# CAGR Exact Dates Calculator

## What is CAGR

The acronym stands for Compound Annual Growth Rate. The acronym itself should give us a good idea of what the indicator does.

If we want to calculate the CAGR of an investment, we are essentially looking for a result in the form of a percentage value, which, if given as the interest rate of an annually compounded investment, would yield the same result as the investment we are calculating the CAGR for, within the same time frame.

In simpler terms, CAGR shows us what is the compound interest rate needed to match the performance of an investment based on its start and end value.

## The CAGR Formula

The formula for calculating the CAGR of investment requires the following data:

- The starting value (this is usually the sum initially invested). We will label this value as SV in our formula.
- The ending value (this is usually the value the investment has at the end of the investment period). We will label this value as EV in our formula.
- The duration of the investment (usually it is in years, as CAGR is an annual indicator, but our calculator can accommodate with accuracy for days). We will label this value as Y in our formula.

The formula, into which we plug our values, is as follows.

CAGR=\left((\tfrac{EV}{SV})^{\frac{1}{Y}}-1\right)*100

This formula is essentially the reversed version of the compound interest formula.

### Worked Out Example

Let’s assume we invested $1,000 for a course of 5 years. Our investment was developing as seen below.

Year | Investment Value in USD |
---|---|

0 | 1,000 |

1 | 1,130 |

2 | 1,508 |

3 | 1,467 |

4 | 1,788 |

5 | 1,800 |

As we can see, our investment was fairly turbulent. Some years, the value was increasing a lot, some years a little less, and there were even times when the value dropped compared to the previous year.

An investor could be interested to see, what kind of annual compound interest would get them to this point. The CAGR formula can be used for this purpose.

We extract the following values from the example.

- Starting Value: 1,000
- Ending Value: 1,800
- Duration: 5 years

Plugging into the formula mentioned earlier, we get the following expression.

CAGR=\left((\tfrac{EV}{SV})^{\frac{1}{Y}}-1\right)*100

=\left((\tfrac{1,800}{1,000})^{\frac{1}{5}}-1\right)*100

We can simplify the expression and get the following (keeping in mind that we round all values to 4 decimal places).

CAGR=\left(1.8^{\frac{1}{5}}-1\right)*100

=(1.1247-1)*100

=0.1247*100=12.47\%

The interpretation of this result is, that if we invested $1,000 at a 12.47% yearly compound interest, we would have an investment valued at $1,800 after 5 years.

We can verify this by simply performing the above-stated action using the compound interest formula, where we would get the following.

1,000×1.1245^{5} = 1,798.03, where the minor difference is caused by the fact, that we are operating with rounded values.

## Using The CAGR Exact Dates Calculator

To calculate the CAGR value for your investment, follow these steps.

# | Step |
---|---|

1 | Choose out of the currencies offered at the top of the calculator. If your currency is not offered, just chose the empty one, and then do not forget to adjust the currency name, if the data is used elsewhere. |

2 | Input the starting value of your investment. |

3 | Input the ending value of your investment. |

4 | Enter the start date of your investment. |

5 | Enter the end date of your investment. |

6 | Click on CONVERT. |

7 | Your result will appear below the calculator, including a summary of the elapsed time, and a table summarizing the value changes of your investment on an annual basis. |