CAGR stands for Compound Annual Growth Rate, which represents the mean annual growth rate of an investment over a specified period of time longer than one year. It's one of the most accurate ways to calculate returns for anything that can rise or fall in value over time.
The CAGR formula assumes that profits are reinvested at the end of each year during the investment period. Unlike simple growth rate, CAGR smooths out the volatility and provides a constant rate of return, making it ideal for comparing different investments.
📌 Key Point:
CAGR describes the rate at which an investment would have grown if it had grown at a steady rate every year, even though actual returns typically vary year to year.
CAGR = (FV / PV)1/t - 1
Where:
To express as a percentage, multiply the result by 100.
Follow these steps to calculate the compound annual growth rate:
Example:
You invested $10,000 in a stock. After 5 years, it's worth $16,000. What's the CAGR?
Step 1: Divide final by initial
$16,000 ÷ $10,000 = 1.6
Step 2: Raise to the power of (1/5)
1.60.2 = 1.09856
Step 3: Subtract 1
1.09856 - 1 = 0.09856
Step 4: Convert to percentage
0.09856 × 100 = 9.86%
Result: Your investment grew at a compound annual growth rate of 9.86%.
Understanding the difference between CAGR and simple growth rate is crucial for accurate investment analysis:
The simple growth rate formula is:
SGR = [(FV - PV) / PV] × 100
SGR shows the total percentage change over the entire period but doesn't account for the compounding effect.
| Aspect | Simple Growth Rate | CAGR |
|---|---|---|
| Time Frame | Total period | Annual basis |
| Compounding | Not considered | Fully incorporated |
| Volatility | Shows actual variation | Smoothed average |
| Comparison | Same time periods only | Different time periods |
💡 Example Comparison:
Investment: $1,000 grows to $1,300 in 3 years
The CAGR of 9.14% is less than 30%/3 = 10% due to the compounding effect!
⚠️ Limitation Example:
An investment worth $5,500 in 2014 and $6,000 in 2018 has different CAGRs depending on the timeframe:
This shows how selecting different time periods can dramatically change the CAGR calculation.
CAGR is widely used across various financial scenarios:
Compare the performance of stocks, mutual funds, ETFs, or portfolios over different time periods on an apples-to-apples basis.
Analyze revenue growth, profit growth, customer acquisition, or market share expansion over multiple years.
Evaluate property value appreciation or rental income growth over time.
Project future retirement savings based on historical portfolio growth rates.
Measure GDP growth, population growth, or inflation rates on an annualized basis.
💼 Real-World Example:
A company's revenue grew from $310,000 in 2012 to $450,000 in 2019 (7 years).
CAGR = ($450,000 / $310,000)1/7 - 1 = 5.47%
This means the company grew at an average rate of 5.47% per year, even though actual year-over-year growth varied.
A "good" CAGR depends on the context and benchmark. For stocks, a CAGR of 8-10% historically matches market averages. For businesses, 15-25% might be considered strong growth. Always compare against relevant benchmarks and consider risk levels.
To double your investment in 5 years, you need a CAGR of approximately 14.87%. This comes from: (2)1/5 - 1 = 0.1487 or 14.87%.
Yes, CAGR can be negative if the final value is less than the initial value. A negative CAGR indicates the investment lost value over the period.
CAGR is a specific type of annualized return that assumes smooth, constant growth. Other annualized return calculations might use different methods (like arithmetic averaging) that don't account for compounding.
CAGR is most meaningful for multi-year investments. For investments shorter than one year, simple return percentages or annualized returns may be more appropriate.
The Rule of 72 is a quick way to estimate doubling time: divide 72 by your CAGR percentage. For example, with a 9% CAGR, your investment doubles in approximately 72 ÷ 9 = 8 years.