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Rule of 72 Calculator

This rule of 72 calculator estimates how many years it takes for an amount to double at a given interest rate: divide 72 by the rate. It shows the shortcut next to the exact calculation and can also solve backwards for the rate you need.

Example: What do you want to find: How long to reach the goal? (rate known) · Interest rate per year 6 % · Target factor 2 → Result: At 6% interest your money doubles in 11.9 years.. Source: Wikipedia – Rule of 72. Updated: .

%
annual compounding, e.g. 6
2 = double, 3 = triple, 1.5 = plus 50%
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Result

Result
At 6% interest your money doubles in 11.9 years.
Calculation
  • Shortcut: 72 ÷ 6% = 12 years
  • Exact: ln(2) ÷ ln(1 + 6%) = 11.9 years
  • The shortcut is 0.88% too high.
  • That is about 11 years and 11 months.
Shortcut compared with the exact value
Interest rateShortcut (years)Exact (years)Difference
1 %7269.73.36 %
2 %36352.85 %
3 %2423.42.35 %
4 %1817.71.85 %
5 %14.414.21.36 %
6 %1211.90.88 %
7 %10.310.20.4 %
8 %99-0.07 %
9 %88-0.54 %
10 %7.27.3-1 %
12 %66.1-1.9 %
15 %4.85-3.22 %

How it is calculated

The rule of 72 says: divide 72 by the interest rate in percent and you get roughly the number of years it takes for an amount to double. At 6% that is 72 ÷ 6 = 12 years; the exact figure is 11.9.

Where the shortcut comes from

With annual compounding the exact doubling time is ln 2 ÷ ln(1 + rate). For small rates ln(1 + rate) is about equal to the rate, and ln 2 ≈ 0.693 – which would give 69.3. Because that approximation comes out 5–10% too small at everyday rates, 72 became the standard: it divides evenly by many numbers (2, 3, 4, 6, 8, 9, 12). It is most accurate around 8%.

Other goals and working backwards

The rule assumes compound interest credited yearly. If you pay in regular savings or deduct taxes, use the compound interest calculator; the future value calculator shows the value after a fixed term, and the CAGR calculator works out the yearly return of an investment.

Frequently asked questions

How does the rule of 72 work?

Divide 72 by the yearly interest rate in percent. The result is the approximate number of years until the amount doubles: 72 ÷ 8 = 9 years.

How accurate is the shortcut?

For rates between 6 and 10% it is usually within 0.5% of the exact value, and a little further off at very low or very high rates.

How do I calculate the doubling time exactly?

With n = ln(2) ÷ ln(1 + rate). At 5% that is 0.693 ÷ 0.0488 = 14.2 years; the shortcut gives 14.4.

Does it work for tripling too?

For tripling use 114 instead of 72, for quadrupling 144. The tool works out the right number for any target factor.

Can I use it to estimate inflation?

Roughly, yes: at 3% inflation money loses half its purchasing power in about 72 ÷ 3 = 24 years.

Sources and legal basis

As of: · Editorial policy

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