• A = final amount after t years
• P = deposit amount
• r = annual interest rate in decimal form
• n = number of times the money is compounded per year
• t = number of years

• A = 4000 (we want the deposit of 2000 to double to 4000)
• P = 2000
• r = 0.04
• n = 12 (compounding 12 times a year; aka compounding monthly)
• t = unknown, which we'll be solving for

Since this refers to DOUBLING, the initial amount is never needed, as the formula is always: 
This gives us:  ------ Substituting .04 for i (interest), and 12 for m (annual compounding periods)
              ----- Converting to LOGARITHMIC form
Time it'll take to double, or  
However, since this investment is being compounded MONTHLY, you need to ROUND UP to the next month, which is month 5. 
So, correct answer should be 17 years, 5 months.

A QUICKER method is to use the Rule of 69.3. This rule is MOST PRECISE for interest rates below 6%. From 6% - 10%, the MOST PRECISE
is the Rule of 72. Depending on the interest rate, other rules (Rule of 70 & 78) can be used to get the most accurate time-estimate. 

Using the Rule of 69.3, we get: i (in percent form) * time (in years) = 69.3
                                                                   4t = 69.3 ------- Substituting 4 for interest rate
                                          Time taken to double, or .

                                               See how precise the Rule of 69.3 is as a time-predictor?