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From my company I am getting RSUs and the default 22% federal income tax is covered automatically by selling some of the vested shares. However, 22% is not sufficient to cover my tax liability.

We have the option of withholding some extra amount per paycheck via W4 or setting a higher supplemental incoming tax rate(so higher than 22%). Which option should I go for? Is there any difference in these two approaches for covering the missing taxes?

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The difference is that with additional extra amount in W4 you'll be withholding a fixed amount per paycheck, whereas with higher supplemental tax rate you'd be withholding a proportional portion of the supplemental income.

Higher supplemental tax rate also means that more of the RSUs will be sold at vest to cover withholding. This may be desirable if the shares are volatile and the trading is limited since you'd be creating a "backdoor autosale" (e.g.: trading blackouts due to insider trading policies, non-public company, etc).

Either way it can work, you'll just need to do the math. For supplemental tax rate - you'll probably want to bring it closer to your expected effective tax rate (not marginal tax rate, note the difference). For fixed amount - you'll be more at risk since if the shares jump or plunge your calculations may be off, but if the shares are relatively stable you can estimate how much more you need to withhold and adjust the W4.

You may also want to adjust the fixed amount to hit the 110% of the tax liability from last year (the "safe harbor") and just pay the difference after the year end at tax time.

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