re: pay the 3% transfer fee or drain my savings?

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Just ask yourself do you want to be out of debt tomorrow or 2 years from now? 

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If you value that psychological achievement sure, but logically he could be making a much smarter move rolling the balance to another card and investing that money.

It all depends on what you're comfortable with though. Personally I'd take the 3% hit and roll the money to a new card. Money now is always better than money later.