tenant moving out mid month but does want to pay full month rent

[Jimmy S.]

I have a tenant who just gave 60 day notice on nov. 22 and they are on a month to month lease with 60 notice required. They have been there for 3 years. They send me a letter saying they are giving 60 days notice on nov. 22 and will be moving out by jan. 22 but will only be paying part of January rent since they will not be there the whole month.

Its a month to month lease so I would imagine they would need to pay the whole month of January rent.

How would you handle this? Should I just wait till they are gone and then take the unpaid amount from the security deposit if it sits vacant those days?

Thanks