Question 255701
Remember that the equation for compound interest is:

{{{A = P(1 + r/n)^(nt)}}}

Here, P = 1000, r = 0.05, A = 2000 (initial amount doubled) and n = 2.  So we have:

{{{2000 = 1000(1 + 0.05/2)^(2t)}}} 

Dividing both sides by 1000 gives

{{{2 = (1.025)^(2t)}}}

Now we take the log of both sides in order to get the exponent down:

{{{log(2) = 2tlog(1.025)}}}

Divide both sides by log(1.025):

{{{log(2)/log(1.025) = 2t}}}

Last, divide both sides by 2:

{{{log(2)/(2log(1.025)) = t}}}

Using the calculator we have t = 14.04 years.