How to add field for length of a specific membership type to Contact Summary page
This requires you write an extension.  I've written similar extensions to show the "original join date" on a contact summary screen.  If you haven't written PHP, you will probably want to hire someone to do this for you.

Your case is a little trickier, because it'll need to be updated once a..day? Month?  Whereas "original join date" only needs to be filled in once.  

Here's the basic approach:


Create a custom field to store the data.  Set it to view-only.
In your extension, define a new API.  When the API is called, it should make an API call to find the folks whose custom field will need updating.  If these folks are defined as a group/smart group, that will help!
Loop through each contact, using the API to query their memberships.
Take the earliest membership join date that applies and do your math, using PHP's date arithmetic functions.
Use the API to update the field that stores the data.
Define a scheduled job (Administer menu » System Settings » Scheduled Jobs) to run the scheduled job on the schedule of your choice.