# How to Use the Rule of 72

2-11-2016, 18:43
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The Rule of 72 is a handy tool used in finance to estimate the number of years it would take to double a sum of money through interest payments, given a particular interest rate. The rule can also estimate the annual interest rate required to double a sum of money in a specified number of years. The rule states that the interest rate multiplied by the time period required to double an amount of money is approximately equal to 72. The Rule of 72 is applicable in exponential growth, (as in compound interest) or in exponential "decay," as in the loss of purchasing power caused by monetary inflation.

### Exponential growth

1. Let R x T = 72, where R = the rate of growth (for example, the interest rate), T = doubling time (in years) (for example, the time it takes to double an amount of money).
2. Insert a value for R. For example, how long does it take to turn \$100 into \$200 at a yearly interest rate of 5%? Letting R = 5, we get 5 x T = 72.
3. Solve for the unknown variable. In this example, divide both sides of the above equation by R (that is, 5) to get T = 72 ÷ 5 = 14.4. So it takes 14.4 years to double \$100 to \$200 at an interest rate of 5% per annum. (The initial amount of money doesn't matter. It will take the same amount of time to double no matter what the beginning amount is.)
• How long does it take to double an amount of money at a rate of 10% per annum? Let 10 x T = 72, so that T = 7.2 years.
• How long does it take to turn \$100 into \$1600 at a rate of 7.2% per annum? Recognize that 100 must double four times to reach 1600 (\$100 → \$200, \$200 → \$400, \$400 → \$800, \$800 → \$1600). For each doubling, 7.2 x T = 72, so T = 10. So as each doubling takes ten years, the total time required (to multiply \$100 by 16) is 40 years.

### Estimating exponential "decay" (loss)

1. Estimate the time it would take to lose half of your money (or its purchasing power in the wake of inflation). Solve T = 72 ÷ R. This is the same equation as above, just slightly rearranged. You simply enter a value for R. For example:
• How long will it take for \$100 to assume the purchasing power of \$50, given an inflation rate of 5% per year?
• Let 5 x T = 72, so that T = 72 ÷ 5, meaning T = 14.4. That's how many years it would take for money to lose half its buying power in a period of 5% inflation.
2. Estimate the rate of decay (R) over a given time span: R = 72 ÷ T. Enter a value for T, and solve for R. For example:
• If the buying power of \$100 becomes worth only \$50 in ten years, what is the inflation rate during that time?
• R x 10 = 72, where T = 10. Then R = 72 ÷ 10 = 7.2%.
3. Ignore any unusual data. If you detect general trends, don't worry about numbers that are wildly out of range. Drop them from consideration.

## Tips

• The value of 72 was chosen as a convenient numerator in the above equation. 72 is easily divisible by several small numbers: 1,2,3,4,6,8,9, and 12. It provides a good approximation for annual compounding at typical rates (from 6% to 10%. The approximations are less exact at higher interest rates.
• Let the Rule of 72 work for you, by starting to save now. At a growth rate of 8% a year (the approximate rate of return in the stock market), you would double your money in nine years (72 ÷ 8 = 9), quadruple your money in 18 years, and have 16 times your money in 36 years.
• You can use Felix's Corollary to the Rule of 72 to calculate the "future value" of an annuity (that is, what the annuity's face value will be at a specified future time). You can read about the Corollary on various financial and investing websites.

## Warnings

• Don't let the rule of 72 work against you by taking on high-interest debt (as is typical with credit cards). At an average interest rate of 18%, credit card debt doubles in just four years (72 ÷ 18 = 4), quadruples in eight years, and never stops growing over time.
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