In more detail
The exact doubling time at a yearly rate r is ln 2 / ln(1 + r); the rule replaces it with 72 / rate in percent, which is easy to divide in your head because 72 has many factors. It works best for rates between about 4% and 12% and drifts at the extremes. For continuous compounding, 69.3 is exact, and some people use 70 for low rates. The same rule estimates halving time, for example how fast inflation halves the value of cash.
Why it matters
It turns abstract percentages into a time you can picture: debt at a high rate doubles frighteningly fast, and a 1% difference in fees changes how many doublings a lifetime of saving gets.
Example
| Rate | Rule of 72 | Exact (yearly compounding) |
|---|---|---|
| 2% | 36 years | 35.00 years |
| 6% | 12 years | 11.90 years |
| 8% | 9 years | 9.01 years |
| 12% | 6 years | 6.12 years |
| 24% | 3 years | 3.22 years |
At 3% inflation, prices double in about 24 years.