Doubling Time Calculator
How long money takes to double, by the rule of 72 and exactly.
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Formula
How the calculation works
The rule of 72 is a shortcut: divide 72 by the annual percentage rate and you get roughly the years to double. At 7% it says 10.29 years, and the exact answer is 10.24. For mental arithmetic on a rate in the middle of the usual range, that is close enough to be genuinely useful.
The exact figure comes from logarithms rather than division, and the two diverge outside a band. At 2% the rule says 36 years when the truth is 35, and at 20% it says 3.6 against an exact 3.8. The rule is tuned to sit near 8%, where it is almost exact, and the tool reports the gap so you can see when the shortcut has stopped being good enough.
The reason a fixed number like 72 works at all is that the logarithm of 1 plus the rate is close to the rate itself for small rates. That approximation is what makes the shortcut possible, and it is also why the shortcut fails as the rate grows -- the approximation breaks down, and the fixed numerator cannot compensate.
Common mistakes
- Treating the rule of 72 as exact. It is an approximation tuned near 8%, and it drifts at low and high rates.
- Using 72 with a rate expressed as a decimal. It takes 7 for 7%, not 0.07.
- Forgetting that doubling time assumes the interest compounds and is left in. Withdrawing the interest makes doubling never happen.
When to use it
- Use it for a quick mental check, and the exact figure whenever the rate is far from 7% or the decision matters.
- It only answers how long doubling takes. It says nothing about whether the rate is achievable or what the money will buy when it doubles.
Worked example
At 7%, the rule of 72 gives 10.29 years and the exact figure is 10.24 -- a gap of 0.04 years.
Common questions
How accurate is the rule of 72?
Between 6% and 10% it is very close: at 7% the gap is 0.04 years. It drifts at low and high rates -- at 2% it says 36 years when the truth is 35. Good for mental arithmetic, but use the exact figure to decide.
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