Actually, rich people at that time were probably the least likely to own a computer. If you're talking about somebody who lives in mansion and has a butler and a chauffeur, that type of person was not buying computers and would not have had any interest in them. (I don't know what those people did with their time, but it sure as hell wasn't computing.)

Personal computers were expensive by middle class standards [1], and the sweet spot was educated professionals like doctors and lawyers because they could afford it and it was interesting/useful to them and their families. A rich person who inherited an oil fortune would have been able to afford it, but not interested. A teacher would have been interested, but unable to afford it.

[1] At a time when a decent, no-frills used car would have been around $1,000, you had something like this: ~$700 for a more limited VIC-20 or Z80-based machine, ~$2,000 for a PC-clone, and maybe double that for the Macintosh. For most buyers, it was a big but not impossible expense.