Headlines love to say "the S&P 500 returned 10% a year," but no calendar year ever returns a smooth 10%. Some years gain 25%, others lose 20%. The single number people quote is usually <strong>CAGR</strong> — Compound Annual Growth Rate — a way of describing the whole trip as if it had grown at one steady rate.

The CAGR Formula

CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) − 1. It answers one question: if my investment had grown at a constant rate every year, what rate would produce the same ending value?

Worked Example

Suppose an account grows from $10,000 to $20,000 over 7 years. CAGR = (20,000 / 10,000)^(1/7) − 1 = 2^(0.1429) − 1 ≈ 0.104 = <strong>10.4%</strong>. Notice we never used the middle years — CAGR only cares about the start, the end, and the time between.

CAGR vs a Simple Average Return

  • •<strong>Simple average adds up yearly returns and divides by the count.</strong> It overstates growth because it ignores the order and the compounding between years.
  • •<strong>CAGR is geometrically correct.</strong> It reflects what actually happened to a dollar invested at the start and withdrawn at the end.
  • •<strong>Example gap:</strong> Up 20% then down 20% looks like a 0% simple average, but your balance is down 4% (1.2 × 0.8 = 0.96). CAGR correctly shows a small negative rate.

Where CAGR Breaks Down

  1. It hides volatility. A wild up-and-down ride and a calm steady climb can share the same CAGR, but the bumpy one is far riskier.
  2. It assumes a smooth path, so it can flatter investments that had one lucky spike.
  3. Short windows are noisy. A 1-year CAGR is just that year's return; it says little about the future.
  4. It ignores cash flows. Adding or withdrawing money mid-period distorts CAGR unless you use a money-weighted return.

Use CAGR to compare investments over the same time window, then check volatility separately. Our CAGR calculator handles the math, and the investment calculator shows how a steady assumed rate compounds with contributions.

<strong>Disclaimer:</strong> The content provided on CompoundFig is for educational and informational purposes only and does not constitute financial, tax, legal, or investment advice. All calculations and projections are hypothetical and based on assumed rates of return, which may not reflect actual market conditions. Individual results will vary. Consult a qualified financial professional before making decisions. CompoundFig does not provide personalized financial recommendations.