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Assuming a person makes over a certain threshold, both a traditional IRA and a Roth IRA aren't tax deductible. Is that correct?

Not really. Roth IRA contributions are never tax deductible. There are income limits where you cannot make direct contributions to a Roth IRA, depending on filing status.

As for deductibility for the Traditional IRA, it depends on additional factors, like filing status and whether or not you and/or your spouse (if married) are covered by a retirement plan at work.

And figuring the income is a different calculation for each type of account.

You can get the details in IRS Pub 590-A https://www.irs.gov/pub/irs-pdf/p590a.pdf

Let's also assume the person takes the standard deduction to make things easy.

Sorry, it's not that simple. Only specific adjustments, not necessarily related to standard vs. itemized deductions, need to be made when determining the income amount. Again, you can find the details in IRS Pub 590-A.

AJ
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