Is zakat obligatory on money deposited in an Islamic bank, when its unemployed owner lives off its monthly profits?

If the money reaches the [nisab] threshold, zakat is due on it along with its profit at the end of the year [hawl]. It is not permissible for you to take zakat because you possess what suffices you and are capable of working and earning, for zakat is not given to the wealthy nor to the strong and capable of earning.