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Withholding additional taxes by making changes to your W4 does not save you money. It withholds more of your own funds to put against your tax liability. It may result in a larger refund, but you are getting your own money back.
Electing to put funds in a FSA could result in tax savings. The funds that go into a FSA are pre-tax. Pretax deductions are taken from your wages before any taxes are withheld. Because they are excluded from gross wages for tax purposes, pretax deductions reduce taxable income and the amount of money owed to the government.
Here is a TurboTax article that will give you a lot of detailed information about FSA's.
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