Amortization is the process of gradually paying off a debt over time through a series of regular payments. Each payment made towards an amortizing loan, such as a mortgage or an auto loan, typically consists of two parts: principal and interest. As you make payments, a larger portion of your payment goes towards the principal over time, while the interest portion decreases.
How to Calculate Amortization
The core of amortization calculation involves determining the fixed periodic payment. The most common formula used for this is the annuity formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Your total periodic payment (what this calculator calculates as the Monthly Payment)
P = The principal loan amount (the amount you borrowed)
i = Your periodic interest rate (annual rate divided by the number of payment periods per year)
n = The total number of payments over the loan's lifetime (loan term in years multiplied by the number of payment periods per year)
For a standard monthly payment scenario:
The annual interest rate is divided by 12 to get the monthly interest rate (i).
The loan term in years is multiplied by 12 to get the total number of monthly payments (n).
Example Calculation:
Let's say you have a loan with the following details:
Loan Amount (P): $200,000
Annual Interest Rate: 5%
Loan Term: 30 years
Step 1: Calculate the periodic interest rate (i).
i = 5% / 12 = 0.05 / 12 ≈ 0.00416667
Step 2: Calculate the total number of payments (n).
n = 30 years * 12 months/year = 360 payments
Step 3: Plug these values into the formula.
M = 200,000 [ 0.00416667(1 + 0.00416667)^360 ] / [ (1 + 0.00416667)^360 – 1]
M = 200,000 [ 0.00416667 * (1.00416667)^360 ] / [ (1.00416667)^360 – 1]
M = 200,000 [ 0.00416667 * 4.467744 ] / [ 4.467744 – 1]
M = 200,000 [ 0.0186156 ] / [ 3.467744 ]
M = 200,000 * 0.00536821
M ≈ $1,073.64
This calculator determines this monthly payment and also computes the total amount paid over the life of the loan and the total interest accrued.
Use Cases for Amortization Calculators:
Mortgage Planning: Understanding your monthly payments for home buying.
Loan Comparison: Comparing different loan offers with varying rates and terms.
Debt Management: Planning how to pay off loans faster or understanding the impact of extra payments.
Financial Forecasting: Projecting future expenses and savings.
Investment Analysis: Understanding the cost of debt financing for investments.
function calculateAmortization() {
var loanAmount = parseFloat(document.getElementById("loanAmount").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var loanTermYears = parseFloat(document.getElementById("loanTermYears").value);
var monthlyPaymentValue = document.getElementById("monthlyPaymentValue");
var totalPaidValue = document.getElementById("totalPaidValue");
var totalInterestValue = document.getElementById("totalInterestValue");
// Clear previous results
monthlyPaymentValue.innerHTML = "$0.00";
totalPaidValue.innerHTML = "$0.00";
totalInterestValue.innerHTML = "$0.00";
// Validate inputs
if (isNaN(loanAmount) || isNaN(annualInterestRate) || isNaN(loanTermYears) || loanAmount <= 0 || annualInterestRate < 0 || loanTermYears <= 0) {
alert("Please enter valid positive numbers for all fields.");
return;
}
// Calculate monthly interest rate
var monthlyInterestRate = annualInterestRate / 100 / 12;
// Calculate total number of payments
var numberOfPayments = loanTermYears * 12;
var monthlyPayment = 0;
var totalPaid = 0;
var totalInterest = 0;
if (monthlyInterestRate === 0) {
// Handle zero interest rate scenario
monthlyPayment = loanAmount / numberOfPayments;
totalPaid = monthlyPayment * numberOfPayments;
totalInterest = 0;
} else {
// Standard amortization formula
var numerator = monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments);
var denominator = Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1;
monthlyPayment = loanAmount * (numerator / denominator);
totalPaid = monthlyPayment * numberOfPayments;
totalInterest = totalPaid – loanAmount;
}
// Display results
monthlyPaymentValue.innerHTML = "$" + monthlyPayment.toFixed(2);
totalPaidValue.innerHTML = "$" + totalPaid.toFixed(2);
totalInterestValue.innerHTML = "$" + totalInterest.toFixed(2);
}