Try this again. Do as a landlord charge someone who refuses to leave the entire month or by day until evicted?

Legally, you have the right to collect the entire month's rent, since your tenants failure to leave has kept you from getting another tenant in. It doesn't matter if they get out on the second, or stay until the 29th, by not being out on the first, they're responsible to pay. But if you don't want to give them a leg to stand on, don't accept any rent, other than for the actual time they'll be there.