All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We have already issued Fatwa 81303 clarifying that it is not permissible to pay Zakat money to schools or for building mosques, so please refer to it. Zakat can only be paid to the eight kinds of people whom Allaah has specified. Allaah Says (what means): {As-Sadaqaat (here it means Zakat) are only for the poor, and for the needy, and for those employed to collect (the funds); and for attracting the hearts of those who have been inclined (towards Islam); and to free the captives; and for those in debt; and for Allaah's Cause (i.e. for those fighting in the holy wars), and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allaah. And Allaah is All-Knower, All-Wise.}[Quran 9:60].
For more benefit and details on these eight kinds of people please refer to Fataawa 88368 and 86546.
In our view you are not acquitted by paying the Zakat to the school which you mentioned, and you are obliged to pay the Zakat for those four years to the people who are eligible for it.
Allaah Knows best.