All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
We do not know exactly what this bank is so that we could give an appropriate ruling about it.
But in general, if a person is in need to open a bank account while there are no banks that do not deal with interest, then he is permitted to do so because of the necessity to open an account in an interest-based bank – without taking the interests for himself.
The fatwa of the Standing Committee reads:
“It is not permissible to deposit money in banks that deal with interest, even if one does not take the interest, as this is helping in sin and transgression; Allah says (what means): {…but do not cooperate in sin and aggression.} [Quran 5:2] However, if a Muslim fears losing his money and does not find another alternative to save it except by depositing it in an interest-based bank, then he is permitted, in such a case, without taking any interest from depositing this money, as a way of committing the lesser of two evils, and avoiding the worst of the two evils.”
Besides, Shaykh Ibn ‘Uthaymeen said, “If you are in need of opening an account in an interest-based bank, then it is permissible, but if you are not in need to do so, then do not open an account there.” [Excerpted from the Open Door meeting]
Hence, it is permissible for a person to open an account without interest in an interest-based bank when there is a necessity to do so and there are no banks that are free from interest. There is nothing wrong with the known amount that the bank takes in return for opening the account and for the services that it provides. This is nothing but a fee for the bank for the benefits that it provides for the client.
Allah knows best.