What is the ruling on purchasing a car from an office that buys it in cash and registers it in its name, then sells it in installments to the prospective buyer, with the condition that the car remains registered in the office's name until all installments are paid, and the prospective buyer bears the costs of repairs and traffic violations during the installment period?

The transaction mentioned is a Murabahah (definition) sale for the one who commands the purchase (Murabahah lil Amireen bil Shiraa). This is permissible if the sale occurs after the commodity has entered the seller's possession and guarantee, and the number and amount of installments are specified without increasing the price for delayed payment. The Islamic Fiqh Academy has permitted this sale under certain conditions, including that the sale must take place after the commanded party has taken possession of the commodity and a legal قبض (qabd - seizure/taking possession) has occurred, and that the promise is binding religiously and legally in specific cases, and that the agreement is permissible with an option for both parties. As for the amount taken from the one who commands the purchase, it is part of the price if it is after the office has taken possession of and sold the car, or it is a earnest money deposit if it is before the purchase. The car remaining in the seller's name after its sale does not affect the validity of the sale; this falls under the category of mortgaging the sold item for its price, which is permissible.