The most-quoted illustration in finance is a small sum doubling every year for thirty years. It is arithmetically correct and practically misleading, and understanding why is worth five minutes.
The idea
Earn a return, and the return starts earning its own return. Over long periods the second part does most of the work — which is why the example uses decades.
What the example hides
It assumes the same return, every year, without fail. In crypto, returns are neither steady nor guaranteed. When a plan publishes a cap, that cap is the maximum, not the expectation — see how a plan is priced.
Volatility does something worse than lowering the average
The sequence matters, and it is not obvious. A loss of 50% needs a 100% gain to recover — not a 50% one. So a year that starts with a large fall and ends with a large rise can leave you behind someone who had a quiet, smaller year, despite the same final figure. This is the single most misunderstood fact about depositing, and market cycles shows what it looks like in practice.
What follows for a plan
- Treat any projection as arithmetic, not a forecast.
- Prefer a position you can hold without reacting to a bad cycle.
- Redeploying a payout is a choice with a cost — the money is no longer available for something else. Holding long term covers the trade-off.