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CAGR turns a multi-year result into one steady yearly growth rate, making it the fairest way to compare investments held for different lengths of time.
CAGR stands for compound annual growth rate. It answers a simple question: if this investment had grown at the same steady rate every single year, what would that rate have been? In other words, it converts a multi-year result into one smooth, comparable yearly number.
Real investments never grow in a straight line. A fund might jump 25% one year, fall 10% the next, and barely move the year after. CAGR ignores that bumpy path and focuses only on where you started, where you ended, and how long it took. That makes it one of the most common ways to describe how an investment, a portfolio, or even a company's revenue has grown over time.
In the previous lesson, you saw that ROI tells you the total gain or loss but says nothing about time. A 60% ROI could have taken three years or thirty, and those are very different outcomes. CAGR fixes this by spreading the total growth across the years it took, giving you an annualized rate you can compare fairly across investments held for different lengths of time.
CAGR = (ending value ÷ beginning value) ^ (1 ÷ number of years) − 1
| Part of the Formula | What It Means |
|---|---|
| Ending value | What the investment is worth at the end of the period |
| Beginning value | What it was worth at the start (the amount you invested) |
| Number of years | How long the period lasted, which can include fractions such as 2.5 years |
| ^ (1 ÷ years) | The "root" step that spreads the total growth evenly across each year |
The result is a decimal, so multiply it by 100 to express it as a percentage. If you use a spreadsheet, the same formula works as =(end/start)^(1/years)-1, and Excel and Google Sheets also have a built-in RRI function that does the same job.
| Step | What to Do | Example ($10,000 grows to $16,000 in 5 years) |
|---|---|---|
| 1. Divide | Divide the ending value by the beginning value | $16,000 ÷ $10,000 = 1.6 |
| 2. Find the exponent | Divide 1 by the number of years | 1 ÷ 5 = 0.2 |
| 3. Raise to the power | Raise the result of step 1 to the power from step 2 | 1.6 ^ 0.2 = about 1.0986 |
| 4. Subtract 1 | Take away the 1 to isolate the growth | 1.0986 − 1 = 0.0986 |
| 5. Convert to a percentage | Multiply by 100 | About 9.9% CAGR |
Notice that the ROI in this example is 60%, but the CAGR is only about 9.9%. They describe the same growth in two different ways: ROI is the total gain, while CAGR is the steady yearly rate that produces it. You can double-check the result by compounding: $10,000 growing at 9.9% a year for five years lands very close to $16,000. You can skip the manual math by using our CAGR Calculator.
Say Elena is comparing three funds with different track records. Each started with $10,000, but she held them for different lengths of time.
| Fund (illustrative) | Start | End | Years Held | ROI | CAGR |
|---|---|---|---|---|---|
| Fund X | $10,000 | $18,000 | 8 | 80% | About 7.6% |
| Fund Y | $10,000 | $14,000 | 4 | 40% | About 8.8% |
| Fund Z | $10,000 | $23,000 | 10 | 130% | About 8.7% |
These figures are simple illustrations, not predictions or guarantees. Judged by ROI alone, Fund Z looks like the clear winner at 130% and Fund Y looks weakest at 40%. But CAGR tells a different story. Fund Z needed ten years to get there, while Fund Y earned a slightly higher yearly rate in only four. Funds Y and Z are nearly tied, and Fund X, despite an 80% ROI, actually grew the slowest each year. That is exactly the kind of comparison CAGR was built for.
A common trap is confusing CAGR with the simple average of yearly returns. They are not the same, and the average can look better than what you actually earned.
Say Jordan invests $10,000, and the investment returns +30% in year one, −20% in year two, and +25% in year three.
| Year | Return | Balance at Year End |
|---|---|---|
| Start | — | $10,000 |
| Year 1 | +30% | $13,000 |
| Year 2 | −20% | $10,400 |
| Year 3 | +25% | $13,000 |
The simple average of the three returns is (30 − 20 + 25) ÷ 3, or about 11.7%. But Jordan's money grew from $10,000 to $13,000, which works out to a CAGR of about 9.1%. If the investment had truly grown by 11.7% every year, Jordan would have ended with roughly $13,925, not $13,000. The average return overstates the result because it ignores how gains and losses compound on each other.
The gap between average return and CAGR gets larger the more volatile an investment is. An extreme example makes the point: a +50% year followed by a −50% year has an average return of exactly 0%. But $10,000 becomes $15,000, then falls to $7,500. Your actual CAGR over those two years is about −13.4%.
This happens because a loss is applied to a bigger balance after a gain, and a gain is applied to a smaller balance after a loss. Recovering from a 50% drop takes a 100% gain, not 50%. It's one reason many investors care about limiting large losses, and we look at volatility and drawdowns in Module 3.
CAGR isn't only for looking backward. You can also use an assumed growth rate to estimate what an investment might become. If you invest $10,000 and assume a CAGR of 8% for 20 years, the estimate is $10,000 × 1.08 ^ 20, or about $46,600.
A handy shortcut here is the Rule of 72. Divide 72 by the growth rate to estimate how many years it takes for money to double. At about 9.9% CAGR, that's roughly 7.3 years. At 8%, roughly 9 years.
Treat projections like this as a way to explore scenarios, not as a forecast. Actual returns are uneven, and no one can promise a steady rate. To see how different rates and time periods change the outcome, try our Compound Interest Calculator.
Like any return, CAGR is usually stated in nominal terms. As we saw in the lesson on nominal vs real returns, inflation quietly reduces what that growth is worth.
Say an investment has a nominal CAGR of 9.9% over five years, and inflation averaged 3% a year over the same period. The real CAGR is about (1.099 ÷ 1.03) − 1, or roughly 6.7%. That is the yearly growth in purchasing power, and it's the number that really matters for goals such as retirement. Our Inflation Calculator can help you estimate the impact.
| Limitation | Why It Matters |
|---|---|
| It smooths out volatility | Two investments can share the same CAGR while one had wild swings along the way and the other grew steadily |
| It depends on the start and end dates | Choosing a start date right after a market drop can make a CAGR look far better than the typical experience |
| It assumes one lump sum | If you added or withdrew money along the way, CAGR doesn't capture the timing of those cash flows |
| It isn't a forecast | A strong past CAGR doesn't guarantee similar results in the future |
If you contribute regularly, for example through monthly 401(k) deposits, a money-weighted measure such as the internal rate of return (IRR) gives a more accurate picture, since it accounts for when each dollar went in. CAGR works best for a single starting amount left to grow.
CAGR is most useful for comparing investments held for different lengths of time, judging the long-run growth of a fund, portfolio, or business, and setting a reasonable growth assumption for planning. Use ROI for a quick look at total gain or loss, CAGR to compare across time periods, and real return to see what happened to your buying power. Together, these three give a much more complete picture than any single number.
1. Confusing CAGR with the average of yearly returns. The simple average ignores compounding and usually looks better than what you actually earned, especially when returns are volatile.
2. Using the wrong number of years. Counting the wrong period, such as five data points instead of four years of growth, changes the answer noticeably. Count the years between the start and end dates.
3. Cherry-picking the start and end dates. A CAGR measured from a market low can look impressive. Check several time periods before drawing a conclusion.
4. Using CAGR when you made regular deposits. CAGR assumes one starting amount. If you added money over time, use a measure that accounts for timing, such as IRR.
5. Treating past CAGR as a promise. Historical growth rates describe what happened, not what will happen. Use them to plan with a range of scenarios, not a single guaranteed number.
Key Takeaway: CAGR converts a multi-year result into one steady yearly growth rate, which makes it the fairest way to compare investments held for different lengths of time — just remember that it smooths out volatility, ignores the timing of deposits, and describes the past rather than the future.
It depends on the asset, the time period, and the risk involved. A useful approach is to compare an investment's CAGR against a benchmark, such as a broad stock market index, over the same period, and to look at the real CAGR after inflation.
ROI measures the total gain or loss as a percentage of what you invested and ignores time. CAGR converts that growth into a steady yearly rate, which lets you compare investments held for different lengths of time.
Yes. If the ending value is lower than the beginning value, the CAGR is negative, meaning the investment shrank by that yearly rate on average.
Because losses and gains compound on each other. The simple average treats each year separately, while CAGR reflects what happened to your actual balance. The more volatile the returns, the bigger the gap tends to be.
Yes. Just express the period in years, using fractions when needed. For example, 18 months is 1.5 years. Keep in mind that annualizing a very short period can exaggerate the result.
CAGR assumes a single starting amount, so it isn't ideal for regular contributions. A money-weighted measure such as the internal rate of return (IRR) accounts for when each deposit was made and gives a more accurate picture.
Disclaimer: This article is for general educational purposes only and does not constitute personalized financial, investment, tax, or legal advice. Figures, rates, and rules mentioned may change over time — verify current details with an official source or a qualified professional before making financial decisions.