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.
It is apparent that the bank you are asking about is a usurious one. So, dealing with such a bank is not permissible. As for the transaction mentioned in the question; i.e. using the deposited money and giving a certain portion of interest to the depositor, then this is the basic way of transaction in all usury-taking banks.
The banks would never exist if people did not deposit their capitals in them.
The banks have two most important tasks:
1) Taking money from depositors against giving a certain interest to them.
2) Lending money to borrowers against certain interest in return.
Both these operations are unlawful, since they constitute Riba. A Muslim should avoid such forbidden usurious transactions. All Muslim scholars have agreed that usury is among the major sins and one of the seven destructive sins (mentioned in a sound Hadeeth).
Know that Allah has declared war against those who indulge in usurious transactions and Jaabir, may Allah be pleased with him, narrated that the Prophet said “Allah has cursed the one who consumes Riba (i.e. usury or interest), the one who gives it to others, the one who records it and the one who witnesses it (its transaction).” He added: “All of them are equal in sin.” [Muslim]
Allah knows best.