I can honestly say I'd turn the money in, or if I knew who it belonged to I'd give it directly to them. I've been in the same predicament a few years back when I found some a Pokemon Silver at a day care center. It belonged to one of my friends, who attended it at the time, and I took it. Let's just say, lesson learned on that. But, it was hard for me not to. I was young and naive. But, then again, it did have a lot of hacks in it and I was willing to do anything to get a Celebi, which was a member of my old friend's team.
I never returned it. In fact, I still have it. I still feel extremely guilty for doing such a thing, and never felt that I deserved anything related to that ever from a friend, due to what I did to him. I have a very strong continence, which may be why I have a problem with my feelings of guilt, and other related feelings.
Like I said, I learned my lesson. Though I may not know that person, I would turn it into people who I could trust to give it back. I've made my mistake when it came to that, and I wouldn't really want something I bought or earned taken from me all because the person "found" it. That's just not right, especially at the age I am now.