Compound Interest: How long does it take to double your money?

If $$P$$ dollars are invested for one year, at a rate of interest $$i$$, it will accumulate to amount $$A$$ at the end of the year by the following equation:

How long does it take in years $$t$$ to double your principal $$P$$ with an interest rate of $$i$$ per annum?
$$!\log_e 2=t\log_e(1+i)$$

$$!t=\frac{\log_e 2}{\log_e(1+i)}\approx \frac{0.7}{i}$$

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