OPT Grace period

[f1visaholder]

Hi,

I had graduated(MBA degree) in April last year and my school DSO had set the start date of Jun when the OPT was applied. It was approved and my OPT expires in Jun 2013. Now if i want to get back to the school can i use the 60 day grace period and start attending the classes in Fall ( August) semester.

Should the start date of the classes be within the 60 day grace period OR Is it OK if the start date of the new I-20 is within the 60 day grace period.

Let's say my opt expires on Jun 15th and i get my new I-20 start date be on August 10th and start date of the classes to be on August 20th. Would that be fine?

Thanks in advance