### How to Use CAGR Calculator

Enter your investment value at the end.

Enter your investment value at the start.

Enter the number of investment periods (years, months, days)

# CAGR Calculator

**CAGR Formula**:`(X / Y )^(1/N)-1`

X: Investment value at the end.

Y: Investment value at the start.

N: Number of investment periods (Months, Days etc.)

### How To calculate CAGR

Example 1:- An investment was made with a starting value of $15,000 in 2015
- It grew to $19,800 in 2018
- Therefore our X is $19,800, Y = $15,000 and N is 3 years
- ($19,800/$15,000)^ 1/3 -1 = 0.0969
- Mulitply result by a hundred 0.0969 X 100 = 9.70% (We round it up to 9.70)
- The compound annual growth rate is 9.70

- An investment was made with a starting value of $850
- It Grew to $5,000 in 4 years.
- Therefore our X is $5000, Y = $850 and N is 4
- `(5000/850)^(1/4)-1 = 0.5573`
- Then multiply it by a hundred to get the percentage: 0.5573 * 100 = 55.73%
- The compound annual growth rate is 55.73%

Example 3:

- An Investment is made with $10,000
- It's ending value is $23,000 in 6 years
- Y: $23,600, Y:$10,000, N: 6
- `(23600/10000)^(1/6)-1 = 0.1538`
- Again multiply the result by a 100: 0.1538 X 100 = 15.38%
- The compound annual growth rate is 15.38%

**Compound annual growth rate** otherwise known as (CAGR) is the annual rate of return for an investment over a specified period of time, assuming that the profits were reinvested into the investment over its measured lifetime.

**CAGR** is a useful calculation as a comparison tool and a forecast for investors in evaluating the best rate of return on an annual compounded basis for different types of investments (stock bonds, mutual funds etc). For singular investments, CAGR represents a pro forma number that shows a ‘smoothed’ rate of growth over a period.

In comparing different types of investments, CAGR can help investors identify the difference in returns. Using an example of two investments, one with $10,000 in 2015 with a fixed annual interest rate 1.5% compared to a stock mutual fund with $10,000 deposited at the same time. In 2020, the first investment’s account balance is now a total of $10,722.84 (barring annual rate of inflation) while the mutual fund reaches a balance of $15,324.96.

**Investment A**: ((10,722.84/10,000)1/5 -1) = 0.0140, We then multiply by a hundred to get our percentage 0.0140 X 100 = 1.14%

**Investment B**: (15,324.96/10,000)^1/5 -1) = 0.0891, We then multiply by a hundred to get our percentage 0.0891 X 100 = 8.91%

Based on the above calculations, it is important to note that CAGR calculations do not factor in the volatile and fluctuating nature of the market. Though investment B has a greater return at first glance, to demonstrate both CAGR and the risk investors take on different investments, you can add a calculation of standard deviation percentage to get a more accurate rate of return. A standard deviation is a statistic that shows how the annual return might defer from the expected returns.

Less volatile stocks will have a lower standard deviation as their annual return is expected to be close to their average annual returns. For a savings account, it has an annual interest rate to provide the annual return; therefore its standard deviation is zero. As opposed to a mutual fund where stock prices vary, thus it is measured with a higher standard deviation to account for the unexpected rate of return.

Using the above example of the mutual fund, we will chart the CAGR, the average annual growth rate (AAGR) and the average standard deviation (STDEV) to get a more realistic examination of investment B in its risk vs rewards profile.

Investment B | CAGR | AAGR | |

2015 - $10,000 | |||

2016 - $11,790.66 | 17.9% | 17.9% | |

2017 - $12,376.13 | 11.2% | 5.0% | |

2018 - $13,980.26 | 11.8% | 13.0% | |

2019 - $14,598.75 | 9.9% | 4.4% | |

2020 - $15,324.96 | 8.9% | 5.0% | |

Average | 11.96% | 9.0% | 2.68(STDEV) |

To incorporate real life risks that investors undertake, you can use a risk-adjusted CAGR calculation to see an accurate measurement of the investments performance; to calculate the risk-adjusted CAGR, multiple the CAGR by one minus the standard deviation. If the standard deviation is zero, the risk-adjusted CAGR is unaffected; with a larger standard deviation, the lower the risk-adjusted CAGR.

In our example, the risk-adjusted CAGR for our investment B is now -20.1%, highlighting its more volatile nature rather than the safe return of profit in investment A. An investor can determine the best profiled investment by comparing their individual risk-adjusted CAGR.

The longer a period of time to determine the CAGR, the more accurate the forecast will be. In real life scenarios as well where investments are not bought and sold on perfect calendar years, the investor must also find the fractional hold period before the CAGR calculation can take place.

The CAGR calculation can also be used for companies to track various business measures such as market share percentage or customer satisfaction percentage. For advertising purposes, CAGR information can be manipulated in selecting a profitable period to take their average from. To compare alternative investments, you must also choose an identical period to calculate.