CAGR
Compound annual growth rate of an investment.
Formula
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Example
Growing from $100 to $200 in 3 years is a CAGR of 2^(1/3) − 1 ≈ 26%.
How it works
CAGR tells you the single constant yearly rate that would turn an initial value into a final value over a given number of years, even if the actual path had ups and downs. It comes from reversing compound growth: if an investment grows by the same rate each year, then V_f = V_i(1+r)^n, so solving for r gives CAGR = (V_f/V_i)^(1/n) - 1. This makes it a useful way to compare investments or business metrics on an equal annual basis.
When to use it
Use CAGR when you need to summarize growth over multiple periods with one annualized rate, such as comparing funds, company revenue, user counts, or market sizes. It is especially helpful when the yearly changes were uneven but you still want a consistent long-term growth rate.
Worked example, step by step
Suppose a portfolio increases from $5,000 to $8,000 over 4 years. Step 1: Identify values: V_i = 5000, V_f = 8000, n = 4. Step 2: Substitute into the formula: CAGR = (8000 / 5000)^(1/4) - 1. Step 3: Simplify the ratio: CAGR = (1.6)^(1/4) - 1. Step 4: Compute the fourth root: (1.6)^(1/4) ≈ 1.1247. Step 5: Subtract 1: CAGR ≈ 1.1247 - 1 = 0.1247. Step 6: Convert to a percentage: CAGR ≈ 12.5% per year.
Common mistakes to avoid
- Using CAGR to describe year-to-year volatility instead of long-term average growth
- Plugging in periods other than years without adjusting n to match the time unit
- Confusing CAGR with arithmetic average return, which gives a different result
Did You Know?
CAGR smooths a bumpy investment into a single steady annual growth rate for easy comparison.
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