Compounding calculator
See what a fixed percentage return applied every period does to a balance, with optional deposits or withdrawals.
Arithmetic, not a forecast. This applies exactly the same return to every period. Real trading results vary from period to period, include losing stretches, and are not known in advance. Nothing on this page suggests any rate of return is achievable.
How it is calculated
Each period, the return is applied to the balance as it stands, then the deposit (or withdrawal) is added:
Here r is the return per period as a decimal, so 2% is 0.02. Repeating that step n times gives a closed form:
The first part is the starting balance compounded for n periods. The second is the deposits: each one compounds for the periods left after it is added, so the last deposit earns nothing and the first earns n − 1 periods of return. When r is zero there is no growth, and the ending balance is simply the start plus all deposits.
The rate and the periods must use the same unit. A return per month goes with a number of months; a yearly rate over a number of months gives a meaningless figure.
Twelve periods at 2%
| Scenario | Working | Ending balance |
|---|---|---|
| 10,000 at +2%, no deposits | 10,000 × 1.02¹² | 12,682.42 |
| 10,000 at +2%, 100 deposited each period | 12,682.42 + 100 × (1.02¹² − 1) ÷ 0.02 | 14,023.63 |
| 10,000 at −2%, no deposits | 10,000 × 0.98¹² | 7,847.17 |
The 1,200 deposited in the second row became 1,341.21, because the earlier deposits compounded for several periods before the end. The third row shows the same arithmetic in reverse: losses compound too.
Pitfalls and assumptions
- Equal ups and downs do not cancel. A gain of 10% followed by a loss of 10% leaves 99% of the start, because the loss is taken from a larger balance. The drawdown recovery calculator shows how large that effect becomes.
- Trading returns are not constant. A steady rate is a simplification for arithmetic. The order of good and bad periods changes the path, and a sequence with the same average return can end in a very different place.
- Costs, tax and withdrawals. Fees and tax are not modelled. A withdrawal can be entered as a negative deposit.
- Rounding. Figures are rounded to two decimals for display; the calculation carries full precision.
Frequently asked questions
How does compounding work on a trading account?
Compounding means each period’s percentage return is applied to the balance including all earlier gains or losses, not just to the original deposit. Two periods of +2% on 10,000 give 10,200 and then 10,404, not 10,400.
What is the formula for compound growth?
Without deposits, ending balance = starting balance × (1 + r)^n, where r is the return per period as a decimal and n is the number of periods. With a deposit at the end of every period, add deposit × ((1 + r)^n − 1) ÷ r.
Are deposits added at the start or the end of each period?
At the end, after that period’s return has been applied. A deposit therefore starts earning from the following period, and the final deposit earns nothing.
What happens with a negative return per period?
The balance shrinks by a percentage of what is left each period, so each loss is smaller in money than the one before. 10,000 at −2% for 12 periods ends at 7,847.17, a fall of 21.5%, not 24%.
How many periods does it take to double a balance?
At a constant rate r with no deposits, doubling takes ln 2 ÷ ln(1 + r) periods. At 2% per period that is 35.0 periods. The “rule of 72” approximates the same figure as 72 ÷ 2 = 36.
Is this a forecast of what an account will do?
No. The calculator shows the arithmetic of a constant return. It does not know what returns are possible, and nothing about the result suggests any particular rate is achievable.
Related calculators
- Drawdown recovery calculatorThe gain needed to return to a previous peak after a drawdown of any size, with a reference table.
- Trading expectancy calculatorThe average amount a set of trades makes or loses per trade, from win rate, average win and average loss.
- Risk of ruin calculatorHow often simulated accounts with your win rate, payoff and risk per trade fall to a set drawdown.
Stop calculating by hand. Journal it.
Import your trades from MetaTrader, cTrader, NinjaTrader, Tradovate or any CSV and see win rate, expectancy, drawdown and your prop-firm room — computed for you, stored only on your device.