Is the increase that the bank takes for installment payments of the commodity's price permissible or forbidden?

As long as the bank's role is merely to pay the price of purchases on your behalf, and then it recoups what it paid from you with an increment, this constitutes an interest-based (riba-based) loan and is impermissible. This is because it pays the price but does not purchase or own the merchandise. This transaction is not permissible, and one must seek out what is lawful, for the Messenger of Allah, peace and blessings be upon him, said: "O people, Allah is good and accepts only what is good..." (the rest of the hadith).