Is zakat obligatory on the remaining amount (10,000 - 15,000 dirhams) that has been held for a full year (hawl), and what is the amount of zakat due, knowing that the amount recently increased to 50,000 dirhams?

The conditions for Zakat (definition) to be obligatory are the possession of the nisab (definition) (minimum threshold) and the passing of a full hawl (lunar year). The nisab is equivalent to twenty gold dinars or two hundred silver dirhams, and the hawl is calculated according to the Hijri calendar. If the wealth reaches the nisab, Zakat becomes obligatory on it, which is a quarter of a tenth (2.5%). As for any increase in wealth, if it is generated from the principal (like trade profit), it is Zakatable along with the principal. If it is not generated from the principal (like an inheritance or salary), the soundest opinion among scholars is that it has its own independent hawl, and it is permissible to pay its Zakat in advance with the principal. One must be diligent in paying Zakat on time.