One growth rate for a bumpy ride
Investments, sales and prices rarely grow by the same amount every year. The compound annual growth rate (CAGR) answers a simple question: what constant yearly rate would take you from the starting value to the ending value over the same period? It smooths out the ups and downs so you can compare a stock, a fund, a business or a home price on equal terms.
The formula
CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1
Years can be fractional: 30 months is 2.5 years. Two related figures come out of the same numbers:
- Total growth = ending value ÷ beginning value − 1
- Doubling time = ln 2 ÷ ln(1 + CAGR), close to the rule of 72 (72 ÷ CAGR in percent)
Worked example: $10,000 to $18,000 in 5 years
- Ratio: 18,000 ÷ 10,000 = 1.8, a total growth of 80%.
- CAGR: 1.8^(1/5) − 1 = 12.47% a year.
- Check: 10,000 × 1.1247⁵ ≈ 18,000.
- At that pace, money doubles in about 5.9 years (the rule of 72 gives 5.8).
Note that 80% ÷ 5 = 16% overstates the yearly growth, because it ignores compounding.
The same growth over different periods
| Period for +80% | CAGR | Doubling time |
|---|---|---|
| 1 year | 80.00% | 1.2 years |
| 3 years | 21.64% | 3.5 years |
| 5 years | 12.47% | 5.9 years |
| 10 years | 6.05% | 11.8 years |
| 20 years | 2.98% | 23.6 years |
The same total gain looks spectacular over three years and modest over twenty, roughly in line with inflation. Always quote a growth figure with its time frame.
CAGR vs average annual return
Suppose a fund gains 50% one year and loses 50% the next. The average of the two returns is 0%, yet $10,000 became $15,000 and then $7,500. The CAGR is √0.75 − 1 = −13.4% a year, which matches what actually happened to your money. Whenever returns swing, the arithmetic average flatters performance; CAGR does not.
Where CAGR is useful
- Investing: compare a fund’s 5- or 10-year CAGR with its benchmark, such as the S&P 500, whose long-run CAGR including dividends has been around 10% before inflation.
- Business: revenue CAGR is a standard line in pitch decks and annual reports.
- Real estate: the CAGR of a home’s value since purchase, compared with inflation, tells you whether it grew in real terms.
- Planning: use a realistic CAGR as the expected return in retirement or savings projections.
What CAGR does not tell you
CAGR hides volatility: two investments with the same 7% CAGR can have very different paths, and the one that fell 40% along the way was much harder to hold. It also ignores money added or withdrawn during the period. If you made regular contributions, use an internal rate of return (money-weighted return) instead, which most brokerages show on their performance pages.