Is it permissible to take out a loan for a car down payment out of necessity, even if that means paying a percentage again as expiation?

You are permitted to seek a legitimate means of acquiring a car for work, without resorting to usurious loans. This could be through Islamic banks for a permissible murabaha or tawarruq transaction, or by finding someone who will sell you a car in installments, with the car serving as collateral until its price is paid. Borrowing with usury is not permissible except in cases of extreme necessity, where there is a strong likelihood of perdition or unbearable hardship, or an inability to achieve a minimum standard of living. Necessity is estimated by its extent, and the permissibility of dealing with usury ceases when the necessity no longer exists.