Zakat is a compulsory provision in Islam. Paying zakat is essential for rich people. The Holy Qur'an says about Zakat-
‘And you establish prayer and you pay zakat and you bow with those who bow.’ (Surah Baqarah, verse-43)

‘And (note) when We accepted the promise of Bani Israel (to the effect that), 'Do not serve anyone but Allah. And do good to parents, relatives, orphans and the needy. And speak nice things to people. And establish Salat and pay Zakat. Then you turned away except a few of you. And you are averse.’ (Surah Baqarah, verse-83)

‘And My mercy encompasses all things, so I will soon prescribe blessings for those who fear and give Zakat.’ (Surah Araf, verse-156)

‘Successful indeed are the believers, who are modest and humble in their prayers, and who refrain from vain talk, and who give zakat.’ (Surah Muminun, Verses 1-4)

‘O believers! Among the (Jewish) preachers and (Christian) rabbis are many who unjustly enjoy people's wealth and turn (others) away from the path of Allah. Give glad tidings of a painful chastisement to those who hoard gold and silver and do not spend it in the way of Allah. On the Day it will be heated in the Fire of Hell, then their foreheads, sides and backs will be pierced by it. (And it will be said) This is what you kept for yourselves. So enjoy the taste of what you have accumulated.’ (Surah Tawba, verses 34-35)

Hadith related to Zakat:
‘Abu Hurairah (RA) said, Abu Bakr Siddiq (RA) declared war against the Quraysh after the death of Rasulullah (SAW) when they refused to pay Zakat on their wealth.’ (Sahih Bukhari, Hadith: 1400)

‘The Messenger of Allah (PBUH) said, 'Islam is based on five things - one. Testifying that there is no god but Allah and that Muhammad (pbuh) is the Messenger of Allah, two. To establish prayer, three. Paying Zakat, four. Hajj to Kaaba and five. Fasting in the month of Ramadan.’ (Sahih Bukhari, Hadith: 8)

It is clear from the above discussion that paying Zakat is obligatory on every wealthy person. To know the excuse of being rich can be learned from Mufti Sahibs.