Is it permissible to purchase a car in installments from an Islamic bank that owns the car in its showroom, with the bank calculating 3% "interest" annually on the remaining amount, and adding a 100 dirham late payment fine that goes to charities? And does this transaction fall under usury (riba)?

It is permissible to purchase a car via murabahah from a bank if the car is in the bank's possession and under its guarantee. The mentioned profits are not usury (riba). Similarly, there is no objection to deferring the price over several years and the profit increasing with the length of the period, as long as the price is agreed upon in the contract, for time has a share in the price. However, imposing a penalty for late payment is forbidden and void, even if it is donated to charities, because it is usury. It is not permissible to agree to this condition or enter into a contract that includes it except out of a genuine need, while being careful to adhere to the payment schedule to avoid paying the penalty.