What is the ruling on investing in a bank that allows the client to determine the amount and duration of the investment, while it is not possible to know the nature of the bank's investments (whether they are permissible or impermissible), in addition to setting a fixed daily profit percentage in advance?

If the investment profit is a fixed, predetermined percentage that is obligatory, then it is a usurious transaction and forbidden. However, if the percentage is determined by way of expectation and not obligation, then there is no harm.

The condition that the client not dispose of the invested amount is a فاسد (invalid/corrupt) condition according to those who permit the dissolution of partnerships (sharika) and Mudarabah. The Mudarabah contract is among the permissible contracts that either party may unilaterally dissolve whenever they wish, with details differing among the madhhabs regarding the conditions for dissolution.

If it is highly probable that the company invests its funds in forbidden areas, then it is not permissible to invest in it, based on the Prophet's (peace be upon him) saying: "The feet of the servant will not move on the Day of Resurrection until he is asked about his life and how he spent it, about his knowledge and what he did with it, about his wealth from where he acquired it and in what he spent it, and about his body and how he wore it out."