# Double your money with the rule of 72

September 10, 2018

The Rule of 72 is a simple rule of thumb for calculating how long it will take an investment to double in value. This, and other tricks of mental math, can help families figure out how to reach their college savings goals.

## How to use the rule of 72

To use the Rule of 72, divide 72 by the interest rate to determine how long it will take your investment to double in value, based on the power of compound interest.

For example, you can estimate the doubling time for a lump sum investment in a 529 plan earning a 6 percent return on investment at about 12 years, by dividing 72 by 6. In contrast, a bank CD earning 3 percent interest will take 24 years to double in value.

Conversely, you can determine the interest rate required to double the value of an investment in a specified number of years by dividing 72 by the investment term. For example, to double an investment in 8 years, you will need an interest rate of about 9 percent, the result of dividing 72 by 8.

## 72 has many factors

The Rule of 72 works well because the number 72 has many factors, including 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Variations on the Rule of 72, such as the Rule of 70, don’t work as well because they have fewer factors. The number 70 has about half as many factors, namely 1, 2, 5, 7, 10, 14, 35 and 70. The Rule of 69, which assumes daily compounding instead of annual compounding, has only four factors, 1, 3, 23 and 69.

## Accuracy of the rule of 72

The Rule of 72 is most accurate for 8 percent and 9 years. The further away one gets from these numbers, the greater the error. For example, the doubling time for a 1 percent interest rate is 69.7 years, not 72 years, and the doubling time for 2 percent is 35 years, not 36 years. But, in practice, the Rule of 72 is good enough.

## Similar rules of thumb

If you want to quadruple your money, just double the Rule of 72 to obtain the Rule of 144.

If you want to triple your money, use the Rule of 120.

To derive these rules, calculate the product of 100 and the natural logarithm of the exponent, and then look for a whole number with many factors at or above that result. For example:

·        The product of the interest rate and doubling time is about 100 * ln(2) = 69.3, yielding the Rule of 69, Rule of 70 and Rule of 72.

·        The product of the interest rate and tripling time is about 100 * ln(3) = 109.9, yielding the Rule of 110 and the Rule of 120.

·        The product of the interest rate and quadrupling time is about 100 * ln(4) = 138.6, yielding the Rule of 144.

·        The product of the interest rate and quintupling time is about 100 * ln(5) = 160.9, yielding the Rule of 160.

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