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My understanding is that your taxes are not due until April 15th.
Giving your money to the government for them to hold until that day is your choice- and a poor investment.
You don't owe them interest... not until after tax day.

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Estimated Tax Penalty

You may owe this penalty if:

• Line 75 is at least $1,000 and it is more than 10% of the tax shown on your return, or
  
• You did not pay enough estimated tax by any of the due dates. This is true even if you are due a refund.