I would like to have a new feature that bounties can also be paid in monetary form e.g. through Paypal?
This would likely increase the competition and quality of answers.
To quote Asaf Karagila
What a terrible terrible ... terrible terrible idea.
(I might have opted for "awful" instead, to squeeze a couple more in there, but the sentiment is the same.)
If you want to pay people to answer your questions, there are already sites which provide this service. So what benefits would it have here?
None that I can see.
In fact, it would completely change the culture of this site.
Instead of being populated by users willing to provide answers for the low, low cost of the possibility of a few imaginary internet points, soon you'll see users who hold their answers ransom unless a paid bounty is promised.
You think the pettiness of downvote arguments is bad? Wait until you start to see the arguments that begin over choosing user38613965's answer over user93222358's answer for a paid bounty.
I, for one, would immediately leave Stack Exchange were this "feature" implemented.
I don't think this is possible. The Terms of Service guarantee that the service is and remains free, so I think your idea would violate that, even if it is voluntary. (Maybe a moderator of SE official can confirm this?)