Rule of 72 formula
The rule of 72 formula is years to double ≈ 72 ÷ annual interest rate (in percent). The SEC's investor.gov teaches the same shortcut: at 9% a year, money doubles about every 8 years.[1]
Reverse it to find the rate: to double in 6 years you need about 72 ÷ 6 = 12% a year. The exact answer comes from the compound interest formula: setting (1 + r)t = 2 gives t = ln 2 ÷ ln(1 + r).[2]
Rule of 72 table: estimate vs exact
The rule is most accurate between about 6% and 10% and drifts at low and high rates:
| Rate | Rule of 72 (yrs) | Rule of 70 (yrs) | Exact, yearly compounding | Error of rule of 72 |
|---|---|---|---|---|
| 1% | 72.0 | 70.0 | 69.66 | +2.34 |
| 2% | 36.0 | 35.0 | 35.00 | +1.00 |
| 3% | 24.0 | 23.3 | 23.45 | +0.55 |
| 4% | 18.0 | 17.5 | 17.67 | +0.33 |
| 5% | 14.4 | 14.0 | 14.21 | +0.19 |
| 6% | 12.0 | 11.7 | 11.90 | +0.10 |
| 8% | 9.0 | 8.8 | 9.01 | −0.01 |
| 10% | 7.2 | 7.0 | 7.27 | −0.07 |
| 12% | 6.0 | 5.8 | 6.12 | −0.12 |
| 15% | 4.8 | 4.7 | 4.96 | −0.16 |
| 20% | 3.6 | 3.5 | 3.80 | −0.20 |
At 2%, the rule of 70 is closer; at 15% and above, 72 understates the true time less than 70 does. With continuous compounding, the exact constant is 100 × ln 2 ≈ 69.3, which is why some textbooks use the rule of 69.3.
Rule of 70 vs rule of 72
The rule of 70 divides 70 by the rate instead of 72: at 2% it gives 35 years against 36, and the exact answer with yearly compounding is 35.0. It is the better shortcut at low rates and for continuous growth, which is why economists use it for population and GDP growth. Above about 5%, 72 gets closer. This calculator shows both next to the exact answer.
Why 72?
The true constant for continuous growth is 69.3, but 72 is divisible by 1, 2, 3, 4, 6, 8, 9 and 12, which makes mental math easy, and it corrects for yearly compounding at the rates people usually face. The same logic gives the rule of 114 for tripling and the rule of 144 for quadrupling (144 = 2 × 72).
Rule of 72 and inflation
The rule also tells how fast inflation halves purchasing power. Consumer prices rose 3.7% in the 12 months to September 2026.[3] At that pace prices double, and a dollar's buying power halves, in about 19 years. A savings rate below inflation loses purchasing power even as the balance grows; the compound interest calculator shows the inflation-adjusted balance.
Using the rule with savings and CDs
- A savings account at 4% APY doubles in about 18 years (exact: 17.7). Model it with deposits in the savings calculator.
- Because an APY already includes compounding, use the APY in the rule, not the nominal rate.
- Doubling twice quadruples: at 8%, $10,000 becomes about $40,000 in 18 years. Doubling about seven times turns $10,000 into $1 million; the millionaire calculator adds monthly saving.
For a complete schedule of how any sum grows, use the future value calculator.
Related calculators
- Compound interest calculatorDeposits, any compounding, inflation, goal seek, chart and CSV
- Future value calculatorA lump sum and a series of payments, grown forward
- Savings calculatorBalance and interest from monthly deposits at an APY
Frequently asked questions
What is the rule of 72?
A shortcut for doubling time: divide 72 by the annual rate in percent. At 6% money doubles in about 12 years.
How accurate is the rule of 72?
Within a few months for rates of 4% to 12%. At 8% it gives 9 years against an exact 9.01.
What is the difference between the rule of 72 and the rule of 70?
Only the constant. 70 is closer at low rates and for continuous compounding; 72 is closer around 8% and easier to divide.
How long does it take to double money at 10%?
About 7.2 years by the rule of 72; exactly 7.27 years with yearly compounding.