Trader Toolkit · Calculator

Compound Growth

What a constant rate does over time, in both directions.

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Small on small, in time, grows tall:and so do losses, after all.

A constant rate, repeated

Result

Starting balance

Account currency

Rate per period

Negative rates are as valid as positive ones.

Number of periods

A period is whatever you decide: a week, a month.

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After 12 periods at +2%

12,682.42 USD

+2,682.42 USD (+26.82%) from the start

The same at −2%

7,847.17 USD

−2,152.83 USD from the start

Balance by period. Solid line: +2% per period, ending at 12,682.42 USD. Dashed line: −2% per period, ending at 7,847.17 USD. The dotted line is the starting balance. An illustration of arithmetic, not a projection of returns.

SimulationA calculation on the figures you entered. A mathematical illustration, not a projection of returns. Educational information, not investment advice or a recommendation to trade.

How it works

Formula

balance after n periods = start × (1 + rate)ⁿ

With your numbers

1Factor applied each period (1 + rate)1 + 2% = 1.02
2Applied 12 times1.02^12 = 1.268242
3Balance at the end10,000.00 × 1.268242 = 12,682.42 USD
4Change from the start12,682.42 − 10,000.00 = +2,682.42 USD (+26.82%)
5The same rate with the opposite sign (−2%)10,000.00 × 0.98^12 = 7,847.17 USD

Assumptions

A mathematical illustration, not a projection of returns. No trading result arrives as a constant rate, period after period.
The same rate is applied to the whole balance every period, with nothing added or withdrawn and no costs.
The opposite-sign path is always drawn beside the one you entered, because a rate is as easily negative as positive.
A gain of a given percentage followed by a loss of the same percentage does not return to the start: it ends below it.

Terms used

In plain language

The same rule, applied again and again, bends a straight line.

Compounding means each period’s rate is applied to the balance as it then stands, including whatever was gained or lost before. A constant positive rate therefore produces a curve that steepens; a constant negative rate produces one that falls quickly at first and then flattens as there is less left to lose.

This page draws both, always, because the mathematics has no preference between them. It is an illustration of a formula. Trading results do not arrive as a constant rate, and nothing here is a projection of what an account will do.

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How it works

Formula

balance after n periods = start × (1 + rate)ⁿ

With your numbers

1Factor applied each period (1 + rate)1 + 2% = 1.02

2Applied 12 times1.02^12 = 1.268242

3Balance at the end10,000.00 × 1.268242 = 12,682.42 USD

4Change from the start12,682.42 − 10,000.00 = +2,682.42 USD (+26.82%)

5The same rate with the opposite sign (−2%)10,000.00 × 0.98^12 = 7,847.17 USD

Assumptions

A mathematical illustration, not a projection of returns. No trading result arrives as a constant rate, period after period.

The same rate is applied to the whole balance every period, with nothing added or withdrawn and no costs.

The opposite-sign path is always drawn beside the one you entered, because a rate is as easily negative as positive.

A gain of a given percentage followed by a loss of the same percentage does not return to the start: it ends below it.

Terms used