Understanding Compound Annual Growth Rate (CAGR)
The Compound Annual Growth Rate (CAGR) is a vital metric used to measure the average annual rate of return for an investment over a specified period, assuming that profits were reinvested at the end of each year. It smooths out volatility, providing a more representative picture of growth than simple average growth rates. CAGR is particularly useful for comparing the performance of different investments over time, as it accounts for the effect of compounding.
How CAGR Works
CAGR answers the question: "What constant annual growth rate would be needed for an investment to grow from its beginning balance to its ending balance over a certain number of years?" It essentially represents the geometric mean growth rate.
The CAGR Formula
The formula for calculating CAGR is as follows:
CAGR = ( (Ending Value / Beginning Value) ^ (1 / Number of Years) ) - 1
Where:
- Ending Value: The value of the investment at the end of the period.
- Beginning Value: The value of the investment at the beginning of the period.
- Number of Years: The total number of years over which the growth occurred.
Why Use CAGR?
- Smooths Volatility: It ignores the ups and downs of the investment during the period, providing a steady growth rate.
- Benchmarking: Allows for easy comparison of different investments or business performances.
- Forecasting: Can be used to project future investment values, although it assumes historical growth rates will continue.
Example Calculation
Let's say you invested $10,000 in a stock portfolio. After 5 years, the portfolio is worth $25,000. To calculate the CAGR:
- Beginning Value = $10,000
- Ending Value = $25,000
- Number of Years = 5
Using the formula:
CAGR = ( ($25,000 / $10,000) ^ (1 / 5) ) - 1
CAGR = ( 2.5 ^ 0.2 ) - 1
CAGR = 1.2011 - 1
CAGR = 0.2011
This means your investment had a Compound Annual Growth Rate of approximately 20.11% per year over the 5-year period.
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function calculateCAGR() {
var beginningValue = parseFloat(document.getElementById("beginningValue").value);
var endingValue = parseFloat(document.getElementById("endingValue").value);
var numberOfYears = parseFloat(document.getElementById("numberOfYears").value);
var resultDiv = document.getElementById("result");
if (isNaN(beginningValue) || isNaN(endingValue) || isNaN(numberOfYears) ||
beginningValue <= 0 || endingValue < 0 || numberOfYears <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
if (beginningValue === 0) {
resultDiv.innerHTML = "Beginning value cannot be zero.";
return;
}
var ratio = endingValue / beginningValue;
var exponent = 1 / numberOfYears;
var cagr = Math.pow(ratio, exponent) – 1;
// Format the result as a percentage
var formattedCAGR = (cagr * 100).toFixed(2);
resultDiv.innerHTML = "The Compound Annual Growth Rate (CAGR) is: