Rule of 72 Calculator
The Rule of 72 estimates how long an investment takes to double: divide 72 by your annual return percentage. At 7%, the rule says about 10.3 years, and the exact logarithmic answer is 10.24 — this calculator shows both side by side for any rate.
Doubling Time at 7%
The Rule of 72 says 10.3 years; the exact answer is 10.24 years.
- Rule of 72 estimate (72 ÷ 7)
- 10.29 years
- Exact (ln 2 ÷ ln(1 + rate))
- 10.24 years
- Estimation error
- +0.05 years
Where does the 72 come from?
The 72 is a friendlier stand-in for 69.3: exact doubling time is ln 2 ÷ ln(1 + r), and since ln 2 ≈ 0.693, the honest shortcut would be "69.3 ÷ rate" — but 69.3 is miserable mental math, and nudging it up to 72 both makes the division easy and quietly offsets the approximation's drift at everyday rates. For the full derivation, step by step, read our Rule of 72 guide article.
How accurate is the estimate?
Between about 4% and 12% — the range covering most real investment questions — the rule lands within a few months of the truth; it overestimates at very low rates and undershoots at high ones. If a decision actually hinges on the difference, use the exact figure this calculator computes. The table below shows the drift at each rate, and the guide article's accuracy section explains why it moves the way it does:
| Annual return | Rule of 72 (years) | Exact (years) | Error |
|---|---|---|---|
| 1% | 72.00 | 69.66 | + 2.34 |
| 2% | 36.00 | 35.00 | + 1.00 |
| 4% | 18.00 | 17.67 | + 0.33 |
| 7% | 10.29 | 10.24 | + 0.05 |
| 10% | 7.20 | 7.27 | -0.07 |
| 15% | 4.80 | 4.96 | -0.16 |
| 20% | 3.60 | 3.80 | -0.20 |
What should you do with a doubling time?
Count the doublings you have left. A 30-year-old investing until 65 at 7% has time for roughly three and a half doublings; each dollar invested today can become about ten. Wait until 45 and you get two doublings — each dollar becomes four. That arithmetic, more than any chart, is why starting early dominates nearly every other choice: delay doesn't shave a little off the end, it deletes your largest doubling. The Rule of 72 turns that from an abstract exponential into something you can calculate while the coffee brews.
Solve for any variable with Goal Mode
This page solves for one thing: how fast money doubles at a given rate. CompoundFX's Goal Mode runs the question in any direction — the return you'd need, the years it takes, the deposit to start with, or the monthly amount to add.
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