Actually ... while the country as such isn't a monarchy, there are quite a few royal families from the tribes before colonization still around and even are considered as somewhat of a ruler in their vicinity. Same for other countries of the region. However, they aren't usually exactly wealthy, there are a few around in Europe making the news when they do blue collar work here to support their regency, so your prince may just be a car repairman in Switzerland or similar.
Unless we're talking of some of the actual princes who made it in US sports, they should at least easily get by.