How is the zakat calculated for an amount of 8,640,000 Iraqi Dinars (5,640,000 of which is for the first year) received as salaries over a year and a half, knowing that she wishes to pay the zakat in Ramadan each year, and is the zakat due for one year or for a year and a half? And what is the ruling on the zakat of the remaining amount after paying off a debt for her mother?

Zakat (definition) is not obligatory on salary unless it reaches the nisab (definition) (minimum threshold) — which is equivalent to 85 grams of gold or 595 grams of silver — and a complete lunar year (hawl) passes over it. If it reaches the nisab and a year passes, then a quarter of a tenth (2.5%) of it is to be given as zakat. It is permissible to give zakat on salaries that have not yet completed their hawl along with what has completed its hawl, for ease of calculation. As for the debt deducted for your mother, there is no harm in it, and you pay zakat on what remains after deducting the debt, if it reaches the nisab and a year has passed over it.