My question involves landlord-tenant law in the State of: NYC

I have a rent agreement with my tenant because he is always late by a week or more so he signed agreement .I want my rent on first of no later than the fifth he pays $1,500.00 a month if it is after the 5th it is $15.00 a day till rent is paid in full he has tried to pay a small portion thinking that since he paid something toward it I wont charge late fee but he would give me the rest of rent 2 weeks later any way now he states he can't pay his rent this month and he will pay next month he will be a month behind I want to know since he sign this agreement dose he have to pay me late charge for almost the whole month? and if he doesn't give me two months rent plus this months late charge am. I able to charge him late fee till he has caught up on all the rent he owes me? if not how soon should I give him eviction notice and how long does he have to get out ? thank you jam1120