what is a compound annual growth rate?

Compound Annual Growth Rate (CAGR) is a measure used to represent the mean annual growth rate of an investment over a specified period of time, assuming that the investment has been compounding over that time frame. It is often used to evaluate the performance of investments such as stocks, mutual funds, or real estate, where the value of the investment may fluctuate over time.

The formula for calculating Compound Annual Growth Rate is:

CAGR = (Ending Value / Beginning Value) ^ (1 / Number of Years) -1

Where:

- Ending Value is the value of the investment at the end of the period.

- Beginning Value is the value of the investment at the beginning of the period.

- Number of Years is the number of years over which the investment has compounded.

CAGR provides a single, smoothed annualized growth rate that represents the geometric progression of an investment's value over time, accounting for compounding effects. It allows investors to compare the annualized growth rates of different investments over the same time period, providing a standardized measure of performance.

For example, if an investment grows from $1,000 at the beginning of the year to $1,500 at the end of the year, the CAGR over that one-year period would be:

CAGR = ($1,500 / $1,000)^ (1 / 1) - 1 = 0.5 = 50%

This indicates that the investment grew at a compound annual growth rate of 50% over the one-year period.