You need to insert a spreadsheet inside your Word document to realize your scenario (
Insert > Table > Excel Spreadsheet). Without the use of Excel, you can't use date formulas in MS Word. Anyway, you can use tables in order to be able to make use of some functions in MS Word. To do that, insert a new table, click inside a cell, go to
Table Tools > Layout > Data box, and click
Formula. A formula window opens and you can enter a formula by selecting a function from the list. In this list, there are only basic functions like
not, etc. You can actually type a date in a cell, and set another cell equal to that one, but the formula result cannot be displayed properly as you are just allowed to select one of the Number Formats which don't include any Date Formats. For more info on how to perform calculations in a table in MS Word, see this page.
I hope this helps.