You don't have to do the sum explicitly. As a turing-complete being (well, probably), you can do all sorts of cool things that fall under the category of mathematical proof. So if you haven't sent Tim your money you either have to not be capable of mathematical proofs, you have to have a bounded utility function, or you have to have no well-defined utility function at all.

Okay, so it's probably the third one for all humans. But what if you were designing an AI that you knew could do mathematical proofs and had a well-defined utility function? Should it to send Tim its money or not?