Key takeaways
Compound growth is multiplication repeated, and a couple of rules of thumb turn it into mental arithmetic good enough for planning.
- Doubling time ≈ 72 ÷ growth rate in percent.
- At 6 % a year, money doubles in about 12 years.
- The rule is accurate between roughly 4 % and 12 %.
The rule of 72
Divide 72 by the yearly growth rate to get the years to double. At 6 %: 72 ÷ 6 = 12 years. At 9 %: 8 years.
Why 72
The exact answer is ln 2 ÷ ln(1 + r), about 0.693 ÷ r for small r. 72 is close to 69.3 and divides neatly by 2, 3, 4, 6, 8, 9 and 12.
Beyond doubling
Tripling takes about 114 ÷ r years; tenfold takes about 240 ÷ r. At 8 %, money triples in 14 years and grows tenfold in 30.
When to stop estimating
Above 15 % or so, the rule drifts. Use the formula, or the calculator on this site.
Related questions
- How long does it take to double money at 7 %?
