Is Zakat obligatory on an amount of $50,0, given a debt of $150,0, no income, and old age?

Borrowing with usury is one of the gravest sins, and repentance from it is obligatory unless there is a permissible excuse. The basic principle is that Zakat (definition) is due on wealth every year. Scholars have differed regarding deducting debt from Zakat-able wealth if it depletes the wealth or reduces it below the nisab (definition). The more cautious approach is not to deduct it. It is obligatory to pay Zakat on wealth, and if you are in need of sustenance, it becomes obligatory upon your children.