Once again, you left this amount on your account.
You kept this amount on the bank account for the next year.
In May 2015 you deposited $1000 on the bank account with an interest rate equal to 9.14%. To understand it, try to follow this example: It is due to the compounding of interest. So the compound annual growth rate of that investment was: In that example, your initial $1000 investment grew to $1300 over three years (from May 2015 to May 2018). Let's go back to our example from the previous section. Note that the CAGR formula is more complex than the simple growth rate formula, as it takes into consideration also the investment time horizon (which may be longer than a year) and the number of compounding periods. Where CAGR is the compound annual growth rate.Īfter the transformation, the formula for CAGR is: The formula that allows you to compute CAGR formula derives from the compound interest formula presented in the section What is the compound interest? It is:Īssuming that that interest is compounded on a yearly basis ( m = 1) we can write: The pros and cons of CAGR are discussed in in detail in CAGR advantages and disadvantages. However, CAGR is mainly used to smooth the rate of return over the whole investment period and therefore is very useful in comparing different investments. Obviously, in real life such a situation is almost impossible. You can say that CAGR is a number that describes the rate at which investment would have grown if it had grown at the same rate every year during the whole investment period (with an assumption that the profits were reinvested at the end of each year). You should be aware that the compound annual growth rate is an approximate figure rather than a true return rate. CAGR is counted with an assumption that profits are reinvested at the end of each year of its time horizon. The formal definition of CAGR says that CAGR is the yearly rate of return that is required for an investment to grow from its initial balance to its final balance within the particular period. t - the numbers of years the money is invested for.įrom a formal point of view, if the interest is compounded once per year (so m = 1), then r is called the compound annual growth rate (CAGR).Īs we have already explained in the introduction, CAGR is an acronym for Compound Annual Growth Rate. 
m - the number of times the interest is compounded per year (compounding frequency).r - the annual interest rate (in decimal).PV - the initial balance (the present value of the investment).FV - the future value of the investment.
The formula for compound interest is quite complex as it includes not only the annual interest rate and the number of years but also the number of times the interest is compounded per year. Note here that a deposit or loan grows at a faster rate thanks to compounding.
In other words, compound interest is the interest calculated on the initial principal as well as the interest which has accumulated during the consecutive periods. In finance, compound interest is defined as interest that is earned not only on the initial amount invested but also on any interest. To understand the idea of the compound annual growth rate, first of all, you should know what compound interest is.
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