My Lease is Ending in 20 Days But I need to Give 60 Days Notice?

[John Ashby]

I already signed a lease with the apartment complex I want to move to. I move in there in 2 weeks. In 3 weeks my current lease expires. I gave them notice and I expected to have to pay for an entire month's rent from today's date, instead of just 3 weeks, but they're claiming I need to pay 60 days with of rent at the month to month price from today's date.

Is this legal? How can a contact be binding after it ends? At this rate I might as well wait until the contract expires, then give notice, then I only have to pay 30 days because it is month to month.