Is zakat obligatory on the sum of 80,0 Saudi Riyals, which the questioner took as a loan from his wife, to be repaid to her in easy installments? If it is obligatory, how is it calculated, taking into consideration that he will continue to borrow from her?

Zakat is not obligatory for the wife regarding your debt to her if you are in hardship. If you repay it, she should pay Zakat on it for one year. However, if you are able to repay and she voluntarily defers it, then Zakat becomes obligatory upon her every year. If you are unable to repay except in installments, and if she possesses the nisab (minimum amount subject to Zakat), she should pay Zakat on each installment she receives. If she does not possess the nisab, she should pay Zakat on the installments that reach the nisab.