CAGR stands for Compound Annual Growth Rate, and it is a financial metric used to express the average annual growth rate of an investment, asset, or any other metric over a specific period of time. CAGR takes into account the compounding effect, which means it considers how an investment’s growth builds upon itself over time.

CAGR is particularly useful when analyzing investments or metrics that experience fluctuations in growth over the years, as it provides a smoothed-out representation of the overall growth rate.

The formula to calculate CAGR is as follows:

\[CAGR = (\frac{E}{B})^{\frac{1}{n}} − 1\]Where:

- E is the ending value of the investment or metric after the specified period.
- B is the beginning value of the investment or metric at the start of the period.
- n is the number of compounding periods (usually years) in the time frame. The formula works by finding the growth rate that, if applied annually, would lead from the beginning value to the ending value over the given number of years.

Here’s a step-by-step example of how to calculate CAGR:

Let’s say you have an investment that started with a value of $1,000 and grew to $1,500 over a span of 5 years.

Beginning Value = $1,000

Ending Value = $1,500

Number of Years = 5

\[CAGR = (\frac{$1,500}{$1,000})^{\frac{1}{5}} - 1\] \[CAGR ≈ 0.0955 \text{ or } 9.55\%\]So, the CAGR for this investment over the five-year period is approximately 0.955 or 9.55%.

This means that on average, the investment grew by about 9.55% each year over the five-year period, taking into account the effects of compounding.

CAGR is a powerful tool for comparing the growth rates of different investments over different time periods because it provides a standardized measure that takes into consideration the impact of compounding. However, it’s worth noting that CAGR doesn’t reflect the actual year-to-year fluctuations that might have occurred within the given time frame.