What is the recognized nisab (minimum amount) for saved money that has reached the nisab for zakat, then increased and fluctuated? And is zakat due on the final amount, or on the amount that completed the hawl (one lunar year)?

The easiest and safest way to calculate zakat (definition) on savings from a monthly salary is to identify the month in which the savings reached the nisab (definition). Then, zakat is paid on all the money after a full lunar year has passed since that nisab was reached, even if some of it has not completed a full year. In this case, its zakat is paid in advance, which is permissible. Sheikh Ibn 'Uthaymeen issued a fatwa (definition) stating that a person should designate a specific month each year to calculate all their wealth and pay zakat on it, both what has completed its hawl and what has not.