RatedrillCAGR
The compound annual growth rate is the constant yearly rate that takes a starting value to an ending value over n years: CAGR = (end / start)^(1/n) - 1. It smooths out year-to-year swings into one comparable number. In Excel: =RRI(n, start, end) or =(end/start)^(1/n)-1.
Syntax
CAGR = (end / start)^(1/n) - 1| Part | What it is |
|---|---|
start | Beginning value |
end | Ending value |
n | Number of years (or periods) between them |
Examples
1,000 grows to 2,000 in 5 years
(2,000 / 1,000)^(1/5) - 1Result: CAGR = 14.87%
Excel: =RRI(5, 1000, 2000) or =(2000/1000)^(1/5)-1
Revenue 100 to 150 over 3 years
1.5^(1/3) - 1Result: CAGR = 14.47%
Investment 5,000 to 8,000 over 6 years
1.6^(1/6) - 1Result: CAGR = 8.15%
Common mistakes
- Counting the number of data points instead of the number of years between them: 2020 to 2025 is 5 years, not 6.
- Averaging annual returns arithmetically: +50% then -50% averages 0% but the CAGR is -13.4% because the money ended at 75% of the start.
- Raising to 1/n on a calculator without parentheses, which computes end/start^1 and then divides by n.
Practice CAGR
These drills check your answer on live data, free, no account needed.
- Compound annual growth rateA company's revenue was $70,000 in 2012 and $135,000 in 2015. What was its compound annual growth rate over that span?
- Return needed to reach a goalYou have $2,000 today and want $3,000 in 5 years, with no further deposits. What annual return, compounded annually, gets you there exactly?
Questions
What is the CAGR formula in Excel?
=RRI(years, start_value, end_value), available since Excel 2013, or the equivalent =(end/start)^(1/years)-1. Both return 14.87% for 1,000 to 2,000 over 5 years.
CAGR vs average annual return: what is the difference?
The arithmetic average adds up yearly returns and divides by the count; CAGR is the geometric average that accounts for compounding. CAGR is always less than or equal to the arithmetic average, and it is the one that reflects what actually happened to the money.
Related
- Holding period returnHolding period return is (ending value - beginning value + income) / beginning value. Stock and bond examples, how to annualize an HPR and common mistakes.
- IRR (internal rate of return)The IRR is the discount rate that makes NPV zero. How to find it by trial, what Excel IRR returns, worked examples, the accept rule and where IRR fails.
- Rule of 72The rule of 72 estimates doubling time as 72 divided by the rate. Examples at 6%, 9% and 18%, how accurate it is, the exact ln(2) formula and Excel NPER.
- Future valueHow to calculate the future value of a lump sum with FV = PV x (1 + r)^n, step-by-step examples, the Excel FV function with its sign convention, and errors.