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Deductions & credits
You say "I just used an example". Change the details of your example and the answer could be different.
When it comes to taxes, it's never simple. Hence, the complicated worksheet to calculate your investment income for purposes of the EIC.
Yes, your $3000 carry over loss reduces your taxable income, for purposes of calculating your income tax. That is, it reduces your total income. But, you're not allowed to target it to your interest income alone.
However, let's use a different example: what if you had a $4000 capital gains distribution (still investment income), on a form 1099-Div, instead of $4000 of interest on a 1099-INT. Then you would only have $1000 of net investment income and your EIC would not be eliminated.
Huh? How can that be? Because the capital gains distribution goes on Schedule D, where it is directly reduced by the capital loss carry forward before it ends up on line 6 of form 1040.
That ain't fair? But, it's the law. Knowing you had that loss carry forward, you shoulda coulda switched your investment from an interest bearing account to a stock mutual fund.