Question 436823
<pre>
How long does it take $875 to double if it is invested at 8% compounded monthly?

Future value of $1 formula: {{{A = P(1 + i/m)^(mt))}}}

Doesn't matter what P is, A will ALWAYS be 2 (DOUBLE). 
So, substituting 2 for A (Accumulated amount/Future Value), 1 for P (Principal, or Initial Investment/Amount), .08 for
i (interest rate, as a percent/decimal), 12 for m (number of annual coumpounding periods), t (time, in years) is UNKNOWN.

With that, {{{A = P(1 + i/m)^(mt))}}} now becomes: 
           {{{2 = (1 + .08/12)^(12t))}}} 
           {{{2 = (1 + .02/3)^(12t))}}}
           {{{2 = ((3 + .02)/3)^(12t))}}}
           {{{2 = (3.02/3)^(12t))}}}
         {{{12t = log((3.02/3), (2)))}}} ----- Converting to LOGARITHMIC form
  Time, or {{{t = (log((3.02/3), (2))/12)}}}, or approximately 8.693189 years, or 8 years, 8.3183 months, or 104.3183 months. 
This amount is then ROUNDED to a time of 105 months, or 8 years, and 9 months.

As stated by Tutor @IKLEYN, the 8.3183 years, or 104.3813 months MUST be ROUNDED UP to the next INTEGER, which is 105.

Note that at the 104th-month, or 8-year, 8-month juncture, the amount will NOT have doubled. One has to wait until the 105th
month to see the invested amount DOUBLE.</pre>