Question 725039
The interest rates are usually given for year-periods.  The 2% interest rate for the year is 2/12 % per month, or 0.1667% per month or 0.001667 as decimal fraction (given to four significant figures, since 1/6 is a repeating decimal).


The compounding is monthly, as given in your description.

Balance is {{{highlight(1000*(1.001667)^t)}}}, where {{{t}}} is count of months.  


When will the original deposited principle double?  How many months?
{{{2000=1000(1.001667)^t}}}
{{{2=1.001667^t}}}
Next, you can choose either base 10 or Natural for taking logarithms of both side.  I will use base 10:
{{{log(10,2)=log(10,1.001667^t)}}}
{{{log(10,2)=t*log(10,1.001667)}}}
{{{t=log(10,2)/log(10,1.001667)}}}
{{{highlight(t=416)}}} months, almost 35 years.