How this calculator works
The Rule of 72 divides 72 by the annual return expressed in percentage points. It is a quick approximation. The exact comparison solves for the time when annual compound growth reaches twice the opening balance. Both assume a constant positive effective return, no cash flows, no taxes and no fees.
Formula
Approximate years = 72/R; exact years = ln(2)/ln(1 + R/100), where R is the effective annual return in percentage points. For 6%, use R = 6. ln is the natural logarithm.
Worked example
At 6%, the shortcut gives 12 years and the exact calculation gives 11.895661 years. At 12%, the shortcut gives 6 years and the exact result is 6.116255 years.
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Frequently asked questions
Why must the return be positive?
At zero or a negative constant return, a positive starting balance does not double through growth alone.
Is the Rule of 72 exact?
No. Its error changes with the return. Compare it with the logarithmic result, especially when the assumed return is far from typical single-digit rates.
Which result should I rely on?
Use the exact result when the annual return is known. The Rule of 72 is a mental shortcut, and its error grows as the rate moves away from single digits.