Hi lookinforhelp,
If this is your last month, you absolutely do not have to pay for it again! And you should know that a lot of landlords do not refund the deposit money, even though they are supposed to. They get away with it by claiming that the apartment sustained damage (even if it is a lie) and the money needs to be used to fix that damage.
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Thank you!
Although you do not have to give notice, it is the courteous thing to do, and it will help you if he tries to claim that you did not move out at when you did. Since you do not have to give notice, you do not have to put it in writing, but it can't hurt to do so, because, again, it can help to prove that you moved out when you said you did.
Yes, it does matter if you leave a couple of days later than the end of the rental term. Technically, if you remain even one day past the end of the rental term, you are liable for the next month's rent - in your case, it would mean that he would not have to refund your deposit.
Attorney
Admitted NYS Bar, member ABA, NYSBA, NYCBA, QCBA, Licensed Real Estate Broker