Answers to most financial questions can be either mathematically correct or emotionally correct and it's rare that one answer is both.
So, the math says pay off the loans. This presumes that you intend to keep an emergency fund completely liquid at all times, which means it won't earn any interest while the student loan is charging you interest. Even if the loan is charging you a crazy small number, which used to be the case but is doubtful these days, the math still says pay off the loan first.
The emotional side says there's peace of mind in knowing that you have actually started an emergency fund even if it's nowhere close to what you want it to be yet. It should be 3 - 6 months of your living expenses, whatever they are. This is pretty important because as obvious as having one seems, the truth is that most people don't quite get around to it.
If you were my customer, I would applaud either direction. I would insist only that you be able to clearly explain why you chose one path and not the other.
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