Interesting question. It all depends of parameters such as what wealth means to you, what is your social origin and background, and where do you live?
For example: many people enjoying a good job and a salary of $100,000 to $150,000 a year do not see themselves as rich persons because they consider that a rich person is supposed to own a big yacht or/and a private jet; while any blue collar will say they are rich people, indeed. But many blue collars consider that an annual income of $100,000 is sufficient enough to make someone a rich person.
I have lived in France and in United States and I have been (somewhat) “rich” at some point in my life and quite poor at some other; and so I assume I have an accurate perception and understanding of what is wealth regardless of the place where one lives.
First of all, to be rich means enjoying certain freedom of choice in daily life. The freedom to say “I will trip to such foreign country next week,” or ”I need a good looking suit and so I’m going to buy one this afternoon,” or “it bothers me to cook and so I go to the restaurant everyday,” or “I’m going to send my son to Yale University.” From this on access to this choice, which is made up of a range of services and goods, implies a varying amount of money.
I once met a man who lives in Lao People's Democratic Republic. He makes about $40,000 a year, according to my own estimate, plus some perks owing to his political connections. With that he affords to own a (fully owned) house that would pass as the average lower middle-class one in the United States. He owns a Japanese middle-range four-wheels-drive and a second Japanese middle-range car for his wife. He travels abroad in some rich countries from time to time. If he wants to, he can afford to go to eat in local good restaurants everyday without changing anything of significance in his daily life. In Laos, he is considered as a rich and influential person.
I know another person, living in France, who owns a little (fully owned) castle and who uses to renew his four wheels drive Mercedes about every 3 years, and who makes about $70,000 to $90,000 a year from interests on savings; plus some perks owing to
certain political and Masonic connections, and one servant. If he wants to, he can afford to go to a good local restaurant about one to thrice a week without changing anything substantial in his daily life. He is considered as a rich and influential person in his country.
In United States, the aforementioned earnings would be insufficient to make a rich person since the admitted threshold between the middle class and the upper class is about $100,000 a year of earnings. However, one will not be a rich person with $100,000 a year in United States. In this last country, as in many other countries, savings or inheritance will make the difference. Owing a paid pleasant house and making $100,000 a year is something very different of paying a credit on a pleasant house on an annual earning of $100,000. In the former case it is possible to enjoy certain comfort and to afford certain extras (boat, luxury car, university for the children, etc.) which are features of wealth; but not in the latter case. Thereupon, all these considerations and parameters may change tremendously depending whether one lives in California or, say, Idaho.
So, the rich Laotian would not be rich in France and he would belong instead to the upper middle class/lower upper class of the French society. With $40,000 a year of income he would barely belongs to the lower middle class of the American society.
My French rich man would be a member of the top upper class in Laos, but, with about $80,000 of yearly income he would barely belong to the American lower upper class.
None of them would easily and willingly spend more than $500 for a pair of shoes, if they all are reasonable persons. As a result, none of them are truly rich, according to our common (occidental) perception of wealth, after all.
It ensues that, to an opinion which is mine nonetheless, the minimum required wealth to claim to be a rich person is made up of yearly income on the one hand, and of inherited or saved wealth on the other. One will necessarily need both to claim to be a rich person.
Home ownership is a fundamental determinant.
So, this minimum required wealth to belong to the “exclusive club” might be about $1,000,000 of savings or the equivalent in real estate, plus an annual income in excess of $100,000.