CAGR Calculator
Calculate the Compound Annual Growth Rate (CAGR), annualized investment returns, total percentage gains, real inflation-adjusted wealth growth, and target future value projections.
Investment Values
Annual Compounded Progression Schedule
| Year | Beginning Value | Year Gain | Ending Value | Cumulative ROI |
|---|
How to Calculate Compound Annual Growth Rate (CAGR)
To calculate CAGR: 1. Divide the ending investment value (EV) by the beginning investment value (BV). 2. Raise the result to the power of 1 divided by the number of years n: (EV / BV)^(1/n). 3. Subtract 1 from the result and multiply by 100 to express CAGR as an annual percentage.
Compound Annual Growth Rate Definition & Mathematical Formula
The Compound Annual Growth Rate (CAGR) represents the constant mean annual growth rate an investment would require to expand from its initial starting balance to its final balance over a specified number of compounding periods.
Geometric Mean vs. Arithmetic Mean (Why AAR Distorts Returns)
A common mistake in financial analysis is using the simple arithmetic average annual return (AAR). The arithmetic average ignores sequence of returns and compounding losses:
If $100 drops by 50% to $50 in Year 1, then gains 50% to $75 in Year 2, the arithmetic average is (-50% + 50%) / 2 = 0.0%. However, you lost 25% of your wealth!
The true CAGR is ($75 / $100)^(1/2) − 1 = -13.40% per year. CAGR correctly accounts for the asymmetric math of portfolio drawdowns.
Inflation-Adjusted Real CAGR & The Fisher Equation
Nominal CAGR shows raw dollar growth, but inflation constantly erodes purchasing power. To calculate your true real wealth expansion, apply the exact Fisher relationship:
For example, a nominal CAGR of 10.0% in an economic climate with 3.5% annual consumer price inflation results in a Real CAGR of (1.10 / 1.035) − 1 = 6.28% real annualized yield.
Target Future Value & Required Growth Rate Projections
By rearranging the CAGR formula, you can solve for any missing variable in your financial model:
Project ending capital given a known expected annual return rate.
Determine how many years are required to reach a specific financial target.
Applications in Stock Portfolios, Venture Capital & Business Revenue
| Domain | Beginning Metric ($BV$) | Ending Metric ($EV$) | Strategic Utility |
|---|---|---|---|
| Public Equity Funds | Portfolio Initial NAV | Portfolio Final NAV | Compare fund manager alpha against S&P 500 benchmark |
| Corporate Finance | Base Year Revenue | 5-Year Revenue Target | Standardizes multi-year corporate expansion for M&A valuation |
| Venture Capital | Seed Round Post-Money | Series B Enterprise Value | Evaluates valuation momentum and startup growth velocity |
Step-by-Step Worked Numerical Solutions
Problem: An index fund investment of $25,000 grows to $68,000 over 12 years. Calculate its CAGR.
Problem: You have $50,000 today and require $200,000 in 15 years. What annual CAGR is required?
Common Pitfalls (Volatility Smoothing & Interim Cash Flows)
Ignoring In-Between Volatility
CAGR connects only two points in time. An investment that drops 60% before recovering has the same CAGR as one that grew smoothly.
Interim Capital Additions (SIPs)
CAGR fails when intermediate cash deposits or withdrawals occur. In those situations, calculate Internal Rate of Return (IRR) or XIRR.
Nominal vs Real Purchasing Power
A 7% CAGR during a period of 6% hyperinflation delivers only 0.94% real annual growth in purchasing power. Always adjust for inflation.
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