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| Annual rate, % | Years to double (rule of 72) | Exact years |
|---|---|---|
| 1% | 72 | 69.66 |
| 2% | 36 | 35 |
| 3% | 24 | 23.45 |
| 4% | 18 | 17.67 |
| 6% | 12 | 11.9 |
| 8% | 9 | 9.01 |
| 10% | 7.2 | 7.27 |
| 12% | 6 | 6.12 |
| 15% | 4.8 | 4.96 |
| 20% | 3.6 | 3.8 |
Rule of 72: years ≈ 72 / rate. Exact: ln 2 / ln(1 + rate), with yearly compounding.
The inputs start with a neutral sample rate. Change it, and both results update next to the input. They show the Rule of 72 estimate, the exact doubling time and the gap between them.
What the Rule of 72 is
The Rule of 72 is a mental shortcut for compound growth. Compound growth means each period's return is added to the balance, and the next return is earned on the bigger amount.
To estimate how long money takes to double, divide the rule's number by the yearly rate written as a percent. It works for savings, loans, inflation or any value that grows at a steady compound rate.
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The formula under the tool
- Shortcut: years to double ≈ the rule's number ÷ rate in percent.
- Exact: years to double = ln(doubling factor) ÷ ln(yearly growth factor).
Here, ln is the natural logarithm. The yearly growth factor is the whole amount plus the rate written as a decimal.
The shortcut is close at moderate rates. It drifts further from the exact answer at very low or very high rates. The calculator shows that gap, so you can see how far to trust the quick estimate at the rate you entered.
How to read the results
- The exact figure assumes the same rate every year and compounding once a year.
- Real rates change, and taxes and fees reduce growth. Treat the result as an illustration, not a forecast.
- The same rule shows how fast inflation halves buying power. Enter the inflation rate instead of a return.
For context, SBP policy rate raised by 50 bps to 12% with effect from 27.10.2026 (MPC). You can type any rate you want to examine. The tool does not suggest which rate or product to choose.
Doubling time and trading
Trading results do not grow at a steady rate. Leveraged forex and CFD trading can lose money fast, and losses compound too. A doubling-time figure says nothing about how likely a return is.
To see how losses work, use the drawdown recovery calculator. For risk control in general, see risk management.
Related calculators
- Compound interest: full balance growth over time
- Inflation calculator and real return calculator
- Savings interest calculator
- SBP rates and economy
- All calculators
Frequent questions
How accurate is the Rule of 72?
It is close at moderate rates and less accurate at very low or very high ones. The calculator shows the exact result next to it so you can compare.
Is this a doubling time calculator for any currency?
Yes. Doubling time depends only on the rate, not on the currency or the amount.
How long does it take to double money?
It depends on the rate and whether that rate stays steady. Enter a rate in the tool to see both estimates.
Where does the shortcut come from?
From logarithms. The exact doubling time is the logarithm of two divided by the logarithm of one plus the rate. At moderate rates that ratio is close to a fixed constant divided by the rate in percent. The constant in the rule's name sits near the exact value and divides evenly by many common rates, which made mental arithmetic easy before calculators. Some textbooks use a slightly lower constant for continuous compounding, which is why you may see other versions of the rule.
Can I use it for loans?
Yes. It shows how fast an unpaid balance grows at a fixed compound rate. For repayment schedules, use the loan calculator.
Does a doubling time mean a return is guaranteed?
No. The result is arithmetic based on an assumed steady rate, not a promise or a forecast.