Is it permissible for a person to buy a car for his brother with a cash payment at a certain price, then sell it to him in installments at a higher price, provided that the car remains registered in the name of the first buyer until the full price is paid, and the second buyer bears its operational and maintenance costs, and in case of his default, the car is appraised or sold, and the agreed-upon amount is recovered? And what is the correct legitimate formula if there are errors?

This transaction is permissible in the form of a Murabaha sale to a party who promises to purchase. The questioner first buys the car, then sells it to its owner with a known profit and on deferred payment terms. The car immediately becomes the property of the buyer, and its costs are borne by him, while the price remains a debt on his liability. It is not permissible for the seller to retain ownership of the car, but it is permissible to mortgage it as security for the price. In case of non-payment of installments, the seller has the right to sell the collateral with the mortgagor's permission.

There is another permissible formula, which is lease-to-own (Ijarah Muntahia bi al-Tameek), where the car remains the property of the lessor, and non-operational maintenance costs are his responsibility.