# What Is Compound Annual Growth Rate?

Compound Annual Growth Rate, or CAGR, is a way to measure return on an investment over time. It is a formula that tells you the rate of return you would need for an investment to grow from a specific starting amount (SA) to a specific end amount (EA) in a specific number of years (Y).

Here's how it works and why it's useful to know.

**How to Calculate CAGR**

To calculate compound annual growth rate, you would use the following formula:

**CAGR = ((EA / SA) ^ (1/Y)) - 1**

To break that down, we have:

• Ending Amount of the investment (EA) divided by Starting Amount of the investment (SA);

• Raise that to the power of 1 divided by the number of Years the investment grows;

• Then subtract 1 from that result.

The result, CAGR, tells you the annual rate of growth your investment would need to have in order to go from its starting amount to its ending amount in the number of years specified.

This can represent your investment in two main ways. For a structured investment, such as money in a savings account, it is a true number. If you have a guaranteed rate of return, your CAGR will accurately represent the annual rate of growth for this investment.

For a market investment, where returns are not guaranteed, the CAGR is best thought of as representative. While your actual results might fluctuate from year to year, if they average out to this rate of return you will reach this ending amount in this number of years.

**Example of How to Use CAGR**

Let's say you invest $1,000 in Mutual Fund A. Over five years your investment grew to a final amount of $8,000. To understand its average rate of return while in this fund you would run the following calculation:

**CAGR = (8,000 / 1,000) ^ (1/5) - 1**

First, divide your ending amount by your starting amount: 8,000 / 1,000 = 8

Next, divide 1 by your number of years invested: 1 / 5 = .2

Now raise your investment figures to the power of your duration: 8 ^ .2 = 1.515

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Now subtract 1 from that result: 1.515 - 1 = 0.515, then render the result as a percentage: 51%

For your $1,000 investment to become an $8,000 investment means you received an average rate of return of 51% per year.

**CAGR vs. Average Annual Rate of Return**

While the CAGR is an average, and we refer to it as such, it is different from calculating an average annual rate of return.

An average rate of return is a simple mean of values. If your investment grew by 10% in 2012, 15% in 2013 and 20% in 2014, your average rate of return would be (10 + 15 + 20) / 3 = 15%.

However, this figure does not consider the effects of compounding on an investment. As a result, it will typically give a somewhat distorted example of what happened in your account.

For example, let's take the investment from above. You invest $1,000 in Mutual Fund A. In year one it loses $500 for a return of -50%. In year two it gains $1,000 for a return of 300%. At the end of two years you have $1,500 in this account.

The average rate of return on this account would be 125% ((-50 + 300) / 2). This would lead you to expect that your account more than doubled.

The CAGR take compounding and losses into account. This formula would give an annual growth rate of (1,500 / 1,000) ^ (1/2) - 1 = 22%. This far more accurately reflects what happened in your portfolio over time.

**CAGR Tells You an Average Rate of Return**

It's key to understand that the CAGR represents your investment's average growth rate over time (taking compound growth into account). It's quite possible that in any given year, your investment could fluctuate significantly above or below this rate. What the CAGR tells you is what that performance ultimately led to.

This can be both useful and unhelpful.

From a useful perspective, this allows you to see the big picture. It lets you see how an investment ultimately performs without getting distracted by the noise of a high performing or slow-growth year. It also allows you to compare otherwise dissimilar investments side by side. Even if two investments are structured very differently and operate in different markets, the CAGR gives you a single number to compare them. This is, essentially, an apples-to-apples figure.

However, the CAGR also buries individual data points. Where sometimes it's useful to see the forest for the trees, sometimes you need to know the actual performance of an investment. For example, say a given mutual fund tends toward highly erratic movement. Only knowing the CAGR will hide that information, meaning that if you want to cash out your investment during a down year you might be surprised by the portfolio's poor performance.

Or, even worse, the CAGR might make an erratic investment seem stronger than it actually is. Wild price swings can indicate weakness in an investment, even if it has trended well overall. You might not see that with an average rate of return.

**The CAGR and Your Investment Plans**

For an individual investor, the most important use of the CAGR formula is typically targeted investing.

Most people invest around specific goals. For example, you might know how much you would like to have in your retirement fund at 65 or you might set up a portfolio for a child's college tuition. In cases like this, you typically know both your desired goals and the time frame you have to meet them.

The CAGR formula, then, lets you know what rate of return you would need to meet those goals. For example, let's say you will want to retire with $1 million in your retirement account at age 65. You are 25 today and have $10,000 to invest. You would need:

CAGR = (1,000,000 / 10,000) ^ (1/40) - 1 = 12.2%

With $10,000 invested at age 25, you would need a 12.2% average rate of return to have this investment worth $1 million at age 65.

**Limits on the CAGR**

The CAGR has several limitations, especially for the individual investor. First, there is the fact that it hides individual fluctuations in an account over time. (In our case above, for example, just looking at the CAGR would never tell you that Mutual Fund A lost half its value in the first year.)

Perhaps more importantly, though, it does not consider additional contributions or withdrawals over the lifetime of the investment. This formula is only structured to consider a single, lump sum deposit's performance over time.

This makes the formula far less useful for individual investing, where you are likely to make additional deposits to long-term funds over time. For example, a retirement account will see steady growth to both its performance and its principle over your working life. Each time you get a paycheck you should be adding more to your 401(k), but cannot take that into account when using the CAGR.

Finally, it is always important to remember the critical rule when investing: Past performance is not a promise of future results. The CAGR of an investment only tells you how it has done in the past. This might indicate sound management or a good underlying product, but it is not a guarantee. Invest accordingly.

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