The formula
final balance = start × (1 + r)^n + deposits × ((1 + r)^n − 1) ÷ r
The first term is compounding on what you began with. The second is what regular deposits become. Keeping them separate matters, because they answer different questions: the first is about trading, the second is about saving, and adding them together hides which one did the work.
What the curve really shows
| Return per month | 12 months | 24 months | 36 months |
|---|---|---|---|
| 1% | +12.7% | +27% | +43% |
| 2% | +26.8% | +61% | +107% |
| 3% | +42.6% | +103% | +190% |
| 5% | +79.6% | +223% | +480% |
| 10% | +214% | +887% | +3,000% |
Two things are worth noticing. The first is how modest 1–2% a month looks and how substantial it becomes — this is the honest case for patience, and it is real.
The second is how quickly the table stops describing anything achievable. A sustained 5% a month is roughly 80% a year, every year, with no losing month. A sustained 10% is a number that would make someone the most successful trader on record within a decade. The arithmetic is correct at every row; the rows stop being about trading somewhere around the third one.
The assumption that breaks
Compounding assumes the return repeats. Trading returns are a sequence, and sequences have order.
Two accounts with identical average monthly returns finish in different places if one had its drawdown early and the other late, because compounding is multiplicative — a 20% loss followed by a 20% gain leaves you at 96%, and the order of those two changes the base each one applies to. That asymmetry is the same one behind drawdown recovery, and it is why smooth projections and real equity curves diverge even when the average is honest.
There is also a behavioural break the arithmetic cannot see. The projection assumes position size grows with the balance — that you will risk 1% of a tripled account as calmly as 1% of the original. Most people do not. Sizing stalls at the level that feels comfortable, and the curve quietly flattens into a straight line.
Using it honestly
It is a useful tool for two questions and a misleading one for a third.
Good: how long would it take at this rate, and how much of my growth is trading rather than deposits. Both are structural questions where the arithmetic is exactly right.
Bad: what will my account be worth in three years. That requires the return to be stable, and the only way to know whether yours is stable is a track record long enough to have an error bar — which most accounts do not have.