How it’s calculated
CAGR is the single steady yearly rate that would grow the beginning value into the ending value over the period. It comes from rearranging the compound growth formula FV = PV × (1 + r)ⁿ.
Example: 10,000 growing to 20,000 in 5 years gives (20,000 ÷ 10,000)^(1/5) − 1 = 2^0.2 − 1 = 14.87% a year. The rule of 72 estimate is 72 ÷ 5 = 14.4%. The simple average (100% ÷ 5 = 20%) overstates the rate because it ignores compounding.
For periods shorter than a year CAGR annualizes the growth, which can exaggerate it: 10% growth in one month is about 214% a year. Use at least a few years where possible.
CAGR smooths out the path: real growth may have been uneven, and past growth does not predict future results.
Frequently asked questions
Is CAGR the same as average annual return?
No. The arithmetic average of yearly returns is usually higher than CAGR when returns vary. CAGR (a geometric average) is the rate that actually reproduces the ending value.
Can CAGR be negative?
Yes. If the ending value is below the beginning value the CAGR is negative.
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Sources
- Principles of Finance, 7.2 Time Value of Money (TVM) Basics (FV = PV × (1 + r)ⁿ) — OpenStax
- Principles of Finance, 7.4 Applications of TVM in Finance (rule of 72) — OpenStax
- Compound Interest Calculator — U.S. Securities and Exchange Commission (Investor.gov)
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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