In NewYork state,If you took a loan.and you are unable to pay back loan at time loan is agreed to pay back.Is establishedment able to charge additiona

Yes, within limits. It depends on who the creditor is and the nature of the loan. As a general matter, it is entirely possible to charge late fees and a post-default higher rate of interest. An attorney would need to review the specifics of your situation to opine on those facts.