Detail solution

Worldwide income of an American citizen or permenant resident is subjected to American tax. However, in consideration of double taxation, the American tax law recogonize the foreign tax paid as tax credit in the US.

The detail calculation is:

1. US tax liability: Worldwide income * US tax rate

2. Foreign income tax: Whatever you paid

3. Tax credit: the lesser of ( Foreign income tax paid) and (Foreign earned income / Worldwide total) * US tax libility.

4. Final tax needed to pay US: 1 - 3

Foreign income is difficult for IRS to audit in most cases, but it is not a wise idea to not report foreign income in your annual tax return. It may not be a serious risk for now, but the potential risk will last forever until you die because tax return is one of the key personal record in this country.