Here’s two ways to calculate how long it will take to double your money based on a certain annual percentage return. The first is a quick, rough calculation you can do in your head. The second “real” calculation requires a calculator or spreadsheet.
The first is the “rule of 72” – a simple rule of thumb to help you determine how fast your investments will double in value at certain rates of return.
Simply divide 72 by the presumed growth rate to get a rough idea on how long it will take for your money to double.
For example, an investment growing at 7.2% a year would double in 10 years.
At 8% growth, it would take 9 years to double your investment.
However, this “rule of thumb” is not 100% correct. It may make it easier to figure out in your head, but is not exactly accurate.
So if you want to be 100% exact, here’s how you do it in excel:
Where ln is natural log and rate is the percent in decimal form (so 1% would be 0.01, 2% is 0.02 etc).
So, at 8% it would take your investment:
Or 9.01 Years to double in value.
So our “rule of 72” was pretty much right on here. However as percentages get small or large, the quick thumb rule does not yield as accurate of a result.
How different of a result do these two ways of calculating how long it will take to double your money give? Consider the table below:
| Rate | Real | “Rule of 72” |
| 1% | 69.66 | 72.00 |
| 1.25% | 55.80 | 57.60 |
| 1.50% | 46.56 | 48.00 |
| 1.75% | 39.95 | 41.14 |
| 2.00% | 35.00 | 36.00 |
| 2.25% | 31.15 | 32.00 |
| 2.50% | 28.07 | 28.80 |
| 2.75% | 25.55 | 26.18 |
| 3.00% | 23.45 | 24.00 |
| 3.25% | 21.67 | 22.15 |
| 3.50% | 20.15 | 20.57 |
| 3.75% | 18.83 | 19.20 |
| 4.00% | 17.67 | 18.00 |
| 4.25% | 16.65 | 16.94 |
| 4.50% | 15.75 | 16.00 |
| 4.75% | 14.94 | 15.16 |
| 5.00% | 14.21 | 14.40 |
| 5.25% | 13.55 | 13.71 |
| 5.50% | 12.95 | 13.09 |
| 5.75% | 12.40 | 12.52 |
| 6.00% | 11.90 | 12.00 |
| 6.25% | 11.43 | 11.52 |
| 6.50% | 11.01 | 11.08 |
| 6.75% | 10.61 | 10.67 |
| 7.00% | 10.24 | 10.29 |
| 7.25% | 9.90 | 9.93 |
| 7.50% | 9.58 | 9.60 |
| 7.75% | 9.29 | 9.29 |
| 8.00% | 9.01 | 9.00 |
| 8.25% | 8.74 | 8.73 |
| 8.50% | 8.50 | 8.47 |
| 8.75% | 8.26 | 8.23 |
| 9.00% | 8.04 | 8.00 |
| 9.25% | 7.83 | 7.78 |
| 9.50% | 7.64 | 7.58 |
| 9.75% | 7.45 | 7.38 |
| 10.00% | 7.27 | 7.20 |
| 10.25% | 7.10 | 7.02 |
| 10.50% | 6.94 | 6.86 |
| 10.75% | 6.79 | 6.70 |
| 11.00% | 6.64 | 6.55 |
| 11.25% | 6.50 | 6.40 |
| 11.50% | 6.37 | 6.26 |
| 11.75% | 6.24 | 6.13 |
| 12.00% | 6.12 | 6.00 |
| 12.25% | 6.00 | 5.88 |
| 12.50% | 5.88 | 5.76 |
| 12.75% | 5.78 | 5.65 |
| 13.00% | 5.67 | 5.54 |
| 13.25% | 5.57 | 5.43 |
| 13.50% | 5.47 | 5.33 |
| 13.75% | 5.38 | 5.24 |
| 14.00% | 5.29 | 5.14 |
| 14.25% | 5.20 | 5.05 |
| 14.50% | 5.12 | 4.97 |
| 14.75% | 5.04 | 4.88 |
| 15.00% | 4.96 | 4.80 |
| 15.25% | 4.88 | 4.72 |
| 15.50% | 4.81 | 4.65 |
| 15.75% | 4.74 | 4.57 |
| 16.00% | 4.67 | 4.50 |
| 16.25% | 4.60 | 4.43 |
| 16.50% | 4.54 | 4.36 |
| 16.75% | 4.48 | 4.30 |
| 17.00% | 4.41 | 4.24 |
| 17.25% | 4.36 | 4.17 |
| 17.50% | 4.30 | 4.11 |
| 17.75% | 4.24 | 4.06 |
| 18.00% | 4.19 | 4.00 |
| 18.25% | 4.13 | 3.95 |
| 18.50% | 4.08 | 3.89 |
| 18.75% | 4.03 | 3.84 |
| 19.00% | 3.98 | 3.79 |
| 19.25% | 3.94 | 3.74 |
| 19.50% | 3.89 | 3.69 |
| 19.75% | 3.85 | 3.65 |
| 20.00% | 3.80 | 3.60 |
| 20.25% | 3.76 | 3.56 |
| 20.50% | 3.72 | 3.51 |
| 20.75% | 3.68 | 3.47 |
| 21.00% | 3.64 | 3.43 |
| 21.25% | 3.60 | 3.39 |
| 21.50% | 3.56 | 3.35 |
| 21.75% | 3.52 | 3.31 |
| 22.00% | 3.49 | 3.27 |
| 22.25% | 3.45 | 3.24 |
| 22.50% | 3.42 | 3.20 |
| 22.75% | 3.38 | 3.16 |
| 23.00% | 3.35 | 3.13 |
| 23.25% | 3.32 | 3.10 |
| 23.50% | 3.28 | 3.06 |
| 23.75% | 3.25 | 3.03 |
| 24.00% | 3.22 | 3.00 |
| 24.25% | 3.19 | 2.97 |
| 24.50% | 3.16 | 2.94 |
| 24.75% | 3.13 | 2.91 |
| 25.00% | 3.11 | 2.88 |
