Money & everyday · 3 min read
The Rule of 72: How Fast Does Money Double?
How to use it
Divide 72 by the interest rate as a whole number. At 8% growth, 72 ÷ 8 = 9 years to double. It works for investments, inflation, population and any steady percentage growth.
How accurate is it?
| Rate | Rule of 72 | Exact (ln 2 / ln(1+r)) | Error |
|---|---|---|---|
| 2% | 36 | 35 | 2.8% |
| 3% | 24 | 23.45 | 2.3% |
| 4% | 18 | 17.67 | 1.9% |
| 6% | 12 | 11.9 | 0.9% |
| 8% | 9 | 9.01 | 0.1% |
| 10% | 7.2 | 7.27 | 1% |
| 12% | 6 | 6.12 | 1.9% |
| 15% | 4.8 | 4.96 | 3.2% |
It is excellent between roughly 6% and 10%.
Why 72?
Exact doubling time is ln 2 / ln(1 + r) ≈ 0.693 / r for small r. Using r in percent gives about 69.3 ÷ rate; 72 is used because it has many whole-number divisors (2, 3, 4, 6, 8, 9, 12) and fits typical rates better. See logarithms.
ln 2 ≈ 0.693
- Natural log ln(2) = 0.693147
- Log base 10 = 0.30103
Step-by-step working 3 steps
- 1Meaning
log_e(2) = y means e^y = 2
A logarithm answers: “what power of the base gives x?”
- 2Change of base
y = ln(2) / ln(e) = 0.69314718 / 1 = 0.69314718
- 3Check
e^0.69314718 ≈ 2
Raising the base to the answer returns x (to rounding).
Going further
Check exact growth with compound interest and the logarithm calculator.
Frequently asked questions
Does the rule work for inflation?
Yes: at 3% inflation, prices double in about 24 years.
What about tripling?
A similar rule uses about 110 ÷ rate.
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