TurboTax has no control nor information regarding the timing of a tax return.
However, The IRS states that nine out of 10 e-filed tax returns with direct deposit will be processed within 21 days of IRS e-file acceptance.
Mailed paper returns: If you filed a paper return, please allow 4 weeks before checking the status. Refund processing time is 6 to 8 weeks from the date the IRS receives your tax return
Where's my refund
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