Choice of Rule
The value 72 is a convenient choice of numerator, since it has many small divisors: 1, 2, 3, 4, 6, 8, 9, and 12. It provides a good approximation for annual compounding, and for compounding at typical rates (from 6% to 10%). The approximations are less accurate at higher interest rates.
For continuous compounding, 69 gives accurate results for any rate. This is because ln(2) is about 69.3%; see derivation below. Since daily compounding is close enough to continuous compounding, for most purposes 69, 69.3 or 70 are better than 72 for daily compounding. For lower annual rates than those above, 69.3 would also be more accurate than 72.
| Rate | Actual Years | Rule of 72 | Rule of 70 | Rule of 69.3 | 72 adjusted | E-M rule |
|---|---|---|---|---|---|---|
| 0.25% | 277.605 | 288.000 | 280.000 | 277.200 | 277.667 | 277.547 |
| 0.5% | 138.976 | 144.000 | 140.000 | 138.600 | 139.000 | 138.947 |
| 1% | 69.661 | 72.000 | 70.000 | 69.300 | 69.667 | 69.648 |
| 2% | 35.003 | 36.000 | 35.000 | 34.650 | 35.000 | 35.000 |
| 3% | 23.450 | 24.000 | 23.333 | 23.100 | 23.444 | 23.452 |
| 4% | 17.673 | 18.000 | 17.500 | 17.325 | 17.667 | 17.679 |
| 5% | 14.207 | 14.400 | 14.000 | 13.860 | 14.200 | 14.215 |
| 6% | 11.896 | 12.000 | 11.667 | 11.550 | 11.889 | 11.907 |
| 7% | 10.245 | 10.286 | 10.000 | 9.900 | 10.238 | 10.259 |
| 8% | 9.006 | 9.000 | 8.750 | 8.663 | 9.000 | 9.023 |
| 9% | 8.043 | 8.000 | 7.778 | 7.700 | 8.037 | 8.062 |
| 10% | 7.273 | 7.200 | 7.000 | 6.930 | 7.267 | 7.295 |
| 11% | 6.642 | 6.545 | 6.364 | 6.300 | 6.636 | 6.667 |
| 12% | 6.116 | 6.000 | 5.833 | 5.775 | 6.111 | 6.144 |
| 15% | 4.959 | 4.800 | 4.667 | 4.620 | 4.956 | 4.995 |
| 18% | 4.188 | 4.000 | 3.889 | 3.850 | 4.185 | 4.231 |
| 20% | 3.802 | 3.600 | 3.500 | 3.465 | 3.800 | 3.850 |
| 25% | 3.106 | 2.880 | 2.800 | 2.772 | 3.107 | 3.168 |
| 30% | 2.642 | 2.400 | 2.333 | 2.310 | 2.644 | 2.718 |
| 40% | 2.060 | 1.800 | 1.750 | 1.733 | 2.067 | 2.166 |
| 50% | 1.710 | 1.440 | 1.400 | 1.386 | 1.720 | 1.848 |
| 60% | 1.475 | 1.200 | 1.167 | 1.155 | 1.489 | 1.650 |
| 70% | 1.306 | 1.029 | 1.000 | 0.990 | 1.324 | 1.523 |
Read more about this topic: Rule Of 72
Famous quotes containing the words choice of, choice and/or rule:
“The fondness or indifference that the philosophers expressed for life was merely a preference inspired by their self-love, and will no more bear reasoning upon than the relish of the palate or the choice of colors.”
—François, Duc De La Rochefoucauld (1613–1680)
“The style of an author should be the image of his mind, but the choice and command of language is the fruit of exercise.”
—Edward Gibbon (1737–1794)
“When great changes occur in history, when great principles are involved, as a rule the majority are wrong.”
—Eugene V. Debs (1855–1926)