The one formula
CAGR = (FV / PV)^(1/t) − 1, final value over initial value, taken to the power of one over the years, minus one. It answers a precise question: what single steady annual rate, compounding, would have turned the starting amount into the ending amount over that period. Real investments never grow steadily; CAGR is the smooth line drawn through a jagged journey, and that is both its usefulness and its blind spot.
Why intuition overestimates
Money doubled in 5 years feels like "20% a year", 100% divided by 5. The real answer is 14.87%, because compounding does part of the work: each year's growth builds on an already-larger base. The gap between the naive division and the true rate widens fast with time:
| Result | Naive (total ÷ years) | Actual CAGR |
|---|---|---|
| 2× in 5 years | 20% | 14.87% |
| 2× in 10 years | 10% | 7.18% |
| 3× in 10 years | 20% | 11.61% |
| 10× in 20 years | 45% | 12.20% |
A ten-bagger over twenty years, a genuinely great outcome, is a 12.2% CAGR, not 45%. Marketing that quotes total returns over long periods is exploiting exactly this intuition gap.
CAGR vs total return vs ROI
- Total return: the whole percentage gain, time ignored. Good for headlines, useless for comparison.
- ROI: gain over cost, the same thing, usually applied to projects and purchases. Still no time axis.
- CAGR: total return converted to an annual compounding rate. The only one of the three that lets a 5-year holding and a 12-year holding be compared fairly.
The conversion habit is worth building: whenever a return is quoted, ask "over how long?" and annualise it before reacting. A "60% gain" is a 9.9% CAGR over five years and a 4.8% CAGR over ten.
CAGR's blind spot
CAGR sees two dots, start and end, and nothing between. It ignores the path: an investment that fell 40% and recovered shows the same CAGR as one that climbed smoothly, though the two demanded very different nerves. More important, it ignores interim cash flows entirely. If you added money monthly or withdrew along the way, a CAGR computed from "total in" and "final value" mixes your deposits into the "growth" and can be wildly wrong in either direction. For SIPs, top-ups and partial withdrawals, the right measure is the XIRR calculator, which weighs every cash flow by its date.
Using CAGR forward, not just backward
The formula also runs in reverse for planning: a target of turning ₹10 lakh into ₹25 lakh in 8 years requires (25/10)^(1/8) − 1 = 12.1% a year, a demanding but not absurd equity-market assumption. Plug candidate rates into the compound interest calculator to see the year-by-year path a given CAGR implies. And always sanity-check against inflation: a 7% CAGR during 6% inflation is a 1% real return, the inflation calculator shows why nominal rates flatter. For monthly investing plans, the SIP calculator handles the contribution math CAGR cannot.