Compounding Calculator
Balance over time at a constant rate with periodic contributions, and how much of the result comes from compounding rather than from the returns themselves.
- Total contributed
- 10,000.00 USD
- Final balance
- 12,682.42 USD
- Gain
- +2,682.42 USD
- Total return
- 26.82%
- Same rate without compounding
- 12,400.00 USD
- Difference compounding makes
- +282.42 USD
A constant return per period is a model, not a projection — real results vary and the order matters. compounding works in both directions: the same mechanism that grows a positive return magnifies a negative one, which is why a sequence averaging zero usually ends below where it started.
The formula
FV = P₀ · (1 + g)ⁿ + C · [((1 + g)ⁿ − 1) ÷ g]
P₀ = starting balance
g = return per period
n = number of periods
C = contribution per periodThe first term grows the starting balance; the second is the future value of a series of contributions, each compounding for the periods remaining after it arrives.
Compounding is symmetric, and that is the part to sit with
The pleasant version of compounding is well covered elsewhere. The version worth understanding is that the same mechanism operates on losses, and it does not cancel out.
A 10% loss followed by a 10% gain does not return you to where you started — it leaves 99%, because the gain is earned on the reduced balance. Enter a negative rate and the comparison row shows this directly: compounding makes a negative sequence worse than simple arithmetic would suggest, by the same mechanism that makes a positive one better.
A sequence of returns averaging zero reliably ends below where it started. The larger the swings, the larger the shortfall. This is the same asymmetry the drawdown recovery calculator measures from the other direction.
Why constant-rate models mislead
A constant rate is the simplest possible model and the least like reality in a specific way: it removes sequence. With contributions involved, the same set of returns in a different order produces a different ending balance, because a poor period early affects a smaller balance than a poor period late.
So a projection built on an average return is not the average of the projections. Treat the output as a way to understand the shape of the curve, not as a forecast of an account.
What it does not include
- Fees and funding. Both come out of the balance each period, so the effective rate is lower than the gross one. See the trading fee calculator.
- Taxes. Jurisdiction-dependent and outside scope.
- Variance. The single largest omission, and the reason a smooth curve is a misleading picture of a trading account.
The useful takeaway
Not that compounding produces large numbers over long horizons — that is well known and is why the calculator exists at all. The useful one is that the mechanism is indifferent to direction, so protecting the balance from large negative periods matters more than the arithmetic of the average return suggests. That is the same conclusion a deterministic loss limit is built on.
FAQ
What is the difference between compound and simple growth?
Simple growth applies the rate to the original balance every period; compound growth applies it to the balance including everything earned so far. Over a few periods the difference is small, and it widens geometrically — which is what the comparison row on this page shows for the inputs you entered.
Why does a sequence averaging zero end below where it started?
Because gains and losses are applied multiplicatively rather than added. A 10% loss followed by a 10% gain leaves 99% of the original, since the gain is calculated on the reduced balance. The average return is zero and the realised return is negative, and the gap widens as the swings get larger.
Is a constant rate per period realistic?
No, and the calculator is a model rather than a projection for exactly that reason. Real returns vary, and their order matters — the same set of returns in a different sequence produces a different ending balance once contributions are involved. Use this to understand the shape of compounding, not to forecast an account.
Where do contributions get added?
At the end of each period, so a contribution does not earn that period’s return. If yours are added at the start, the result will be slightly higher than shown. The difference is small over a few periods and becomes visible over many.