Compound annual growth rate, or CAGR, is the steady yearly rate that takes a value from where it started to where it ended. It is a standard way to compare investments of different lengths.
The formula
CAGR = (end value ÷ start value) ^ (1 ÷ years) − 1
For example, $10,000 that grows to $20,000 in 10 years: (20,000 ÷ 10,000) ^ (1 ÷ 10) − 1 = 7.2% a year. Check it in the CAGR calculator.
Why it is not the simple average
Say an investment goes up 50% in year one and down 40% in year two.
- The simple average is (50% + −40%) ÷ 2 = +5% a year. That sounds like a gain.
- In fact $100 becomes $150, then $90. You lost money. The CAGR is about −5.1% a year.
Growth builds on growth, so ups and downs do not cancel the way a simple average pretends. That is why a simple average of yearly returns can overstate what you really earned.
The rule of 72
A quick way to guess how long it takes to double: divide 72 by the yearly rate as a number. At 8%, it is about 9 years. At 6%, about 12 years. The exact figure uses logarithms, which the calculator does for you.
What CAGR does not show
- The bumps along the way. Two investments can have the same CAGR but very different ups and downs.
- Money you added or took out. CAGR only compares the start and end values. For regular contributions, use the IRR calculator.
- Inflation. A 3% CAGR when prices rise 3% means no gain in buying power.
Good uses
- Comparing two funds over the same period.
- Checking a company's revenue growth over several years.
- Seeing what yearly rate you need to reach a goal.
Sources
- Background reading, Investor.gov: Annual return
- Background reading, Investor.gov: Compound interest
- Background reading, Investor.gov: Compound interest calculator
This article is for education and is not financial, tax or legal advice. Figures are checked against the sources above and may change. Read the full disclaimer.