Is it permissible to buy cars from the manufacturer by paying a certain installment, then receiving the car and paying the remaining installment, with a discount that increases the longer the delivery period, and a refund of the amount to the buyer plus 20% of the paid value if the deal is canceled before delivery?

If the intended transaction, for which accountability is sought, is a buyer's request to a factory to manufacture a specific car for delivery at a specified time, then this is a permissible manufacturing contract (Istisna') under certain conditions. These conditions include: the manufactured item must be precisely defined by a description that eliminates any ambiguity, a specific delivery date must be set, the contract must be binding on both parties, it is permissible to pay the price in advance or partially with the remainder deferred, and it is permissible to stipulate a penalty clause.

As for the transaction mentioned in the question, it is not permissible in Sharia due to the uncertainty regarding the delivery date and the price (the longer the term, the greater the discount). This is also because it involves a trick for financing or a usurious loan, as the buyer has the right to cancel the deal and receive a refund of the paid amount with a 20% increase, which makes the manufacturing company a borrower with an increase. Therefore, it is forbidden to enter into this transaction unless the aforementioned reasons for prohibition are removed.