Is Zakat obligatory on a sum of 4500 Jordanian Dinars lent to a brother against a car used as collateral for the debt, and if obligatory, what is its amount?

You are not obliged to pay zakat on the mortgaged car because it is not your property; rather, it belongs to your brother. Your brother is not obliged to pay zakat on it unless the car is part of trade goods. What is obligatory upon you is to pay zakat on the amount you lent to your brother.