A doubling-time shortcut
The rule of 72 estimates doubling time by dividing 72 by the annual percentage rate. It is a mental shortcut for compound growth, not the exact logarithmic solution. Its usefulness comes from being quick: rates such as 6%, 8%, and 9% give immediately understandable rough horizons without entering a full schedule.
Worked six-percent estimate
At a 6% annual rate, 72 divided by 6 gives 12.0 years. Starting with $10,000, the shortcut points to about $20,000 after that interval. The exact compound formula gives about 11.9 years, so the approximation is close at this rate but is not identical.
Where the shortcut fits
The shortcut assumes a positive rate compounded over time and no withdrawals, fees, or added contributions. It works best for moderate rates, where 72 is a convenient approximation to the logarithmic relationship. Very low, very high, variable, or negative rates need the exact formula and often a period-by-period projection.
A horizon is not a promise
Do not turn a doubling time into an account promise. A 6% market return may not occur every year, and a stated bank rate can change before twelve years pass. Inflation creates another distinction: doubling a cash balance does not necessarily double what that money can buy.
Questions it cannot answer
This page cannot model a savings goal because regular contributions change the question from doubling one balance to accumulating a stream of deposits. Nor can it compare a nominal rate with APY without first identifying the compounding convention. It is deliberately a quick scale check, not a product-selection tool.
Choose exact math when dates matter
Use the exact result when the date affects a contract, retirement plan, or other commitment. Use the shortcut when deciding whether a rate is in the neighborhood of a five-, ten-, or twenty-year horizon. Writing down the rate source and whether it is guaranteed keeps the estimate from becoming a false certainty.
A rate comparison
At 9%, the shortcut gives eight years; at 3%, it gives twenty-four. That contrast is useful for seeing how a few percentage points alter a long horizon, but the underlying rate still needs to be plausible and consistently compounded.
Why the shortcut drifts
The exact doubling time is ln(2) divided by ln(1 + r), with r written as a decimal. The rule replaces that curved logarithmic relationship with 72 divided by the percentage rate, so its error changes as the rate moves away from the range where the approximation is close. Use the displayed exact figure for a deadline; retain the shortcut for quick rate intuition.
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It is an educational estimate, not financial, tax, or legal advice.