The correct answer is $\boxed{\text{D}}$.
A is regularly drawing Rs. 500 on the 16th of every month. This means that he is drawing interest on Rs. 6000 for 15 days every month. The interest for the total period will be 15 days * 12 months = 180 days. This is equal to $\frac{180}{365} = \boxed{{5}\frac{1}{2}}$ months.
Option A is incorrect because it is the number of months in a year. Option B is incorrect because it is the number of months in a year plus one month. Option C is incorrect because it is the number of months in a year plus two months.