FIRE & Compounding

CAGR (Compound Annual Growth Rate)

CAGR stands for compound annual growth rate. It is the single yearly growth rate that would take a value (an investment, a company's sales, your net worth) from where it started to where it ended over a set number of years, as if it had grown by the same percentage every year. The formula is (end value ÷ start value) raised to the power of 1 divided by the number of years, minus 1. Real growth is never perfectly smooth, so CAGR is a summary of the whole journey, not a record of any single year. It is not the same as the simple average of the yearly returns, which can look quite different when the returns swing up and down.

Worked example

Say Fund A is worth $10,000 at the start and $14,641 four years later. CAGR = ($14,641 ÷ $10,000) ^ (1 ÷ 4) - 1 = 1.4641 ^ 0.25 - 1 = 1.10 - 1 = 10% a year. Check it: $10,000 × 1.10 × 1.10 × 1.10 × 1.10 = $14,641. Now the trap with averages: a value starts at 100, rises 50% in year one (to 150) and falls 50% in year two (to 75). The simple average of +50% and -50% is 0%, yet the value ended 25% lower. The CAGR gives the honest figure: (75 ÷ 100) ^ (1 ÷ 2) - 1 = about -13.4% a year.

Why it matters

CAGR lets you compare growth over different periods on one scale: your net worth, a fund, a company's revenue or earnings can all be boiled down to one yearly figure. It is also the right way to turn a start and an end value into a rate when nothing was added or withdrawn along the way. The limits matter. It hides the bumps, so two very different paths can share the same CAGR. It depends heavily on the start and end dates you pick. It ignores deposits and withdrawals made during the period, which is why money-weighted measures such as the internal rate of return exist. And a past CAGR is a description of what happened, not a promise of what comes next. Treat a high or low figure as a question to look into.

Frequently asked questions

Divide the end value by the start value, raise the result to the power of 1 divided by the number of years, then subtract 1. For example, $10,000 growing to $14,641 in 4 years gives 1.4641 ^ 0.25 - 1 = 10% a year. In a spreadsheet you can type =(end/start)^(1/years)-1.

The average return adds up the yearly returns and divides by the number of years, so it ignores compounding. CAGR is the steady rate that links the start value to the end value. When returns swing a lot the two differ: +50% then -50% averages 0%, but the value actually falls about 13.4% a year.

No. It only looks at the start value and the end value, so money added or taken out along the way would distort it. If you made regular contributions, a measure that accounts for the timing of cash flows, such as the internal rate of return, is more suitable.