those already rich should not be rewarded, but only who have small amount of btc
There is no difference between interest paid for your bank account and interest of a PoS coin.
Except your bank's interest is probably lower, and you give all your money out of your own hands
Everyone gets the same % in PoS.
In my example:
My bank pays me 0.01% per year
My PoS coin pays me ~0.5% year
To make the poor earn more interest than the rich is very very hard to do in crypto, because of sybil attack.