if your lease doesn;t specify charges if you give lerss than a 60 day notice is it right for the apartment complex to charge you

Your rights are governed both by the written lease and Georgia law. If the lease requires 60 days notice and you give less, the courts pretty uniformly are going to uphold the lease (you agreed to it and it isn't against public policy) and require you to pay rent for the two months. Under Georgia law, the tenant typically has to give a minimum of one period of a periodic tenancy (whatever the tenancy is, i.e. week to week, you give one week, landlord must give two weeks notice to terminate. Here you are month to month but you contractually agreed to expand the requirement under the statute.

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