How to Calculate Compound Annual Rate of Return

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Compound Annual Growth Rate (CAGR) Calculator

Calculation Result

Your Compound Annual Growth Rate (CAGR) is: 0%

function calculateCAGR() { var begin = parseFloat(document.getElementById('beginningValue').value); var end = parseFloat(document.getElementById('endingValue').value); var years = parseFloat(document.getElementById('durationYears').value); var resultBox = document.getElementById('cagr-result-box'); var cagrDisplay = document.getElementById('cagrValue'); var summaryDisplay = document.getElementById('cagrSummary'); if (isNaN(begin) || isNaN(end) || isNaN(years) || begin <= 0 || years <= 0) { alert("Please enter valid positive numbers. Initial value and years must be greater than zero."); return; } var cagr = (Math.pow((end / begin), (1 / years)) – 1) * 100; var totalGain = ((end – begin) / begin) * 100; resultBox.style.display = "block"; cagrDisplay.innerText = cagr.toFixed(2) + "% per year"; summaryDisplay.innerText = "Over a period of " + years + " years, your investment saw a total absolute return of " + totalGain.toFixed(2) + "%. This is equivalent to a smoothed annual return of " + cagr.toFixed(2) + "%."; }

How to Calculate Compound Annual Rate of Return (CAGR)

The Compound Annual Growth Rate (CAGR) is one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time. Unlike simple average returns, CAGR accounts for the effect of compounding, providing a "smoothed" annual rate that represents what an investment would have yielded if it had grown at a steady rate each year.

The CAGR Formula

CAGR = [(Ending Value / Beginning Value) ^ (1 / t)] – 1

Where:

  • Ending Value: The value of the investment at the end of the period.
  • Beginning Value: The value of the investment at the start of the period.
  • t: The number of years (or periods) the investment was held.

Step-by-Step Calculation Example

Imagine you invested $10,000 in a stock portfolio. After 5 years, your portfolio is worth $18,000. To find the annual rate of return:

  1. Divide the ending value by the beginning value: 18,000 / 10,000 = 1.8
  2. Raise the result to the power of 1 divided by the number of years: 1.8 ^ (1/5) = 1.8 ^ 0.2 ≈ 1.1247
  3. Subtract 1 from the result: 1.1247 – 1 = 0.1247
  4. Multiply by 100 to get the percentage: 12.47%

This means your investment grew at a compound rate of 12.47% every year for five years.

Why Use CAGR Instead of Average Return?

The simple average return can be misleading in finance. For example, if a $100 investment drops 50% in year one (to $50) and gains 50% in year two (to $75), the "average" return is 0% [(-50+50)/2]. However, you have actually lost $25. The CAGR would correctly show a negative annual return of -13.4%, reflecting the actual loss of capital over time.

Limitations of CAGR

While CAGR is an excellent tool for comparing different investments, it does have limitations:

  • Ignores Volatility: It assumes steady growth and does not reflect the "rollercoaster" of market fluctuations.
  • Intermittent Cash Flows: CAGR does not account for money added to or withdrawn from the investment during the period (for those scenarios, use Internal Rate of Return – IRR).
  • Historical Only: Past CAGR does not guarantee future performance.

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