If my leasing term is up, can I be charged a prorated amount for not giving the time of notice specified in the lease contract?

Question Details:

My lease stated that I must give a 60 day notice prior to moving out. I gave the notice about 15 days late (mid November), but before the lease term was up on the last day of last month. The lease states that if 60 days notice was not given, it would be assumed that the lease was to be renewed. The apartment complex is now trying to charge me a prorated amount for this month to account for 60 days from when I gave my notice. Is this legal?

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