Rule of 72 Calculator
How many years money takes to double at a given return, by the rule of 72 and exactly, and the rate needed to double in a given time.
By the rule of 72, money doubles in 72 ÷ rate years: 9 years at 8%. The exact answer at 8% is 9.01 years. To double in 6 years you need about 12% a year (exactly 12.25%).
The words on this page, explained simply
New to this? Here is what each term means, in plain English.
- Rule of 72
- Years to double money ≈ 72 ÷ yearly rate.
- Doubling time
- How long money takes to double at a given compound rate: exactly ln 2 ÷ ln(1 + rate).
- Compound interest
- Interest earned on earlier interest as well as on the original amount, so growth snowballs over time.
The rule of 72 is a shortcut for compound growth: divide 72 by the yearly return to get the years needed to double. It works for investments, inflation (how fast prices double) and debt alike.
Why 72 works, and how accurate it is
The exact doubling time is ln 2 ÷ ln(1 + r). For small rates ln(1 + r) ≈ r, giving 0.693 ÷ r, or 69.3 ÷ rate in percent. 72 is used instead because it divides evenly by 2, 3, 4, 6, 8, 9 and 12 and happens to be closer for the 6-10% returns most people use.
| Rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 years | 35.00 years |
| 4% | 18.0 years | 17.67 years |
| 6% | 12.0 years | 11.90 years |
| 8% | 9.0 years | 9.01 years |
| 10% | 7.2 years | 7.27 years |
| 12% | 6.0 years | 6.12 years |
| 15% | 4.8 years | 4.96 years |
| 20% | 3.6 years | 3.80 years |
Other uses
Inflation: at 6% inflation prices double in about 12 years, so money's buying power halves. Debt: a credit card at 24% doubles an unpaid balance in about 3 years. Tripling: divide 114 by the rate.
Key takeaways
- Years to double ≈ 72 ÷ yearly rate.
- Rate needed ≈ 72 ÷ years.
- Exact: ln 2 ÷ ln(1 + r).
- Most accurate around 8%; less so at very high rates.
Frequently asked questions
What is the rule of 72?
A shortcut: divide 72 by the yearly interest rate or return to estimate how many years money takes to double. At 6% that is 12 years.
How accurate is the rule of 72?
Very close between about 5% and 12%. At 8% it says 9 years against an exact 9.01; at 20% it says 3.6 against 3.80.
What return do I need to double my money in 5 years?
About 72 ÷ 5 = 14.4% a year by the rule; exactly 14.87%.