# Compound Annual Growth Rate (CAGR) Calculator

LAST UPDATE: October 17th, 2019

## What is “CAGR” (or Compound Annual Growth Rate)?

CAGR is the rate of return an investment needs to reach a target amount.

The result is smoothed out over the years. A company with a CAGR of 7% over 5 years may have had:

• A 7% growth rate in each of those years
• A growth rate of 40% in the first year followed by near-0% growth in the remaining 4 years.
• A growth rate of -50% in the first year followed by a CAGR of 41.42% over the remaining 4 years.
• Any combination of growth within each of those years that resulted in a smoothed out 7% over 5 years.

## When is CAGR used?

CAGR is found in the financial industry, primarily to gauge returns of companies or investment/mutual funds.

It is helpful to analyze and compare the return of financial instruments.

## Equation

$\text{CAGR} = (\frac{\text{Ending Balance}}{\text{Begining Balance}})^{\frac{1}{\text{Number of Years}}} - 1$

To find CAGR:

1. Divide the value and the begining of the period by the value at the end of the period.
2. Take that result and raise it to the exponent of (1/number of years).
3. Subtract 1 from the result.
4. Your result will be a decimal value which can be converted to a percentage.

## Example

An investment has a starting balance of $10,000 with an ending balance of$20,000 in 5 years.

$\text{CAGR} = (\frac{20,000}{10,000})^{\frac{1}{5}} - 1$

$\text{CAGR} = 2^{\frac{1}{5}} - 1$

$\text{CAGR} = 2^{0.2} - 1$

$\text{CAGR} = 1.148698 - 1$

$\text{CAGR} = 0.1487$

Therefore, the compound annual growth rate is 0.1487, or 14.87%.