Is it permissible to purchase a car in installments from an institution that deals in usury, by paying half the price upfront and agreeing on a profit margin without mentioning interest in the contract?

There are two permissible forms of installment sales:

The first is when the seller (the bank) sells a commodity it owns to the buyer for a known price that is not subject to increase, with an agreement on the method of installments.

The second is when the seller (the bank) purchases the commodity at the request of the buyer and based on their promise to buy it. The bank must then own the commodity and it must be under its guarantee before selling it to the buyer for a known price that is not subject to increase, even if payment is delayed.