Is zakat obligatory on a family cooperative fund spent on charitable acts such as marriage assistance, banquets, and help in solving problems, knowing that the money is not invested commercially and is collected annually at the beginning of every Hijri year?

If the money is allocated for specific purposes and its owners have relinquished ownership such that it cannot revert to them, then it is treated as an endowment (waqf) and no zakat is due on it. However, if it remains under the ownership of its proprietors, then zakat is due on it according to each person's share. So, whoever's share reaches the nisab (minimum threshold) (or reaches it by adding other money to it) must pay zakat, and whoever's share does not reach it is exempt.