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IRS.gov Website
Publication 513
taxmap/pubs/p513-005.htm#en_us_publink10008634

Estimated Tax Payments(p10)

rule
You may have income from which no U.S. income tax is withheld. Or, the amount of tax withheld may not equal the income tax you estimate you will owe at the end of the year. If this is true, you may have to pay estimated tax and file Form 1040-ES (NR). A penalty may be charged if you underpay your estimated tax by a certain amount.
Generally, you must make estimated tax payments for 2011 if you expect to owe at least $1,000 in tax and you expect your withholding and credits to be less than the smaller of:
  1. 90% of the tax to be shown on your 2011 income tax return, or
  2. 100% of the tax shown on your 2010 income tax return (if your 2010 return covered all 12 months of the year).
If your adjusted gross income for 2010 was more than $150,000 ($75,000 if your filing status for 2011 is married filing separately), substitute 110% for 100% in (2) above if you are not a farmer or fisherman. Item (2) also does not apply if you did not file a 2010 return.
taxmap/pubs/p513-005.htm#en_us_publink10008635

When to pay estimated tax.(p11)

rule
Generally, you must make your first payment of estimated tax by the due date for filing the previous year's Form 1040NR or Form 1040NR-EZ.
taxmap/pubs/p513-005.htm#en_us_publink10008636

Additional information.(p11)

rule
For more information, refer to the instructions for Form 1040-ES (NR) and see Estimated Tax Form 1040-ES (NR) in chapter 8 of Publication 519.
taxmap/pubs/p513-005.htm#en_us_publink10008637
Residents of Puerto Rico.(p11)
If you expect to be a resident of Puerto Rico during the entire year, use Form 1040-ES or Formulario 1040-ES (PR).