Is it permissible to purchase a car through a loan from a commercial bank that pays its price directly to the dealership, and the bank collects the amount from the buyer in installments without any increase to the advertised price, apart from a small sum for administrative fees, knowing that the amount the bank pays to the dealership is less than the advertised price, and that late payment does not result in an increase?

This transaction is an interest-based loan (riba) because the bank lends the questioner the price of the car with an increase (the bank pays the dealership 950 and takes 50). This is an amount of riba that the customer will pay to the bank in installments, and it is not a goodly loan (qard hasan). Therefore, it is not permissible to enter into this transaction, whether there is a condition for increasing the amount upon delay or not.