A 60 per cent gain means nothing until you know whether it took two years or twenty. Compound annual growth rate converts any total return into the constant yearly rate that produced it, which is the only way to compare investments held over different periods.
Up 50 per cent then down 50 per cent averages to zero, but leaves you down 25 per cent — 100 becomes 150 becomes 75. The arithmetic mean of yearly returns systematically overstates what you actually earned, and the more volatile the investment, the wider the gap. CAGR is the geometric mean: the single constant rate that genuinely turns your start value into your end value.
Divide 72 by the annual rate for the years to double. At 8 per cent that is 9 years against an exact 9.006. It holds well between roughly 4 and 12 per cent and drifts at the extremes — good enough to sanity-check any investment claim in your head.
Inflation, fees and tax. A 7 per cent return with 3 per cent inflation is 4 per cent in real terms. A 1 per cent annual fee sounds trivial and consumes roughly a quarter of a 4 per cent real return over a lifetime. Enter figures already net of costs if you want an honest answer.
CAGR assumes a single lump sum left alone. If you added money along the way it will overstate your return, because it credits the growth of later contributions to the whole period. That case needs a money-weighted return — an internal rate of return — not this.
The arithmetic average overstates what you actually earned. Up 50% then down 50% averages to zero but leaves you down 25%. CAGR is the geometric mean and describes the rate that actually turned your start value into your end value.
Very, between roughly 4% and 12%. Divide 72 by the rate for the years to double: 8% gives 9 years against an exact 9.006. It drifts at the extremes but stays close enough for mental arithmetic.
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