How long until your money doubles? Get the exact answer for any growth rate, and see how close the famous Rule of 72 shortcut comes.
Doubling means (1 + r)t = 2. Solve for t and you get:
Here’s the shortcut you can do in your head: divide 72 by the growth rate.
At 8%, that’s 9 years, which is very close to the real 9.01. Keep in mind it’s an estimate. It works best between about 6% and 10% and drifts further off at very low or very high rates. When precision matters, use the exact answer above.
| Yearly rate | Exact | Rule of 72 | Difference |
|---|---|---|---|
| 1% | 69.66 yrs | 72.00 yrs | +2.34 |
| 2% | 35.00 yrs | 36.00 yrs | +1.00 |
| 3% | 23.45 yrs | 24.00 yrs | +0.55 |
| 4% | 17.67 yrs | 18.00 yrs | +0.33 |
| 5% | 14.21 yrs | 14.40 yrs | +0.19 |
| 6% | 11.90 yrs | 12.00 yrs | +0.10 |
| 7% | 10.24 yrs | 10.29 yrs | +0.04 |
| 8% | 9.01 yrs | 9.00 yrs | −0.01 |
| 9% | 8.04 yrs | 8.00 yrs | −0.04 |
| 10% | 7.27 yrs | 7.20 yrs | −0.07 |
| 12% | 6.12 yrs | 6.00 yrs | −0.12 |
| 15% | 4.96 yrs | 4.80 yrs | −0.16 |
| 20% | 3.80 yrs | 3.60 yrs | −0.20 |
| 25% | 3.11 yrs | 2.88 yrs | −0.23 |
| 30% | 2.64 yrs | 2.40 yrs | −0.24 |
| 50% | 1.71 yrs | 1.44 yrs | −0.27 |
The “true” number for small rates is about 69.3. Bumping it up to 72 makes the rule more accurate at the rates people usually care about, and 72 divides evenly by lots of handy numbers (2, 3, 4, 6, 8, 9 and 12). That makes the mental math easy.
No, it’s a shortcut. It slightly overestimates the time at low rates and underestimates it at high ones. The reference table above shows you exactly how far off it is.
Those versions work better for very low rates or continuous compounding. Since the exact formula is right here, you don’t really need to choose a rule at all.
Absolutely. Anything growing by a steady percentage works. At 3% inflation, prices double in about 23.45 years.
Something that shrinks every year will never double. The calculator tells you how long it would take to lose half its value instead.