What is the Islamic legal ruling on a family cooperative fund investing its money in purchasing goods and then selling them to members in installments at an increased price, or lending them cash loans in exchange for a fixed administrative fee?

It is permissible to establish a cooperative fund with Sharia-compliant controls, and to sell goods in installments at a higher price (Murabaha for the one who commands the purchase) is permissible. As for lending with the payment of fixed fees exceeding the principal amount of the loan, it is not permissible because it is usury (riba).