Correct Option (D)

To determine when a calendar repeats, one must calculate the cumulative sum of "odd days" from the reference year until the sum becomes a multiple of 7 (or 0 odd days). An ordinary year has 1 odd day (365 days = 52 weeks + 1 day), and a leap year has 2 odd days (366 days = 52 weeks + 2 days).

Let's calculate the odd days starting from 2009:

Year 2009 (Ordinary year): 1 odd day
Year 2010 (Ordinary year): 1 odd day
Year 2011 (Ordinary year): 1 odd day
Year 2012 (Leap year): 2 odd days
Year 2013 (Ordinary year): 1 odd day
Year 2014 (Ordinary year): 1 odd day

The cumulative sum of odd days up to the end of 2014 is 1 + 1 + 1 + 2 + 1 + 1 = 7 odd days.

Since the sum is 7, which is equivalent to 0 odd days (7 mod 7 = 0), the calendar for the year immediately following 2014, which is 2015, will be identical to the calendar of 2009.

Incorrect Options:

The years 2018, 2017, and 2016 are incorrect because the cumulative sum of odd days from 2009 to the end of the year preceding each of these options does not result in a multiple of 7. A calendar repetition only occurs when the net odd days accumulated become zero, indicating that the starting day of the week for the subsequent year will be the same as the reference year.