Is it permissible to buy a car in installments from an agency that charges compound interest on the remaining amount after the down payment, whereby the interest rate is determined based on the number of installment years, knowing that the agency buys the car before selling it in installments?

If the seller owns the car before selling it to you in installments, there is no harm in that, even if the deferred price is higher than the spot price, for deferment has a share in the price. Similarly, there is no harm in stipulating an upfront installment payment. The determination of the profit margin based on the installment period and the amount paid in advance does not affect the contract if a specific, known price is agreed upon at the time of the contract.