How this calculator works
With discrete compounding, each period multiplies the current amount by 1 + r. Continuous growth instead uses an exponential with rate r per period. Solving either model for a factor of two gives its doubling time. The starting amount changes the doubled amount but not the time, provided growth stays proportional and constant. The table samples growth through two doubling intervals, including fractional periods.
Formula
Compound: t = ln(2)/ln(1+r). Continuous: t = ln(2)/r. Reverse compound rate: r = 2^(1/t) - 1.
Worked example
At a compound rate of 100% per period, one period doubles any positive starting amount. At about 41.421356% per period, two periods double it because 1.41421356 squared is 2.
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Frequently asked questions
Is the rule of 72 used?
No. The logarithmic calculation is used. The rule of 72 is a convenient approximation when the entered rate is a small percentage.
Can a zero or negative rate double the amount?
A constant non-positive rate cannot double a positive amount in a positive time under these models.
Is the answer always a whole number of periods?
No. The exponential model interpolates between compounding dates. If changes happen only on discrete dates, round up to the next complete period for the first observed doubling.