CAGR (Compound Annual Growth Rate)
The single smoothed yearly growth rate that would take a value from its start to its end over several years - the honest way to summarize multi-year growth.
What it is
CAGR is the constant annual growth rate that, if applied every year, would carry a starting value to its ending value over a given number of years. Real growth is lumpy - up 40% one year, down 10% the next - and CAGR is the smooth, compounded average that represents that bumpy path as a single clean number. It matters because it respects compounding: growing 10% a year for three years is not 30% total, it is more, because each year builds on the last. CAGR is the standard, comparable way to describe how fast something grew over multiple years without being fooled by the noise of any single year.
When to use it
Use it whenever a case gives you a start value, an end value, and a number of years and asks how fast something grew, or asks you to project growth forward at a steady rate. It is ideal for comparing the growth of two things over the same period, or for stating a market's or a company's multi-year trajectory in one figure. It is less appropriate when the year-by-year path matters (a business that is highly volatile is poorly described by a smooth rate), and it can hide a collapse-then-recovery story. Do not use it to imply steady growth actually happened - it only describes the endpoints.
How to apply it
The formula is: CAGR = (Ending value / Beginning value)^(1 / number of years) - 1. The units cancel because it is a ratio of the same quantity, so CAGR is a pure percentage per year. In an interview without a calculator, reason with the compounding shortcut and round numbers: the Rule of 72 says a value doubling over N years grew at roughly 72/N percent per year (something that doubles in 6 years grew about 12% a year; in 9 years, about 8%). For non-doubles, bracket the answer - if a value grew 60% over 4 years, the annual rate is a bit under 12.5% because compounding makes the true rate lower than the simple 15% you would get by dividing. Interpretation: state it as 'grew at X% per year, compounded' and remember it is an average that says nothing about the journey.
Common mistakes
The most frequent error is computing simple average growth - total growth divided by the number of years - which ignores compounding and overstates the rate. Another is confusing CAGR with the arithmetic average of the yearly rates, which can differ substantially when growth is volatile. People also forget the endpoints trap: CAGR is entirely determined by the first and last values, so an unusual start or end year can distort it badly. And they present a smooth CAGR as if the growth was actually steady, hiding a boom-bust pattern that changes the story.
Example
A regional retailer's revenue went from 200 million to about 350 million over 5 years, and the interviewer asks for the growth rate. The tempting simple answer: 75% total over 5 years is 15% a year. But compounding pulls the true rate down. Using the Rule of 72 as a sanity check, the revenue did not quite double (which over 5 years would be about 14.4% a year), and 350/200 = 1.75 is below 2, so the CAGR is somewhat under 12%, roughly 11-12% per year. That distinction matters: an outside partner projecting off '15% a year' would materially overstate future revenue. The compounding-aware estimate is both more accurate and defensible without a calculator.
Practice it
Practice on growth, market-sizing, and projection cases by computing compounded rather than simple growth, using the Rule of 72 and round-number bracketing to estimate CAGR mentally, and stating clearly that it is a smoothed average. The skill to build is respecting compounding under time pressure and knowing when a single rate hides a story the endpoints do not tell.