One number tells you how fast money doubles: 72.
Divide 72 by an annual growth rate and you get the years it takes to double. At 6 per cent, money doubles in about 12 years; at 9 per cent, about 8. It works for debt and inflation too, which is exactly why it's worth knowing.
Compound growth is hard to feel intuitively. Our brains think in straight lines, but compounding bends upwards: each year's growth is added to the pile, and next year grows on the bigger pile. The Rule of 72 is a mental shortcut that makes this curve easy to picture.
The rule says the doubling time is roughly 72 divided by the percentage growth rate. At 4 per cent a year, money doubles in about 18 years. At 8 per cent, about 9. At 12 per cent, about 6. It is an approximation derived from logarithms, and it is most accurate for rates between about 6 and 10 per cent. The number 72 is popular partly because it divides neatly by 2, 3, 4, 6, 8, 9 and 12.
The rule works in reverse, which is where it becomes a warning. A credit card charging 24 per cent doubles an unpaid balance in about three years. Inflation of 3 per cent halves the buying power of cash in about 24 years. Anything growing steadily, whether a population, a debt or an economy, can be run through it.
Versions of the idea appear in Luca Pacioli's 1494 book on mathematics, the Summa de arithmetica, which also popularised double-entry bookkeeping. The deeper lesson is about time. Money invested at 7 per cent doubles roughly every decade, so a sum invested at 25 has around four doublings before 65, and a sum invested at 45 has only two. Starting early matters more than starting big.
Source: Wikipedia — Rule of 72 · Text summarised from Wikipedia (CC BY-SA 4.0)
