What is the ruling on purchasing a car with a loan from a bank owned by the car manufacturing company, knowing that this bank deals exclusively with financing the sale of the company's cars?

If purchasing the car from a company owned by the bank is a condition in the loan contract, then this transaction is forbidden, due to the Prophet's (peace be upon him) prohibition of "a sale and a loan." A loan that brings benefit has been forbidden because it is a contract of benevolence, and the condition of benefit removes it from its original purpose. The combination of a loan and a sale has been forbidden because it is a means to usury.