Compound annual growth rate (CAGR) is a simple metric that shows the annual rate of return of an investment (can be broadly defined) over a certain number of years, assuming the profits are reinvested. An investment may grow at different rates over different years, but, given an initial balance and an ending balance, CAGR answers the question, “At what rate must my initial balance grow each year in order to reach the end balance?” You’ll often find CAGR’s attached to bar charts or line graphs in order to get a quick understanding of roughly how much something is growing each year.

The formula for CAGR only involves three parts and is relatively easy to compute, even by hand. All you need is the beginning balance, the ending balance, and the number of years. The CAGR formula is shown below:

Where:

**CAGR**= growth rate**EndingBalance**= the balance at the end of the time period**BeginningBalance**= the balance at the beginning of the time period**n**= number of time periods

A CAGR can be found for almost anything. If you’re training for a hotdog eating contest, you can calculate a CAGR based on the number of hot dogs you ate at the start of training versus at the contest. If you’re growing a colony of bees (not sure how one counts bees, but just go with it), you can see how much the colony grows by on average each year. If you want to see how much your portfolio has grown each year, you can do that. As long as there are balances at two points in time, you can calculate a CAGR.

### Example

Let’s take a look at an example related to a portfolio. Suppose you buy a plethora of stocks and bonds for a well-balanced portfolio. You spent $10,251 buying those assets, and you simply want to sit back and watch those assets grow. You don’t buy anything else, nor do you sell anything in the portfolio. Suppose then that after five years, the portfolio balance reads $16,509. Congrats, you did well. But how well, one might inquire? Did your portfolio beat average market growth? We can use the CAGR formula to answer these questions.

Your beginning balance is $10,251, your ending balance is $16,509, and the number of periods is five. All we have to do is plug those numbers into the formula. The steps are provided below.

And voila, we have a compound annual growth rate of 10%. This means that your portfolio grew on average 10% every year, which means you most likely beat the market during that run. Congrats!

#### Notes:

- One thing to keep in mind is that this formula is time agnostic, meaning that the formula can be used with any time interval, such as days or months, but you would then be calculating compound daily growth rate (CDGR) or compound monthly growth rate (CMGR), respectively. The interpretation would be the same as above, but rather than growth over years, you would be calculating growth over days or months, or any other time interval for that matter. You could even calculate a compound growth rate over year-and-a-half intervals. Though the interpretation may not make sense for everyday life, some may want to see what that looks like. Hey, if you’re curious, you’re curious.
- Also, to double check your work, use the compound interest formula with your CAGR as the rate!