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The short answer is yes, you would have completed 28 years of life at 11:55 am on January 14, 2016 (Happy birthday, if that is your actual birthdate!).
The longer answer depends on how picky you wish to be about things like leap years, leap seconds, and how one wishes to define one year.
One definition of a "year" is 365 periods of 24 hours. If one wanted to be strict about this, you would have completed 28 full "years" a week prior to January 14th, due to the seven leap years that have occurred between January 14, 1988 and January 14, 2016.
Another definition of a "year" is the time that it takes for the Earth to complete one revolution of the Sun and return to its "starting point" in its orbit. This period is approximately equal to 365.25 days. After four years that additional 0.25 days per year adds up to a full day, which is why we have a Leap Day every four years (with some exceptions).
There are also occasional "leap seconds" added to make small adjustments to the current time.
Thus, the "exact" time depends on how one defines a year, and how one wishes to treat the various adjustments.
From a civil/legal perspective though, you would have been considered to turn 28 at the stroke of midnight between the 13th and the 14th of January, without regard to the exact time of your birth on that day, or any of the various adjustments made to the calendar during those years.
I hope this helps. Please feel free to ask if you have any additional questions about this.
Well, that's part of the problem. How does one define that "moment"? Is it the passage of a certain number of hours/minutes/seconds? Or is it when the Earth returns to that same position in space? An argument could be made for either definition, so what really matters here is how YOU want to define it.
Ok, in that case, we are talking about the "sidereal year", which is the time required for the Earth to return to the same position relative to a fixed frame of reference. The length of that year is 365.25636 days.
28 sidereal years is then 28 * 365.25636 = 10,227.17808 days, or 10,277 days, 4 hours, 16 minutes, and 26 seconds.
Adding this number of days/hours/minutes/seconds to the birth time of 11:55 am on January 14, 1988, the 28th return of the Earth to the same position would be at 4:11 (and 26 seconds) PM on January 14th, 2016.
Note that you do not have to account for leap years in this case, as the leap day added to the calendar during a leap year is intended to help the "regular" calendar "keep up" with this sidereal year. If we didn't add in the leap day, then the seasons would slowly migrate through the calendar months.
In that case, we would define a year as 365 days of 24 hours each. This is a "civil" definition of a year, and is not exactly related to the movement of the Earth. It is a value that is rounded off for convenience for civil purposes (which is not an uncommon practice in many areas, because perfection is often not worth the effort or expense). Again, this rounding off is the reason why we have leap years. The leap day corrects for the sloppiness in rounding a year off to just 365 days.
28 full years under this definition would be 28 years * 365 days per year = 10220 days.
Adding this number of days to the birthdate of 11:55 am on January 14, 1988 would give 11:55 am January 7, 2016 as the date of the 28th anniversary.
What I meant by that is that as far as any legal consideration would be concerned, you would "turn 28" at the moment that the calendar date changed from the 13th to the 14th.
For instance, if the drinking age is 21 years, you would be considered to have attained that age in the first minute of the calendar date of your birth, even if you were actually born very late in the day. So, if you happened to be born just before the stroke of midnight at the end of your birthday, you would be considered to turn 21 at the beginning of the day. You would technically be almost a full day short of actually being "21 years old" in terms of elapsed time, but it would be close enough for civil purposes.
I can't really say which one is more "accurate" as there is no agreed-upon standard for what would be considered "correct".
I would tend to think of the sidereal calculation (the one that came up with 4 pm-ish on January 14th) as being more meaningful, since it relates the return of the Earth to the same starting position that it occupied at the time of birth. This is really an arbitrary method of measurement, but at least it's based on something real and measurable.
The civil calculation is rounded off to such a degree that while it may be "correct", I think that most people would balk at the idea that their "28th birthday" falls on a day that is a week before the usual date on the calendar. Socially, we are too accustomed to having our birthday recognized on the same calendar day each year to allow for that.
I hope this helps.
You're quite welcome. :)