Tenant gave Notice but now wants to Stay

[Demetri T.]

A little less than a month ago my tenant gave me notice that they would be out by the 31st of this Month, it is now the 25th.  Today they let me know that their financing isn't going well and they need at least 7 more days and may be staying much longer if their financing for the new house falls apart.

The problems with this is that this is a tenant I inherited and haven't raised the rent up to market levels (but I did raise it on them).  The units are very popular in my college town and I have been able to get significantly increased rent and I actually just accepted and processed an application for new tenants to start on the 4th.  We did not enter into a new lease agreement yet with the "new tenants" but we have talked about move in dates and deposits and prorated stuff. I can figure out the new tenants- I have some storage on site at the worst and another place they can stay - but I dont think it will be an issue. 

What are my options with the "old" tenants?  I don't mind them staying those extra 7 days but I would really like the extra $200/m I was going to get with no turnover.  

I am not sure I got ahead of myself- I was just planning ahead- didnt expect this.