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)
“European society has always been divided into classes in a way that American society never has been. A European writer considers himself to be part of an old and honorable tradition—of intellectual activity, of letters—and his choice of a vocation does not cause him any uneasy wonder as to whether or not it will cost him all his friends. But this tradition does not exist in America.”
—James Baldwin (1924–1987)
““Reason is an exception in me, too,” said Zarathustra: “Chaos and necessity and spinning stars—that is also the rule in the wisest world.””
—Friedrich Nietzsche (1844–1900)