It's fun to hope but have you gathered any data that suggests that people are frustrated with having to create accounts for bill-sharing apps?
If you built this to further your own education/skills, great job. If you built this to turn into a product, do your research first or else a lot of your talent/effort/time will be wasted.
No thorough analysis done, just some hours with Google and observations of the way people I know deal with expense sharing (excel/paper).
The problem is real tough: calculating this stuff by hand is painful. And because people still do that, it could be solved better than it already is. Choice between free, easy to use tool and paper is a no brainer (if you know that the tool exists, that is)
--> No signup, because it makes it more likely that you know about the tool. (easier to start using, and a lot more likely to spread)
How many people can I spread this to then? I have no idea, but I think this is the fastest way to find out. If it spreads, awesome, and if it doesn't, I'll just swap to some other project. Not much lost here.
(And yes, education is also a big motivator. This is my first tool after all. I still see some value in just shipping tools some people will actually use, profitable or not. A simple, fast project is good for this.)
http://www.venmo.com (has payments)
http://www.billmonk.com (the very first)
http://www.splitterbug.com (now defunct)