The rule and the exact formula
Rule of 72: Years ≈ 72 ÷ Rate
Exact: Years = ln 2 ÷ ln(1 + Rate ÷ 100)
Exact: Years = ln 2 ÷ ln(1 + Rate ÷ 100)
Example: At 8% a year, the rule of 72 says your money doubles in 9 years. The exact answer with annual compounding is 9.006 years. After 30 years at 8%, $1 grows to about $10.06 — just over three doublings.
Quick doubling table
- 2% → 36 years · 4% → 18 years · 6% → 12 years
- 8% → 9 years · 10% → 7.2 years · 12% → 6 years
Model exact growth with deposits in the compound interest calculator.
Frequently asked questions
What is the rule of 72?
A mental shortcut: years to double ≈ 72 ÷ annual rate. At 8% a year, money doubles in about 9 years. It also works in reverse: to double in 6 years you need about 12%.
How accurate is the rule of 72?
Very close for rates between about 6% and 10% with annual compounding. At 8% the rule gives 9.00 years and the exact answer is 9.01. It becomes less accurate at very low or very high rates.
When should I use 69 or 70 instead?
For continuous compounding, 69.3 is the exact constant (ln 2 = 0.693). The rule of 70 is handy for low rates such as inflation or GDP growth.
Can I use it for inflation?
Yes. At 3% inflation, prices double in about 24 years — meaning money loses half its purchasing power in that time.