F1 Confusion: Completing I-20 Course, 60 day grace, 5 month rule

[Alex3344 10]

So I'm a bit (or a lot) confused.  I will finish my program in a few weeks, the same date as my current I-20 ends.  I plan to continue taking the next offering of my current course at the same school, but that is not until July.  I would like to back to my home country in between the end of this course (beginning of March) and the start of the next one (early July).  

 

The Immigration office at my school says I have 60 days to leave the country (the grace period), but that I have to apply for a new I-20, pay the SEVIS fee again, and then can return within 30 days of the new course start date.  Generally that plan is fine with me.  But the office did not know if I would also need a new visa.  Also, they don't know about the 5 month rule (see here: https://studyinthestates.dhs.gov/2015/01/what-is-the-five-month-rule).  So my confidence in their recommendations is a little shaky.

 

If I read that last link correctly, I am not out of status because my I-20 would not be terminated for more than 5 months, and I will not have spent more than 5 months out of the US.  So I guess the questions are:

 

- Do I need a new I-20?

- Can an I-20 be extended to cover an additional course after completing a previous course?

- Do I need to apply for a new visa?  (I hope not!)

- Is the immigration office right that I need a new I-20 and pay the SEVIS fee again?  I was told by another school that I can just continue and the school will just update the I-20 end date, or something like that.  

 

Hopefully that makes sense what I am trying to figure out - I'm a bit confused as well.  Thanks as always!