Question on Black-Scholes model

[Dazarath]

I'm taking a finance class right now, and we just learned about the Black-Scholes model. We were taught that it is meant to price European options. Is there a model for pricing American options? I mean, everything else equal, an option that allows the owner to exercise it anytime up until the expiration date, should have more value than an option that only allows the owner exercise it on the expiration date. Sorry if this is a really beginner's question.