That's silly. If that was the case, then you and me would be "rich." Neither one of us is in danger of getting the lights shut off or our cars repo'd.
But since we're playing around, how about this:
How big of a lump sum would it take hitting your bank account (let's assume after taxes or tax free) for you to consider yourself rich?
I think that is a trick question from one standpoint, again, we are not accustomed to thinking of ourselves as rich. I suspect Gates seldom thinks of himself as rich.
But if $120,000 is that cutoff to be in the top 10%, then if one had 4 million in the bank they could live on the 3% rule for life at a top 10% income.
But that in NYC would not mean nearly as much as in Indiana. So if wanted to be rich with that, they may want to give up the idea of living on Park Avenue.
It also depends on the status of kids. A single person bringing in $120,000 is much more likely to feel rich than someone with a spouse and 4 kids.
Also I recall a book that suggested our position to friends matter. The poorest person in Trump Tower feels much poorer than the wealthiest person in Martinsville even if the Park Avenue person has multiples of income over the Martinsville person.
I see that in real life, my household wealth is significantly greater than my HS friends, but significantly less than my college friends. With one group, just getting together and gaming and eating pizza is our extravaganza, the other group it is multiple cruises in a year (something I cannot afford).
So I think that to people who have household incomes of $50,000, I am rich today. To people with incomes of $500,000, I am poor. I came from the poor side, so I actually would argue that I am probably wealthy right now though I afford to drive a 2017 Kia, live in a 2200 sq foot home (which is huge compared to what I grew up in), and cannot afford to do more than National Park vacations (Acadia in October).
Roughly just north of $3 million would let me lead this life without working (less with social security). So $3.25 million in the bank in southern Indiana with no kids.