"How long until this doubles?" is one of the most common questions in investing, and the Rule of 72 answers it in the time it takes to do one division problem - no calculator, no formula, no spreadsheet.
Compound growth is notoriously hard to eyeball. A rate of return that sounds modest - 7%, 9%, 11% - compounded over enough years produces results that feel almost unintuitive compared to simple, non-compounding math. The Rule of 72 exists to close that intuition gap in seconds: divide 72 by an annual rate of return, and the answer is roughly how many years it takes that amount of money to double.
This guide covers the formula, the math for why 72 is the number that was chosen, and - using real computed 10-year returns rather than a hypothetical example - exactly how accurate the approximation actually is, and where it starts to break down.
The Rule of 72 Formula
Years to Double = 72 ÷ Annual Rate of Return
Plug in the rate as a whole number (use 8, not 0.08, for an 8% return) and the result is the approximate number of years needed for an investment to double in value, assuming that rate holds steady and all gains compound.
| Annual Rate | Years to Double (Rule of 72) |
|---|---|
| 2% | 36.0 |
| 4% | 18.0 |
| 6% | 12.0 |
| 8% | 9.0 |
| 10% | 7.2 |
| 12% | 6.0 |
| 15% | 4.8 |
| 20% | 3.6 |
The relationship isn't linear - doubling the rate of return more than halves the time required, which is itself a small preview of how nonlinear compound growth is in general.
The rule also works in reverse. Flip the formula to solve for the rate instead of the time: Required Rate = 72 ÷ Desired Years to Double. An investor who wants to double their money in 6 years needs to find something averaging roughly 72 / 6 = 12% a year.
Why 72? The Math Behind the Approximation
The exact relationship for compound growth comes from natural logarithms: Years to Double = ln(2) ÷ ln(1 + rate). The constant ln(2) is approximately 0.693, so expressed as a percentage rate, the mathematically precise divisor is closer to 69.3, not 72.
72 was chosen instead of the more "correct" 69.3 for one practical reason: divisibility. 72 splits evenly into far more whole numbers relevant to real interest rates - 1, 2, 3, 4, 6, 8, 9, 12, and 18 - which makes the mental math clean across exactly the range most people use it for (roughly 6% to 10%). The tradeoff is a small, deliberate accuracy cost in exchange for a formula that can be done in your head, which is the entire point of a rule of thumb.
How Accurate Is the Rule of 72, Really?
Textbook examples of the Rule of 72 almost always use a clean, moderate rate like 8%, where the approximation looks essentially perfect. Real markets don't hand out clean, moderate, steady rates - so here is the rule tested against real, computed 10-year annualized returns (2015-2025) for the S&P 500 and four widely held stocks, comparing the Rule of 72's estimate to the mathematically exact doubling time:
| Investment | 10-Year CAGR | Rule of 72 Estimate | Exact Doubling Time |
|---|---|---|---|
| Coca-Cola (KO) | 5.0% | 14.4 years | 14.2 years |
| S&P 500 | 12.8% | 5.6 years | 5.7 years |
| Microsoft (MSFT) | 24.2% | 3.0 years | 3.2 years |
| Apple (AAPL) | 26.3% | 2.7 years | 3.0 years |
| NVIDIA (NVDA) | 72.0% | 1.0 years | 1.3 years |
Two patterns stand out:
- At moderate rates, the rule is remarkably tight. Coca-Cola's real 5.0% decade CAGR and the S&P 500's real 12.8% CAGR both produce Rule of 72 estimates within roughly a tenth of a year of the mathematically exact answer - well inside the margin that matters for a mental estimate.
- At extreme rates, the gap widens noticeably. NVIDIA's real 10-year CAGR of 72% is high enough that the Rule of 72's own numerator equals its rate - a coincidence that produces a suspiciously clean "1.0 years" estimate. The exact answer is 1.28 years, meaning the rule understates the true doubling time by about 22% at that rate. The approximation's error scales with the rate, so it should be trusted less at the tails and more for the high-single-digit to low-double-digit returns most diversified portfolios actually target.
Rule of 114 and Rule of 144: Tripling and Quadrupling
The same shortcut extends past doubling using the same logic - a rounded, easily divisible constant standing in for an exact natural-log relationship:
- Rule of 114 estimates years to triple: 114 ÷ annual rate. At 8%, that's 114 / 8 ≈ 14.3 years to triple.
- Rule of 144 estimates years to quadruple: 144 ÷ annual rate. At 8%, that's 144 / 8 = 18 years to quadruple - exactly double the time it took to double once, which makes sense since quadrupling is just doubling twice.
Using the Rule of 72 on Inflation, Not Just Growth
The same math cuts the other way: it also estimates how fast a fixed amount of money loses half its purchasing power to inflation. Divide 72 by the inflation rate instead of an investment return.
At the Federal Reserve's long-standing 2% inflation target, purchasing power would take about 72 / 2 = 36 years to fall by half. At a more elevated 6% inflation rate - closer to what the US experienced in 2022 - that same erosion happens in just 72 / 6 = 12 years. Framed this way, the Rule of 72 is a fast way to see why holding cash (or any asset with a return below the inflation rate) is a guaranteed, if slow-moving, loss of real value.
Where the Rule of 72 Falls Short
The rule is an estimation tool, not a forecasting one, and it carries the same limitations as any single-rate compounding model:
- It assumes one constant rate held for the entire period. Real returns are lumpy - a stock or index rarely returns exactly its CAGR in any individual year, even when the multi-year average lines up neatly. The S&P 500's 12.8% 10-year CAGR above, for instance, was built from years as different as a 28.9% gain and a 19.4% loss - not ten identical 12.8% years.
- It only measures a single lump sum, not ongoing contributions. An investor adding money regularly - the dollar-cost averaging pattern behind most retirement accounts - will reach a given balance faster than the Rule of 72 alone would suggest, because new contributions are compounding on their own separate timelines.
- It ignores taxes, fees, and trading costs, all of which quietly reduce the effective rate the formula should actually be run on. A "10% return" fund with a 1.5% annual expense ratio is really compounding closer to 8.5%, and the Rule of 72 will overstate how fast it doubles if that drag isn't backed out first.
Using Alerts to Track a Compounding Position
The Rule of 72 is most useful as a sanity check before committing to a position: run a stock's or fund's historical CAGR through the formula to see roughly what timeline you're actually signing up for, rather than anchoring on the headline percentage alone. Once you're holding a long-term position built around that math, a price alert in Stock Alarm Pro at your estimated doubling milestone gives you a natural checkpoint to reassess the thesis - is the position still compounding at the rate you originally planned for, or has something changed? Use the Screener to compare a candidate's trailing growth rate against the market before running the math in the first place.
