Calculate Compound Rate of Return

Compound Annual Growth Rate (CAGR) Calculator

function calculateCAGR() { var startVal = parseFloat(document.getElementById('cagr_start_val').value); var endVal = parseFloat(document.getElementById('cagr_end_val').value); var periods = parseFloat(document.getElementById('cagr_periods').value); var resultBox = document.getElementById('cagr-result-box'); if (isNaN(startVal) || isNaN(endVal) || isNaN(periods)) { resultBox.style.display = 'block'; resultBox.innerHTML = 'Please enter valid numeric values for all fields.'; return; } if (startVal <= 0 || periods <= 0) { resultBox.style.display = 'block'; resultBox.innerHTML = 'Beginning Value and Number of Periods must be greater than zero.'; return; } // CAGR Formula: (Ending Value / Beginning Value) ^ (1 / n) – 1 var ratio = endVal / startVal; var exponent = 1 / periods; var cagrDecimal = Math.pow(ratio, exponent) – 1; var cagrPercent = cagrDecimal * 100; // Absolute return calculation var absoluteReturn = endVal – startVal; var absolutePercent = (absoluteReturn / startVal) * 100; resultBox.style.display = 'block'; resultBox.innerHTML = '' + '' + ''; }

Understanding Compound Rate of Return

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, which can be misleading when an investment fluctuates, CAGR provides a smoothed annual rate that describes the growth of an investment as if it had grown at a steady rate on an annually compounded basis.

Why Not Use Simple Average Return?

Imagine you invest $10,000. In Year 1, it grows 100% to $20,000. In Year 2, it drops 50% back to $10,000. A simple average return calculation would suggest your average return is 25% ((100% – 50%) / 2). However, your actual money shows you have made exactly $0 profit. CAGR corrects this illusion and would correctly show a 0% return.

The CAGR Formula

The mathematical formula used in the calculator above is:

CAGR = ( Ending Value / Beginning Value )^1/n – 1

Where:

• Ending Value: The value of the asset at the end of the period.
• Beginning Value: The initial investment amount.
• n: The number of periods (usually years).

Example Calculation

Let's look at a realistic example of a stock portfolio:

• Initial Investment (2018): $50,000
• Current Value (2023): $85,000
• Time Elapsed: 5 Years

Using the formula:

1. Divide Ending by Beginning: 85,000 / 50,000 = 1.7
2. Raise to the power of (1/5): 1.7^0.2 = 1.112
3. Subtract 1: 1.112 – 1 = 0.112
4. Convert to percentage: 0.112 * 100 = 11.2%

This means that effectively, the portfolio grew at a steady rate of 11.2% every single year to reach $85,000, regardless of the actual volatility experienced during those 5 years.

When to Use This Calculator

This tool is essential for investors and business analysts in several scenarios:

• Comparing Investments: Comparing the performance of a volatile stock against a fixed-income bond or a savings account.
• Business Growth: Measuring the annual growth of revenue, user base, or market share over a multi-year period.
• Portfolio Analysis: Determining the true performance of retirement accounts like 401(k)s or IRAs over decades.

Limitations of CAGR

While CAGR is a powerful metric, it does not account for investment risk. It implies a smooth growth curve, masking the volatility that may have occurred during the investment period. For a complete picture, investors should consider CAGR alongside standard deviation or other risk metrics.