Is it mandatory for me to pay Zakat, even though I don't have my own job and I always save my money as cash? Also, not to mention that I'm saving up for a PS4 or a custom PC, which are quite expensive to buy.
All Praise to Allah Swt and blessings on Prophet Muhammad peace be upon him His family and companions
Zakat is obligatory on every free adult and sane Muslim when he or she possesses the nisab and a lunar year has passed over it. Zakat is due on Gold Silver Cash Trade-goods,freely-grazing livestock kept for milk or breeding like camels, cows, sheep and goats.
Now as per your query ,if you are saving this amount for a long time like a year has passed over it and you have reached your age of puberty then you have to figure out the month the day and the amount when it reached the nisab level,, you can calculate from zakat calculator too, and if after calculation you figure out that your zakatable valauables reaches the value of the nisab and year has passed over it then you are liable to pay the zakah whether you work or not and if you dont possess for an year then you dont need to .Your Query is useful as there are so many misconceptions among people that if head of the family is paying zakah then its enough for all.
Man , woman or adult children each are due to pay zakah if above conditions are applicaple over them.Scholars have mentioned in their fatawas that it is permissible if someone from family pays the zakah on behalf of nisab holder like a woman has enough gold but she doesnt earn then her husband or other could give on behalf of her otherwise she has to give zakat from her Gold.
Narrated Abu Huraira: Allah's Messenger (ﷺ) said, "Whoever is made wealthy by Allah and does not pay the Zakat of his wealth, then on the Day of Resurrection his wealth will be made like a baldheaded poisonous male snake with two black spots over the eyes. The snake will encircle his neck and bite his cheeks and say, 'I am your wealth, I am your treasure.' " Then the Prophet (ﷺ) recited the holy verses:--And let not those who [greedily] withhold what Allah has given them of His bounty ever think that it is better for them. Rather, it is worse for them. Their necks will be encircled by what they withheld on the Day of Resurrection. And to Allah belongs the heritage of the heavens and the earth. And Allah , with what you do, is [fully] Acquainted.. (3.180)
Allah Swt and His Messenger knows best.