Praise be to Allah.
It is haraam to deposit money in riba-based banks, unless that is needed in order to protect the money, in which case one should limit it to using current accounts, and it is not permissible to put it in savings accounts, even if one will get rid of the interest payments, because putting it in savings accounts is tantamount to a riba-based loan, in contrast to a current account which, even if it is helping the bank, the customer is not entering into a riba-based contract with the bank.
It says in Fataawa al-Lajnah ad-Daa’imah (13/346): It is not permissible to deposit money in riba-based banks and the like, such as riba-based financial institutions, whether that is with or without interest, because that comes under the heading of cooperating in sin and transgression, and Allah, may He be exalted, says (interpretation of the meaning): “but do not cooperate in sin and transgression” [al-Maa’idah 5:3].
But if there is the fear that the money may be lost, through theft, illegal seizure, and the like, and there is no way to protect it except by putting it in a riba-based bank, for example, then there is a concession allowing one to put it in banks or other riba-based financial institutions, without interest, so as to protect it, because that is committing the lesser of two evils. End quote.
It is permissible to invest the money in banks whose transactions are regulated by Islamic teachings, and there is nothing wrong with making use of the profits that result from that in all ways.
The bank mentioned in the country of the questioner invests a large portion of its money in riba-based government bonds and stocks, according to its annual report as published on its website. Therefore it is not permissible to invest money in this bank; rather it should be limited to putting money into a current account in that bank, when necessary.
If it is possible to deal with a better bank, then that is preferable.
For more information, please see the answer to question no. 126073.
And Allah knows best.