How is zakat paid on the profits from an investment account whose owner stipulated to the bank that it should not deal in usury, and is zakat obligatory on the full amount (principal and profits) even if that leads to a decrease in the principal, or is zakat paid only on the profits?

If the bank is usurious, depositing money in it is forbidden, and stipulating no usurious dealings does not change this. The usurious profits must be disposed of by spending them on the poor or for the benefit of Muslims, and then the principal amount of money should be purified (through zakat (definition)). However, if the bank is Islamic, depositing money in it is permissible, and the profits are purified (through zakat) along with the principal amount at the end of each lunar year. Zakat is one of the pillars of Islam; it increases wealth and blesses it. Abandoning it is a grave sin. Zakat must be paid with a good heart, and it is not permissible to withhold it for fear of decreasing wealth.