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The Rule of 72

The Rule of 72 is a simplied rule to estimate the # of years to double the money you invest, here's the formula:

Years to double the money = 72 / Interest Rate

This formula is useful for financial estimates and understanding the nature of compound interest. Examples:

* At 6% interest, your money takes 72/6 or 12 years to double.

* To double your money in 10 years, get an interest rate of 72/10 or 7.2%.

Why "72" is so special?

The rule of 72 apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference;
69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible.

Why the rule of 72 is true?

The rule of 72 comes from a mathematics approximation, to be more exact, it comes from Taylor expansion for log function. It has very logic and rigious mathematics proof.