Formula and Execution

The compound annual growth rate

The mean rate of return at which the investment is steadily growing every year.

Number of periods

For how many years the amount is invested.

Initial value

The initial investment is called the initial value.

Final value

The value of your investment at the end of the investment period.

Difference

The difference between the initial value and final value.

Total growth

The average growth of your investment in percentage is called total growth.

Compounding Annual Growth Rate Calculator (CAGR)

Investors always want high returns on their investments. In search of high returns, they invest their money in different projects with the hopes that these projects will yield high returns. Before investing their money, investors use different methods to find the profitability of the investment. Investors can invest their money either in stock or bonds. Rate of return is always a point of concern for investors in these financial securities. Financial analysts use different methods to find the correct rate of return on stock and bonds. One such method is the compound annual growth rate. Calculating the compound annual growth rate manually is a challenging and arduous task. The revolution in modern technology makes it possible to develop different tools for the ease of financial analysts. One such tool is a compound annual growth rate calculator, also known as the CAGR calculator.

 

Why is the CAGR calculator used?

Due to the technical nature of finance, calculating financial values manually always bear the risk of error. To get rid of such complications, we use the CAGR calculator.

 

How can it help?

CAGR calculator is helpful in many ways such as:

  • It is economical and efficient.
  • There is no chance of error in calculations, depend on the values you put in the calculator.
  • It saves a lot of your time, as it calculates calculations of minutes in seconds.

 

To whom it will help:

CAGR calculator is useful for all those who need to find compound annual growth rate on investment. It is more beneficial for the following peoples:

  • Students while solving their assignments on the compound annual growth rate
  • Researchers who are publishing their research papers on investment in the stock and bonds market.
  • Stock exchange brokers who give consultancy on investment in the stock market and bond market can also use this calculator to find growth rates on stocks and bonds.
  • Teachers, while giving lectures on compound annual growth rate.

 

Steps Involved in CAGR Calculator

CAGR calculator operates in two modes (1) Simple mode (2) Advance mode

 

Simple mode:

Three steps are required while calculating Future value or final value in simple mode. These three steps are:

  1. Growth rate: Put the percentage at which the investment will grow in the future.
  2. The number of periods: Put the number of years the amount is invested.
  3. Initial value: Insert the value of an initial investment in its box.

Once the values of all these terms are placed in their respective portions, it gives us the value of the future value or final value.

 

Example: An individual invested $1,000 in company XYZ on the fixed rate of return of 10% for two years. What is the future value of his investment?

Solution:

                Initial investment = $1,000

               Rate of return = 10%

              Number of periods = 2

               Final value =?

Put all these values in the CAGR calculator; you get the following result.

 

To find compound annual growth rate, you need three values, i.e., "final value, initial value, and the number of periods."

 

Example: An individual invested $1,000 in company XYZ, and he wants his investment to yield $2,500 in two years. What will be the rate of return on his investment?

Solution:

               Initial value = $1,000

               Final value = $2,500

               Number of periods = 2

               CAGR =?

Put these three values in their respective boxes; you will get the value of CAGR, as shown below.

 

Note: If any value of the three terminologies mentioned above is missing, the final value and growth rate will show no result, as shown in the below picture.

 

Advanced mode:

The same three steps are involved while calculating future value and CAGR; the only addition is of “difference and total growth." Putting values in the three essential boxes, i.e., "Growth rate (In case of future value calculation), number of periods and initial balance, Final value (In case of CAGR calculation)” is compulsory otherwise the other portions will show no result as shown below:

Note: The formula of total growth is (current balance – previous balance / previous balance); in the CAGR calculator, the current balance is represented by final value, and the initial value represents previous balance.

 

Formulas used in CAGR Calculation

There are four formulas used in the CAGR calculator:

 

Future value formula: This formula is used to find the future value of the investment. The method to find the future value is {Present value (1+r) ^n} where “r” is the rate of return on investment, and “n” is the number of years.

 

Note: In the CAGR calculator, the future value is represented by the final value, and the initial value represents the present value. Rate of return, i.e., "r" is represented by the growth rate, and the number of years is represented by the number of periods in the CAGR calculator.

 

Total growth: It tells you how much your investment grow over the years. The formula of total growth is (current balance – previous balance / previous balance).

 

Difference formula: It tells you the difference between your initial investment and the final value of your investment. The formula of difference is (final value – initial value).

 

CAGR formula: Compounding annual growth rate is the mean annual growth of your investment. The formula of CAGR is ( ending value/beginning value)^1/n – 1

 

Note: ending values is also called future value, and the beginning value is the present value of your investment, while "n" is the number of periods.

 

Example: An individual invests $10'000 in company XYZ on a 10% interest rate for two years. Find the future value of this investment.

Solution:

              Present value = $10,000

             Rate of return = 10%

             Number of periods = 2

 

             Future value = Present value (1+r) ^n

                                     = 10,000(1+0.1) ^2

                                     = $12,100

          Future value = $12,100

 

         Total growth = Current value – previous value / previous value

                                  = 12,100- 10,000 / 10,000

                                  = 0.21 or 21%

       Total growth = 21%

 

     Difference = final value – initial value

                         = 12,100 – 10,000 = 2,100

     Difference = $2,100

Compounding annual growth rate = (future value / present value) ^1/n – 1

                                                      = (12,100 / 10,000) ^ ½ - 1

                                                       = 0.1 or 10%

Compounding growth rate = 10%

 

Note: The actual growth of your investment is 10%, not 21%. As this 21% ignore the effect of compounding and it can overestimate the growth of an investment. The reason behind 21% growth is that that the profit you earned in the first year of your investment is re-invested and the next return you get is calculated on principal amount plus the profit you made in the first year.

In the example mentioned above, the profit earned in the first year is $1,000, i.e. (10,000*0.1). Now when the profit for the next year is calculated, it will be calculated on $11,000, i.e., principal amount plus profit earned in the first year (10,000+1,000).

 

Solving it manually is quite a hectic and challenging task. You can quickly solve it through the CAGR calculator. Put the necessary values in their respective portions in the calculator, and the following results appear in the CAGR calculator.

 

Note: The value of total growth and difference is there in the advanced mode of the calculator.  

 

FAQS

What is reverse CAGR calculator?

The calculator, which gives you the future value of the investment, is called a reverse CAGR calculator. The condition in the CAGR calculator is that, that you must put the values of "CAGR, initial value, and the number of periods." Once these values are put in the calculator, it gives you future value.

 

What is the difference between the CAGR calculator and reverse CAGR calculator?

CAGR calculator gives you the compounding annual growth rate while the reverse CAGR calculator gives you the future value of your investment. For the CAGR calculator, the values of “final value, number of periods, and initial value" are compulsory. In contrast, for reverse CAGR calculator, the values of “growth rate, initial values, and the number of periods" are necessary.

 

Note: To find the values of compounding annual growth rate and future value of your investment, you can put values in the CAGR calculator but in different orders, as explained above.

 

How do I calculate CAGR in excel?

There is no specific formula in excel for the calculation of compounding annual growth rate, but you can calculate it in excel manually.

Example: An individual invests $10,000 in company XYZ for four years. His investment grows over the four years as $12,000 in 2nd years, $15,000 in 3rd years, and $22,000 in 4th year.

Solution: You can solve this question in excel using CAGR formula as follow:

 

How do you calculate growth in the investment

There are two approaches to find the growth rate of stock or bonds.

  1. Simple growth rate: The growth in your investment in a single period. The formula of a single growth rate is ( current balance – previous balance ) / previous balance
  2. Compound growth rate: The growth in your investment over time taking compounding effect into account. The compound growth rate is also called a smoothing rate because of it smoother the fluctuation in the rate of returns over time. The formula of compound growth rate is (Ending value/beginning value) ^ 1/n – 1.

 

Example: An individual invests $10,000 in company XYZ for two years. His investment grows over to $16,000 in the second year. Find a simple growth rate and compound growth rate.

Solution: Simple growth rate

 

              Year 1 = $10,000

               Year 2 = 16,000

               Year 3 = 17,000

   Simple growth rate year 1 = 16,000 – 10,000 / 10,000 = 0.6 0r 60%

 

Simple growth rate year 1 = 60%

 

Simple Growth rate year 2 = 17,000 – 16,000 / 16,000

                                                 = 0.0625 or 6%

Simple growth rate year 2 = 6%

 

Compound growth rate

 

                    Year 1 = 10,000

                     Year 2 = 16,000

                     Year 3 = 17,000

  Compound growth rate= (17,000 / 10,000) (1/ 2) – 1

                                             = 0.3 or 30%

Compound growth rate = 30%

S.NOYearInvestmentSimple growth rateCompound growth rate 
1110,00060%

30%

2216,0006%
3317,000 

From the above table, you can see that a simple growth rate shows high volatility in return over the years. The drawback of a simple growth rate is that that it doesn't account for high volatility. While on the other hand, the compound growth rate takes this volatility into consideration and smoothers the effects of volatility through compounding.

 

Note: If you are facing a problem in understanding compounding, then you can refer to our APY calculator. APY calculator will clear your concept about compounding.

 

Can I use CAGR for months?

The word annual in CAGR doesn't mean that it can only account for the yearly rate of return. You can also calculate monthly returns through a compounding annual growth rate formula.

Example: An individual buys a TV set for $500 on January 1st, 2020, and sells it for $850 on March 1st, 2020. How much profit does he earn in percentage?

 Solution:

                Initial value = $500

                Final value = $850

              Number of periods = 3 months

             CAGR = (850 / 500) (1/3) - 1

                         = 0.1934 or 19%

            CAGR = 19%

 

What is a good CAGR percentage?

There is no such standard that fixes the rate that it is a good CAGR and bad CAGR. Generally, the growth rate above 10% is considered good, while below 8% growth rate is regarded as a bad one.

 

What does negative CAGR mean ?

The compound annual growth rate can be negative if the company is not performing well, and the final amount of your investment is less than the initial investment, then the growth rate will show a negative value. 

Example: An individual invests $1,000 in company XYZ for two years. At the end of 2nd year, his value of the investment is $950. What is the CAGR of his investment? 

Solution:

             Initial investment = $1,000

             Final balance = $950

             Number of periods = 2

              CAGR =?

           CAGR = (950/ 1000) ^ (1/2) – 1

                     CAGR = -3%

    This means that your investment lost the value by 3%.

 

What is year over year (YOY) growth?

The growth rate which compares values of one period with another. The comparison of portfolio growth in January 2019 with January 2020 is year over year growth. Year over year, growth mainly uses to check the increase or decrease in company sales in a particular period. Year over year growth is significant for two reasons

  1. Remove seasonality: Year over year comparison remove seasonality from the sales. For example, in January 2019, the company sales increase by 15%, while in January 2020, it increases by 12%. Here you can see that in January of both the years the sales of the company grows. But if you compare the two periods, i.e., January – January, then the sales of the company drop by 3% in January 2020.
  2. Recognizing trends:  This method identified a trend analysis of previous periods. For example, if a business is growing at a steady rate of 5% a month and if it grew at 4% a month in previous periods. It means that the trend is showing an increase over the period.

 

What are the pros and cons of the year over year growth?

Pros of the year over year growth

Following are the advantages of the year over year growth

  • This method compares period to period values, so it negates seasonality.
  • The returns are volatile, i.e., there is up and down in the rate of return, year over year growth smoother the volatility.

Cons of the year over year growth

  • The information obtained is not complete. It depends on other metrics for complete information.
  • If one-period growth is negative and another period growth is positive, it gives the meaningless result.

 

What are the drawbacks of compound annual growth?

·        Compound growth smoother the volatility effect and shows that the increase over time is steady, which is not the case.

·        While calculating the rate of return on the stock, it doesn't take into account the risk related to stock.

·        CAGR doesn't consider the fund added to the portfolio before redemption of investment, e.g., the investment is for five years; the fund added to the portfolio in the third year is not considered by CAGR in the calculation, which is inaccurate.

 

What is the difference between CAGR and IRR?

CAGR stands for compound annual growth rate, and IRR stands for internal rate of return. CAGR only take beginning values and ending value of investment into account. And this is the main disadvantage of CAGR that it only takes beginning and ending values into consideration and ignore the other values. To solve this problem, the financial analyst now using the internal rate of return to find the growth of the investment over time. The internal rate of return takes all the values into account while calculating the growth of the investment.

 

What is YTD growth?

YTD stands for the year to date growth; YTD growth gives profit or loss on the portfolio from the start of the year to the current period. The formula of YTD growth is (current value – starting value/ starting value).

 

What does negative YTD mean?

YTD can be positive or negative. Positive YTD growth means that the portfolio is making a profit, while negative YTD growth means that the portfolio is in the loss.

 

What is QOQ growth?

QOQ stands for the quarter over quarter growth. The increase in the investment which compares the growth of one quarter with another. For example, the growth rate of your portfolio in the 1st quarter of 2019 and the 1st quarter of 2020. When we compare these two growth rates, this is called QOQ growth. The formula of QOQ growth is (current quarter growth – previous quarter growth / previous quarter growth).

 

What is YOY profit?

YOY stands for the year over year. In YOY profit, the profit for periods is compared. It is one of the most effective ways to compare the financial performance of the company for two or more periods. Investors look into YOY profit of the company while making investment decisions about the company.

 

What is the benefit of YOY profit?

Following are the benefits of YOY profit

  • Based on YOY profit, we can make a cross-sectional comparison of the company's financial performance. It gives us a complete picture of how the company performed financially during the year.
  • YOY profit negates the seasonality factor.