filter by actual date

1) since you're using CALCULATE, you don't need the explicit FILTER

2) If you don't convert the literal string 1/1/2016 to a date by use of DATE() (e.g. DATE(2016,1,1)) then PowerBI interprets it as "1 divided by 1 divided by 2016", giving a number value that converts to Dec 30, 1899 (I believe - somewhere around there).  Try

ActiveByDate = calculate(
		countrows('Table A'),
		'Table A'[Period] > date(2016, 1, 1)  //or = or <, etc
)

Hope this helps.

David