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:
“Fervor is the weapon of choice of the impotent.”
—Frantz Fanon (1925–1961)
“Once women begin to question the inevitability of their subordination and to reject the conventions formerly associated with it, they can no longer retreat to the safety of those conventions. The woman who rejects the stereotype of feminine weakness and dependence can no longer find much comfort in the cliché that all men are beasts. She has no choice except to believe, on the contrary, that men are human beings, and she finds it hard to forgive them when they act like animals.”
—Christopher Lasch (b. 1932)
“School days, school days; dear old golden rule days.
Readin’ and ‘ritin’ and ‘rithmetic; taught to the tune of a hick’ry stick.”
—Will D. Cobb (1876–1930)