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| Re: rule of 72 |
| Posted by: Ed |
| Date: June 16, 2005 11:17:23 PM |
| It's a quick way to approximately compute how fast your money will double without a calculator. Example: you're earning 8% on your money in an investment. You can divide 72 by 8, the result is 9. In approximately 9 years your money/investment will double if the rate of return is 8% per year for 9 years. Obviously this doesn't work if the rate is variable, or if in one year the return is 12% and another is 4% because of compounding. |
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| Re: rule of 72 |
| Posted by: REL |
| Date: June 18, 2005 12:09:23 PM |
| The Rule of 72 says that dividing the number 72 by the interest rate (in percent) gives you the number of years it takes to double an amount that is invested at that rate and, likewise, dividing 72 by the number of years you during which you want to double your money gives you the interest rate you need in order to accomplish the doubling.
As an example of the application of the Rule of 72, suppose that you invest an amount at an annual interest rate of 6 percent, compounded monthly. How long will it take to double your money? Dividing 72 by 6 gives the answer that it will take 12 years.
Now suppose that we want to have our money double in 10 years. What interest rate is required to do this? Dividing 72 by 10 gives the answer that it will require and interest rate of 7.2 percent.
Finally, the formula can be applied more than once in order to get information about longer periods of time. If we know that it takes 12 years to double our money at a 6 percent interest rate, we then know that it will double again in another 12 years. In other words, in 24 years the amount will have quadrupled. And, it will have doubled again in another 12 years, giving us 8 times the original amount at the end of 36 years, and doubled again in another 12 years, giving us 16 times our original investment in 48 years. From this, you see again the power of compounding.
The Rule of 72 and various other rules can be derived from the equation for calculating compound interest that you have likely seen at some time in your life. That formula is
T = P ( 1 +I / N ) YN
where
P = original principal amount
I = annual interest rate (in decimal form)
N = number of compounding periods per year
Y = number of years
T = total of principal and interest to date (after n compounding periods)
You may also have met the binomial expansion formula in high school algebra. Expanding the above compound interest formula using the expansion formula and retaining only the most significant terms leads one to the rule of 72. The rule is most accurate for small interest rates, say 12 percent or less, with accuracy deteriorating with increasing rates. |
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