Annualized Rate of Return Calculator
What is the Annualized Rate of Return?
The Annualized Rate of Return (ARR), often simply called the compound annual growth rate (CAGR), is a measure of the average annual growth of an investment over a specified period of time longer than one year. It represents the smoothed-out rate of return, assuming that profits were reinvested at the end of each year. This metric is crucial for comparing the performance of different investments, especially when they have different time horizons.
Unlike a simple average rate of return, the annualized rate of return accounts for the effect of compounding, providing a more accurate picture of an investment's growth potential. It helps investors understand how their money has grown on average each year, making it easier to set realistic future investment goals and evaluate the success of their strategies.
How to Calculate the Annualized Rate of Return
The formula for calculating the Annualized Rate of Return is as follows:
ARR = [ (Final Value / Initial Investment) ^ (1 / Number of Years) ] – 1
Where:
- Initial Investment: The starting amount of money invested.
- Final Value: The total value of the investment at the end of the period.
- Number of Years: The total duration of the investment in years.
The result is typically expressed as a percentage.
Example Calculation:
Let's say you invested $10,000 (Initial Investment) in a stock that is now worth $15,000 (Final Value) after 5 years (Number of Years).
Using the formula:
ARR = [ ($15,000 / $10,000) ^ (1 / 5) ] – 1
ARR = [ 1.5 ^ 0.2 ] – 1
ARR = 1.08447 – 1
ARR = 0.08447
As a percentage, the Annualized Rate of Return is approximately 8.45%.
function calculateAnnualizedReturn() {
var initialInvestment = parseFloat(document.getElementById("initialInvestment").value);
var finalValue = parseFloat(document.getElementById("finalValue").value);
var numberOfYears = parseFloat(document.getElementById("numberOfYears").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(initialInvestment) || isNaN(finalValue) || isNaN(numberOfYears)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (initialInvestment <= 0) {
resultDiv.innerHTML = "Initial Investment must be greater than zero.";
return;
}
if (numberOfYears <= 0) {
resultDiv.innerHTML = "Number of Years must be greater than zero.";
return;
}
// Calculate Annualized Rate of Return
var ratio = finalValue / initialInvestment;
var exponent = 1 / numberOfYears;
var annualizedReturn = Math.pow(ratio, exponent) – 1;
// Display the result
var formattedReturn = (annualizedReturn * 100).toFixed(2);
resultDiv.innerHTML = "Your Annualized Rate of Return is:
" + formattedReturn + "%";
}
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