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To pay off a student loan, should I save up a lump sum payoff payment or pay extra each month?
If you pay extra now you will pay less in interest over the life of the loan. Unless your savings account has a higher interest rate than the loan's rate you are not saving anything. That being said, you may have a greater need for savings due to other things (e.g. you might need a emergency fund). But if you are only saving for the loan: compare the rates to see if it is worth it.