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Say a person's income is above the limit of making a tax deductible contribution to a traditional IRA account. If he/she still decides to make a contribution of say $6000 per year to a traditional IRA account, will the person be able to have capital gains free trades in his/her IRA account?

Also what would happen if the person then decides to convert this traditional IRA account to a Roth-IRA account? This would be a backdoor roth-ira right? What would be the tax consequences for this rollover given that the person's traditional IRA account was not tax deductible in the first place?

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Yes, you always have capital gains tax-free trades inside a traditional IRA, regardless of whether contributions were deducted. The difference comes in when you make withdrawals. The proportion of the withdrawal that is non-taxable is the proportion of your non-deductible contributions over the total account value (considering all traditional, SEP, and SIMPLE IRAs as one); the rest of the withdrawal is taxable.

If you were to convert to Roth IRA, the taxability would be determined by the above formula. So ideally you would convert immediately while the total account value is the same as your non-deductible contributions, making the entire conversion non-taxable. Or, let's take a simple case where you make a non-deductible contribution of $6000 to a traditional IRA. You do a couple trades and the account value is now $9000. If you convert the entire IRA to Roth, you'd pay regular income tax (not capital gains tax, even if it was long-term) on $3000.

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