You should consult with an attorney about these issues, as owner-occupied premises do have special considerations under New Jersey Law. That being said, I'm unaware of any section of the Rent Security Deposit Act which permits an owner-occupier to either not deposit the security deposit in a properly-chartered bank, or excuses the her from providing tenants with written notice of where the money is deposited.
As far as late charges or other arrears go, your LL's going to have to prove the losses and you may be able to argue he waived late fees by ratification if there's been sufficient time.
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I agree with Mr. Keppler. Your LL was supposed to deposit the funds and you were entitled to interest on your money. Further, your LL was required to apply your deposit to the outstanding rent. As for the late fees, the LL will be required to prove that same are called for in the lease and that you infect paid the rent late. Good luck.
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I agree with the other two counsel. While the LL may be exempt from some provisions of the anti eviction act, he needs to comply with the rent security act. You are entitled to have the security applied to the rent. He has waived his right to late fees by accepting the rent.