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My employer has a 401K plan to which I contribute the maximum allowed of $10K per annum.

Am I eligible to open a SIMPLE IRA and contribute $6K from my self employed income?
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No. The SIMPLE and 401(k) are both income deferral plans, so the limit of the *sum* of the contributions is $10k

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If not, would I be eligible to open a SEP IRA and contribute 13.04% of my self employed income (which would be less than $6K in my case)?
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Yes.

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In either case, can I still contribute $2K to a ROTH IRA (assuming that my AGI does not go beyond the phase out limits)?
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Yes.