HOW TO create a Gmail filter to automatically delete emails Older than X amount of days
Let's say you want to AUTOMATICALLY delete all "Promotional" emails from your Gmail after 90 days.
Step 1:
Go to Settings -> Filters -> Create a new filter
Step 2:
Type the following into "Has the words" field:
category:promotions older_than:90d
Step 3:
Click "Create filter with this search"
Step 4:
Select "Delete it" and finally click "Create filter" button...
And... we're done!
The key here is older_than:90d, you can just as easily create whatever time-based filter you want with that.