Rule of 72 vs Rule of 70 (and the Rule of 69.3)

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Written with AI assistance · Reviewed by the Talreon team · Updated 21 October 2026 · Figures log · Educational, not financial advice

The Rule of 72 and the Rule of 70 are mental-maths shortcuts for doubling time: how many years it takes an amount growing at a steady compound rate to double. They are also used the other way round, for example to see how fast inflation halves the value of money. This guide explains where each number comes from and which to use.

The formulas

Here r is the rate as a decimal, so 8% is 0.08.

Where the numbers come from

With continuous compounding, money doubles when e^r×t = 2, so t = ln(2) ÷ r. Since ln(2) is about 0.693, the "true" constant is 69.3 when the rate is written as a percentage. That is why the Rule of 69.3 is exact for continuous compounding.

Most savings and investment returns are quoted with annual or monthly compounding, which takes slightly longer to double than continuous compounding at the same nominal rate. Rounding up to 70 or 72 compensates for that. 72 has a second advantage: it divides evenly by 2, 3, 4, 6, 8, 9 and 12, so the maths is easy to do in your head.

Comparison table

Years to double at each annual rate, compared with the exact figure for annual compounding. Values are calculated directly from the formulas above.

At 2%, the Rule of 70 matches the exact answer almost perfectly. From about 6% to 10%, the Rule of 72 is closest. Above that, all three rules start to understate the exact doubling time a little.

Worked example: savings at 6%

You have $10,000 earning 6% a year, compounded annually. The Rule of 72 gives 72 ÷ 6 = 12 years. The Rule of 70 gives 70 ÷ 6 = 11.67 years. The exact answer is ln(2) ÷ ln(1.06) = 0.6931 ÷ 0.05827 = 11.90 years. Both rules are within about a quarter of a year, which is close enough for planning.

Worked example: continuous compounding at 5%

If an amount grows continuously at 5%, the exact doubling time is 0.6931 ÷ 0.05 = 13.86 years. The Rule of 69.3 gives 13.86 exactly, the Rule of 70 gives 14.0, and the Rule of 72 gives 14.4. For continuous growth, the lower constant wins.

Using the rules backwards

Divide the constant by the number of years to find the rate you need. To double money in 6 years you need about 72 ÷ 6 = 12% a year. To double in 10 years you need about 7.2%.

The same maths works for anything that grows or shrinks at a steady rate. At 3% inflation, prices double, and the buying power of cash halves, in about 72 ÷ 3 = 24 years (exact: 23.45 years).

Which rule should you use?

• Rule of 72: annual compounding at roughly 6% to 10%, and any time you want easy mental division.
• Rule of 70: low rates (around 1% to 4%), and growth figures such as population or GDP that are often quoted as continuous rates.
• Rule of 69.3: continuous compounding, or when you want the most accurate quick estimate at low rates.
• Exact formula: anything that matters financially. The Rule of 72 calculator shows all three rules next to the exact answer.

Common mistakes

• Entering the rate as a decimal (0.08) instead of a percentage (8). The rules use the percentage.
• Applying the rules to very high rates, such as 25% or more, where all three drift away from the exact answer.
• Forgetting fees and tax, which lower the real growth rate and lengthen the doubling time.
• Assuming an investment will actually grow at a steady rate. Real returns vary year to year.

Related tools

• Rule of 72 calculator — compare 72, 70 and 69.3 with the exact answer.
• Compound interest calculator — growth with regular deposits.
• CAGR calculator — the annual growth rate between two values.
• Inflation calculator — how prices change over time.

Related guides

• How compound interest works
• Simple vs compound interest

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