This calculator helps you determine the annualized rate of return for an investment over a specified period. The annualized rate of return (ARR), also known as the compound annual growth rate (CAGR), represents the geometric progression ratio that provides a constant rate of return on an investment, assuming that profits were reinvested at the end of each year of the investment's evaluation period.
Understanding Annualized Rate of Return (ARR)
The Annualized Rate of Return (ARR), often referred to as Compound Annual Growth Rate (CAGR), is a vital metric for investors to understand the performance of their investments over multiple periods. It smooths out volatility and provides a single, representative growth rate that would have achieved the same cumulative growth if the investment had grown at a steady rate each year.
The formula used is:
ARR = ( (Final Value / Initial Value) ^ (1 / Number of Years) ) – 1
Where:
Initial Value: The starting value of your investment.
Final Value: The ending value of your investment.
Number of Years: The total duration of the investment in years.
A positive ARR indicates growth, while a negative ARR signifies a loss in value over the period. It's crucial for comparing different investment opportunities with varying timeframes.
Example Calculation:
Let's say you invested $10,000 (Initial Investment) which grew to $15,000 (Final Investment) over a period of 5 years (Number of Years).
Calculation:
ARR = ( ($15,000 / $10,000) ^ (1 / 5) ) – 1
ARR = ( 1.5 ^ 0.2 ) – 1
ARR = 1.08447 – 1
ARR = 0.08447 or 8.45%
This means your investment grew at an average rate of 8.45% per year over the 5-year period.
function calculateAnnualizedReturn() {
var initialInvestment = parseFloat(document.getElementById("initialInvestment").value);
var finalInvestment = parseFloat(document.getElementById("finalInvestment").value);
var numberOfYears = parseFloat(document.getElementById("numberOfYears").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(initialInvestment) || isNaN(finalInvestment) || isNaN(numberOfYears) || initialInvestment <= 0 || numberOfYears <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
// Calculate Annualized Rate of Return
var arr = Math.pow((finalInvestment / initialInvestment), (1 / numberOfYears)) – 1;
// Display the result
var formattedArr = (arr * 100).toFixed(2);
resultDiv.innerHTML = "