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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
This fund is permissible and there is no harm in it, Allaah willing. Shaykh Ibn Baaz was asked about a group of teachers who, at the end of each month, collect an amount of money from their salaries and it is given to one of them. At the end of the second month, it is given to another, and so on, until all of them take their share. Some people call this Jam'iyyah. What is the religious ruling on such financial cooperatives?"
He answered, "There is no harm in that. It is considered a loan with no extra interests for any of the participants. The Council of Senior Scholars studied the matter and decided by a majority that such financial cooperatives are allowable given the benefits that they yield for all the participants with no harm incurred on any of them..." [Fataawa Islaamiyyah 2/413]
That the participant who collects the fund each month is chosen by draw is permissible, and there is no harm in that. Drawing lots is a lawful means in such matters.
Allaah knows best.