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Yes, if you've underpaid your taxes, you will get an IRS tax notice, but the IRS works at it's own pace.  You can receive the notice at any time.

The IRS provide guidance on the Underpayment of estimated tax by individuals penalty.

The underpayment penalty will be assessed if any of these apply:

• "If you don’t pay enough tax through withholding and estimated tax payments, you may have to pay a penalty."
• "You also may have to pay a penalty if your estimated tax payments are late, even if you are due a refund when you file your tax return."

To avoid the under payment penalty:

• The amount you owe is less than $1,000, after subtracting withholding and refundable credits.
• You paid 90% of the tax that you owed for the current year.
• You paid 100% of the previous year tax, (110% for higher incomes).
• If your previous year's adjusted gross income was more than $150,000 you will have to pay in 110% of your previous year's taxes to satisfy the "safe-harbor" requirement.

"Typically, underpayment penalties are charge a percentage of the underpaid amount, and they're capped at 25%. 

Underpaid taxes also accrue interest at a rate that the IRS sets annually."

To avoid this situation it is recommended that you adjust your W-4 with your employer or pay estimated taxes.