Doubling Time and Half-Life

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Calculate

Example: an investment returning 6% a year. In how many years does the money double? Enter a negative rate, such as −10%, to get the half-life: the time to fall by half. Change the value to work out your own case.

Rate per period r (%) Negative: time to halve.

Step by step

What each term means

Doubling Time (T): How many periods until the value doubles. It doesn't depend on the starting value: from 100 to 200 takes as long as from 1,000 to 2,000.
Log of 2 (ln 2 ≈ 0.693): The target: doubling. To triple, it would be ln 3; to halve, ln ½, and T becomes the half-life.
Log of the Factor (ln(1 + r)): How much the value grows per period, on the log scale. For small rates, ln(1 + r) ≈ r, which gives the rule of 70: T ≈ 70 / r%.