The Rule of 72: Mental Maths for Investors
Divide 72 by an annual growth rate and you get, near enough, the number of years for the amount to double. At 6 per cent, twelve years. At 9 per cent, eight. The Rule of 72 Calculator does it and shows the exact figure beside it.
Why 72
The exact answer involves logarithms: the years to double are the natural log of 2 divided by the natural log of one plus the rate. The natural log of 2 is about 0.693, so for small rates the years to double are roughly 69.3 divided by the percentage rate.
69.3 would be more accurate and 72 is far more useful, because 72 divides neatly by 2, 3, 4, 6, 8, 9 and 12. The small loss of precision buys mental arithmetic you can actually do, and the number was chosen for that reason.
The approximation is most accurate around 8 per cent, where it is almost exact. It drifts either side: at 2 per cent the true doubling time is 35 years against the rule's 36, and at 20 per cent it is 3.8 years against the rule's 3.6. Reliable between about 4 and 12 per cent, which is the range most ordinary questions fall in.
What it is genuinely good for
Sanity-checking a claim. Someone promising to double your money in three years is implying roughly 24 per cent a year, sustained. That is a useful thing to notice in the moment rather than later.
Comparing rates intuitively. The gap between 4 and 8 per cent sounds like a modest difference and is the difference between doubling in eighteen years and doubling in nine - over a forty-year horizon, two doublings against four, which is four times the end result.
Seeing what fees cost. A 1 per cent annual charge turns a 7 per cent return into 6, which moves doubling from about ten years to twelve. Over a long horizon that is most of a doubling lost to a number that looks small on a statement.
Use it on inflation too
The same arithmetic works on prices. At 3 per cent inflation, prices double in about 24 years - which is to say the money loses half its purchasing power over an average working life.
That is the most useful application for most people, because it reframes "cash is safe" as a real cost rather than a neutral choice. The Compound Interest Calculator is where to see the same effect in detail.
What it cannot do
It assumes a constant rate, and real investment returns are not constant. A sequence averaging 7 per cent with large swings does not behave like a steady 7 per cent, and the order of good and bad years matters - particularly when you are drawing money out.
So it is a mental shortcut for understanding the shape of compounding, not a projection. Nothing here is advice about what to do with money, and anything you are actually deciding is worth discussing with a regulated adviser.
Common questions
Is there a rule for tripling?
Divide 114. For ten times, 231.
Does it work backwards?
Yes - divide 72 by the years to get the required rate. Doubling in nine years needs about 8 per cent.
Why do some people use 70?
Closer to the true 69.3 and harder to divide. 72 wins on usability.
Want the quick answer and the exact one?