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I know this is a very trivial question, but how does one calculate a tax refund?
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how does one calculate a tax refund?

One prepares a tax return (Form 1040 or one of its variants, plus possibly additional forms) to compute what one's income tax obligation is for year 2004, then subtracts off the amount of taxes already paid (typically through payroll withholding, but may include quarterly estimated tax payments, etc.). If one had already paid more taxes that the Year 2004 tax obligation, the excess is refunded to you (the "tax refund"). If the amount already paid isn't enough to cover the Year 2004 tax obligation, you are suppose to send payment for the shortage.

On the 1040,

Line 62 is your "Total tax" (Your Year 2004 tax obligation)

Line 70 is your "Total payments"

Line 71 is the amount of the overpayment, line 72a is your refund
Line 74 is the amount you still owe

On the variants of 1040 (1040EZ, etc.) the actual line numbers are different but one will still find "Total tax", "Total payments", "overpayment" and "amount you still owe".

All the complications, planning, restructuring investments, making use of various deductions, etc., is to come up with the "total tax", preferably in such a way that one maximizes one's after-tax income.
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