Cumulative Gain Calculator

Formula

The formula to calculate the Cumulative Gain (CG) is:

\[ CG = P \cdot ((1 + r)^t - 1) \]

Where:

$ CG $ is the cumulative gain ($).
$ P $ is the initial investment ($).
$ r $ is the gain rate per period (expressed as a decimal).
$ t $ is the time period (years).

What is Cumulative Gain?

Cumulative gain is the total amount of gain an investment has earned, not just the amount it has increased in value over a specific period. It takes into account the compound interest effect, where the gains from one period benefit from the gains of previous periods. This concept is crucial for understanding the long-term growth potential of investments and for comparing different investment opportunities.

Example Calculation

Consider an example where:

Initial Investment (P): $1000
Gain Rate per Period (r): 0.05 (5%)
Time Period (t): 10 years

Using the formula to calculate the Cumulative Gain:

\[ CG = 1000 \cdot ((1 + 0.05)^{10} - 1) = 1000 \cdot (1.6289 - 1) = 628.89 \]

This means that the cumulative gain for this example is approximately $628.89.