is the process of paying off a debt over time through regular, scheduled payments. Each payment you make goes towards both the principal (the original amount borrowed) and the interest charged by the lender. An amortization schedule details how each payment is allocated and how the loan balance decreases over its lifespan.
How Amortization Works
In a standard amortizing loan, early payments are heavily weighted towards interest, with only a small portion going to the principal. As time progresses, this allocation shifts, with more of each payment applied to the principal. The formula for calculating the standard monthly payment (M) is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
P is the principal loan amount.
i is the monthly interest rate (annual rate divided by 12).
n is the total number of payments (loan term in years multiplied by 12).
Each month, the interest due is calculated on the remaining principal balance. The remainder of the payment is then deducted from the principal.
The Power of Extra Payments
Making extra payments, even small ones, can significantly impact the life of your loan and the total interest paid. When you make an extra payment, it is typically applied directly to the principal balance. This reduces the amount on which future interest is calculated, leading to:
Shorter Loan Term: You pay off your loan much faster.
Reduced Total Interest Paid: Less interest accrues over time.
This calculator helps you visualize these benefits. By inputting your loan details and an optional extra monthly payment, you can see how much time and money you can save.
Calculator Logic Explained
Our calculator first determines the standard monthly payment without any extra payments using the amortization formula. Then, it simulates the loan payoff month by month, incorporating the extra payment. In each period:
Calculate the monthly interest based on the current balance.
Determine the total payment: standard payment + extra payment.
Subtract the calculated interest from the total payment to find the principal reduction.
Update the remaining balance by subtracting the principal reduction.
Keep track of the total interest paid and the number of months passed.
This process continues until the loan balance reaches zero. The results show the original loan terms, the estimated payoff time with extra payments, the total interest saved, and the total amount repaid.
function calculateAmortization() {
var loanAmount = parseFloat(document.getElementById("loanAmount").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var loanTermYears = parseInt(document.getElementById("loanTermYears").value);
var extraPayment = parseFloat(document.getElementById("extraPayment").value);
var resultDiv = document.getElementById("result");
var originalLoanAmountResult = document.getElementById("originalLoanAmountResult");
var annualInterestRateResult = document.getElementById("annualInterestRateResult");
var loanTermYearsResult = document.getElementById("loanTermYearsResult");
var extraPaymentResult = document.getElementById("extraPaymentResult");
var totalInterestResult = document.getElementById("totalInterestResult");
var totalAmountPaidResult = document.getElementById("totalAmountPaidResult");
var payoffTimeResult = document.getElementById("payoffTimeResult");
// Clear previous results
resultDiv.style.display = "none";
originalLoanAmountResult.textContent = "";
annualInterestRateResult.textContent = "";
loanTermYearsResult.textContent = "";
extraPaymentResult.textContent = "";
totalInterestResult.textContent = "";
totalAmountPaidResult.textContent = "";
payoffTimeResult.textContent = "";
// Input validation
if (isNaN(loanAmount) || loanAmount <= 0 ||
isNaN(annualInterestRate) || annualInterestRate < 0 ||
isNaN(loanTermYears) || loanTermYears <= 0 ||
isNaN(extraPayment) || extraPayment 0) {
standardMonthlyPayment = loanAmount * (monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments)) / (Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1);
} else {
standardMonthlyPayment = loanAmount / numberOfPayments; // Simple division if interest rate is 0
}
var totalInterestPaid = 0;
var totalAmountPaid = 0;
var remainingBalance = loanAmount;
var months = 0;
var actualMonthlyPayment = standardMonthlyPayment + extraPayment;
// Amortization loop
while (remainingBalance > 0) {
var interestThisMonth = remainingBalance * monthlyInterestRate;
var principalThisMonth = actualMonthlyPayment – interestThisMonth;
// Ensure we don't overpay the last payment
if (principalThisMonth > remainingBalance) {
actualMonthlyPayment = remainingBalance + interestThisMonth;
principalThisMonth = remainingBalance;
}
remainingBalance -= principalThisMonth;
totalInterestPaid += interestThisMonth;
totalAmountPaid += actualMonthlyPayment;
months++;
// Prevent infinite loops for edge cases
if (months > loanTermYears * 12 * 5) { // Arbitrary limit to prevent infinite loops
alert("Calculation exceeded maximum iterations. Please check your inputs.");
return;
}
}
// Format results
var formattedLoanAmount = loanAmount.toLocaleString('en-US', { style: 'currency', currency: 'USD' });
var formattedTotalInterest = totalInterestPaid.toLocaleString('en-US', { style: 'currency', currency: 'USD' });
var formattedTotalAmountPaid = totalAmountPaid.toLocaleString('en-US', { style: 'currency', currency: 'USD' });
var formattedExtraPayment = extraPayment.toLocaleString('en-US', { style: 'currency', currency: 'USD' });
var years = Math.floor(months / 12);
var remainingMonths = months % 12;
var payoffTimeString = "";
if (years > 0) {
payoffTimeString += years + " year" + (years !== 1 ? "s" : "");
}
if (remainingMonths > 0) {
if (years > 0) payoffTimeString += ", ";
payoffTimeString += remainingMonths + " month" + (remainingMonths !== 1 ? "s" : "");
}
if (payoffTimeString === "") payoffTimeString = "N/A";
originalLoanAmountResult.textContent = formattedLoanAmount;
annualInterestRateResult.textContent = annualInterestRate.toFixed(2) + "%";
loanTermYearsResult.textContent = loanTermYears;
extraPaymentResult.textContent = formattedExtraPayment;
totalInterestResult.textContent = formattedTotalInterest;
totalAmountPaidResult.textContent = formattedTotalAmountPaid;
payoffTimeResult.textContent = payoffTimeString;
resultDiv.style.display = "block";
}