What is the ruling on purchasing a car from an Islamic bank in Germany that buys it then sells it in installments, with a fixed profit margin determined beforehand, and this margin decreases as the repayment period increases?

If the bank owns the commodity and takes possession of it, then sells it in installments at a known price, this is permissible. An increase in price for installment payments by a certain percentage, varying with the duration, is not problematic, as long as the sale is concluded at a known price and the bank does not stipulate a late payment penalty.