**Compounded Annual Growth Rate Formula (Table of Contents)**

## What is the Compounded Annual Growth Rate Formula?

Compounding is the effect where an investment earns interest not only on the principal component but also gives interest on interest. So compounded annual growth rate is the effective annual growth earned on investment considering compounding into the picture. This basically assumes that the interest earned every year is reinvested and it earns the same interest as the principal amount. That is the reason that compounded annual growth rate is always higher than the simple interest rate. Many investments like mutual funds, stock market returns are not very linear and in a very unstable fashion.

Compounded annual growth rate helps in smoothing out that return and will tell how much an investor has earned over the term of the investment given the fact that all the earnings between that period are reinvested at the same rate. Because of this smoothing effect, it helps us in comparing data sets with different level of volatility. It is very frequently used for the purpose of financial analysis.

**Ending Investment Amount = Start Amount (1 + CAGR) ^ Number of Years**

The formula for Compounded Annual Growth Rate –

**CAGR = (Ending Investment Amount / Start Amount) ^ (1 / Number of Years) – 1**

This formula is applicable if the investment is getting compounded annually, means that we are reinvesting the money on an annual basis. But sometimes it happens that we want to calculate the rate where the compounding in happening on a quarterly, monthly, daily basis. So for that, we use the below formula:

**Ending Investment Amount = Start Amount (1 + CAGR / Compounding Frequency) ^ (Number of Years * Compounding Frequency)**

So, a formula for Compounded Annual Growth Rate –

**CAGR = Compounding Frequency * ((Ending Investment Amount / Start Amount) ^ (1 / (Number of Years * Compounding Frequency)) – 1)**

Compounding Frequency:

- Semiannual Compounding: 2
- Quarterly Compounding: 4
- Monthly frequency: 12 and so on

**Examples of CAGR Formula (With Excel Template)**

Let’s take an example to understand the calculation of CAGR Formula in a better manner.

#### CAGR Formula – Example #1

**Let say you have invested $1000 in mutual funds 3 years ago. Following is the return which you have got for these 3 years:**

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**1**^{st}year, you got a 20% increase in value. So the total value is $1200 at the end of 1^{st}year**2**^{nd}year, you got a 10% increase in value. So the total value is $1320 at end of 2^{nd}year**3**^{rd}year, you got a 10% increase in value. So the total value is $1452 at end of 3^{rd}year

CAGR is calculated using the formula given below

**CAGR = (Ending Investment Amount / Start Amount) ^ (1/ Number of Years) – 1**

- CAGR = ($1,452 / $1,000) ^ (1 / 3) – 1
- CAGR =
**13.24%**

Here we can see that annual return for all the 3 years is different and varies but compounded annual growth rate gives us a single rate which we can compare with different investment opportunities.

#### CAGR Formula – Example #2

**Let say you have invested $1000 in the bank and you want to keep the money in the bank for 4 years. Now let’s say the total amount which you get after 4 years is $2500. A bank is offering a rate with monthly compounding. Calculate CAGR.**

CAGR is calculated using the formula given below

**CAGR = Compounding Frequency * ((Ending Investment Amount / Start Amount) ^ (1/ (Number of Years * Compounding Frequency)) – 1)**

- CAGR = 12 * (($2,500 / $1,000) ^ (1 / (4*12)) – 1)
- CAGR =
**23.13%**

So compounded annual growth rate is **23.13%.**

### Explanation of Compounded Annual Growth Rate Formula

Although the compound annual growth rate is the annual rate for the investment, it is only a theoretical figure and is not the true return. The major assumption here is the all the earnings are getting reinvested at the same rate for the investment period but the rate will not remain for all the years and we may not invest our money at the same rate. So it is an only representative rate that tells us that what we might end up with if all the money is reinvested at the end of each year at that rate. So there are some key points which we should take into consideration while using compounded annual growth rate.

Also, we will be really careful about an investment which is long in period. For example, if an investment period is very long, say 20 years, the compounded annual interest rate might give us the wrong indication because it can happen that we are not earning any profits during the first 15 years and all the returns are coming in the last period. Earning no profits for 15 years is not acceptable for any business to sustain.

Similarly, if two investment opportunities have the same CAGR, it can be the case that one is more attracted than the other because of the reason that growth in one is happening in the initial period while for other, it is concentrated at the end of the period.

### Relevance and Uses of Compounded Annual Growth Rate Formula

The compound annual growth rate is really helpful in calculating the average growth rate of the investment and can help in comparing different investments. As we have seen in the above example, the year-to-year growth of investment is uneven and erratic. But using compounded annual growth rate, the return smoothens out. Another factor that makes compounded annual growth rate a critical method in determining the growth of an investment is that it takes into consideration the compounding effect, which annual return rate doesn’t. Compounded annual rate does not give us the actual picture of the return since it only calculates the return on the principal amount and ignores the interest on the interest component, but this is not the case with the compounded annual growth rate.

### Compounded Annual Growth Rate Formula Calculator

You can use the following Compounded Annual Growth Rate Calculator

Ending Investment Amount | |

Start Amount | |

No. of Years | |

CAGR | |

CAGR = | [(Ending Investment Amount / Start Amount)
^{1 /No. of Years}-1] |

= |
[(0 / 0)^{1 / 0}-1] =
0 |

### Recommended Articles

This has been a guide to Compounded Annual Growth Rate formula. Here we discuss how to calculate CAGR along with practical examples. We also provide Compounded Annual Growth Rate calculator with a downloadable excel template. You may also look at the following articles to learn more –