Really stupid question from an ignorant person

I have a really ignorant question for my Christian friends. I am under the impression that, if you are a fundamentalist Christian, accepting Christ as your savior is the one and only road to salvation. I think I’ve read this described as “faith, not acts.”

If I’m correct about this basic principle, and it’s faith and not acts that lead to salvation, what is the incentive for Christians to engage in affirmative good acts and lead a moral life? That is, could one say (and mean), “I accept Christ as my savior,” but at the same time live a life of immoralities big (e.g., theft) and small (e.g., acting without respect to ones parents)?

I can’t believe that this approach — accepting Christ but living immorally — can be correct based on the evidence of my own experience. As Dennis Prager likes to say, if he found himself alone in a dark alley, he’d feel a lot safer if the group of men heading his way came from a Bible study class, as opposed to any other point origin.

In other (inarticulate) words, my observations show me that having attained salvation by accepting Christ, Christians nevertheless do go on to live moral lives. But do they really need to if, as I understand it, their salvation is already assured? Clearly, I’m confused here.