|At numerous points in life, people reach defining moments that truly depict who and what they are. You are at one of those points right now, and the question is how you want to define yourself. Since you took the time to write this letter, you obviously know the right thing to do, so do it.|
Some could advise you that letting management know about this error is going to bring accolades and recognition for you, and you can actually profit by what has happened here. That may or may not happen, but that should not be the driving force that motivates you. You should let management know because it is only right.
When people are in doubt about what steps to take in ethically challenging situations, there are several barometers that can help them decide. For example, is this matter keeping you up at night? How would you feel about telling your spouse, significant other, parents, or children about the $50 per week? What is the pit of your stomach telling you?
Tell management that you noticed the error and see what happens. In all respects, it is worth far more than $50 per week.