Definition
Compound annual growth rate is the constant annual rate at which an initial amount would have to grow to reach a final amount over a specified number of years, used as a single-figure summary of investment or asset performance over a period.
Why it matters
Multi-year investment performance rarely proceeds in equal annual steps, and the sequence of actual annual returns can obscure the average rate of growth over the period. Compound annual growth rate compresses the period into a single interpretable figure and enables comparison of investments over identical spans. The compression discards the sequence, which matters more in some contexts (retirement decumulation) than in others (accumulation with steady contributions).
How it works
Compound annual growth rate is derived from three inputs: the beginning value, the ending value, and the number of years. The calculation solves for the annualized growth rate that, applied every year and compounded, would produce the ending value from the beginning value. It is a geometric mean rather than an arithmetic mean, which is why it is systematically lower than the arithmetic average of the annual returns over the same period whenever those annual returns vary. An investment that grows from $100,000 to $150,000 over 10 years has a compound annual growth rate of approximately 4.14 percent, meaning $100,000 growing at 4.14 percent per year compounded for 10 years produces $150,000.
In practice
When you compare investments or asset classes over a period, compound annual growth rate is the correct summary; the arithmetic mean of the annual returns is not. When you see a stated long-run return for stocks or bonds, it is almost always a compound annual growth rate. Be alert to the beginning and ending dates the figure uses. Endpoint sensitivity is significant for long-horizon returns, and different starting years produce different figures for the same asset class. In retirement income planning, compound annual growth rate characterizes accumulation-phase performance well but does not capture the sequence-of-returns risk that shapes decumulation outcomes.
Related terms
- Real versus nominal returns
- Total return
- Discount rate
- Internal rate of return
- Sequence of returns risk
- Safe withdrawal rate
- Sharpe ratio