2009-08-01 by damo
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:
$$!A=P(1+i)$$
How long does it take in years $$t$$ to double your principal $$P$$ with an interest rate of $$i$$ per annum?
$$!2P=P(1+i)^t$$
$$!2=(1+i)^t$$
$$!\log_e 2=t\log_e(1+i)$$
$$!t=\frac{\log_e 2}{\log_e(1+i)}\approx \frac{0.7}{i}$$