How is Zakat calculated on money that has completed a Hawl (one lunar year) in the fourth month, knowing that I started saving an additional sum of money in the eighth month of the same year?

Zakat (definition) is not due on money merely because a year has passed; rather, it becomes obligatory if a year has passed after it reaches the nisab (definition) (the equivalent of 85 grams of gold or 595 grams of silver). If the money reaches the nisab, a full year is counted from the date it reached the nisab, then one-quarter of one-tenth (2.5%) of it is given out. Money gained later, if it is profit generated from the nisab, is zakatable along with it. If it is not profit generated from it (such as a salary or inheritance), it is permissible to pay zakat on it in advance along with the nisab, or to pay zakat on each sum of money in its respective month.