Is it permissible for an Islamic bank or a benevolent loan fund to offer its clients and depositors in-kind or monetary prizes that are not predetermined, in order to encourage them to deposit? And if not, what are the legitimate methods of encouragement?

The borrower's benefiting the lender is impermissible. The reason for this is what was narrated from the Prophet, peace and blessings be upon him, that "every loan that draws a benefit is usury (riba)." However, scholars have made an exception to this if the benefit arises from another pre-existing reason between them, or a new reason emerges, or if there is evidence that the sole purpose of their action was to benefit the borrower. Holders of fixed deposits and current accounts are generally lenders to banks, and banks benefit from the deposited amounts. Therefore, it is not permissible for the bank to give gifts to account holders. If the bank does give a gift, it is not lawful for the beneficiary to accept it.