Peter Vale, a Dublin-based corporate tax expert for the accounting firm Grant Thornton, calculated that Tuesday's decision, if upheld, could ultimately cost Apple $21 billion because the European Union order also includes interest for unpaid taxes going back more than a decade. Both the Irish Finance Minister and Apple have denounced the ruling and say they will seek appeals.

The US has been quick to criticise a decision by the European Commission that Apple should pay back taxes in Ireland - saying the move will "undermine foreign investment".

She said a three-year investigation found Ireland granted such lavish tax breaks to Apple over many years that the multinational's effective corporate tax rate on its European profits dropped from 1 percent in 2003 to a mere 0.0005 percent in 2014.

Last week, the Treasury had accused the European Union of using a different set of criterial to judge cases involving American companies and called the effort "deeply troubling".

The department also accused the commission of unfairly singling out USA companies for punishment under its "new approach" to dealing with legal tax breaks given to multinational corporations operating within its member states.

Apple has had a base at the southern city of Cork since 1980 and employs 5,000 people in Ireland, through which it routes its global sales, avoiding billions in corporation taxes.

In the letter, Cook says Apple expects the EU's ruling to be reversed after its appeal.

The country has for years offered low corporate tax rates to multinationals to benefit from the jobs they create.

It said it would challenge the EU action in the European courts.

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It's also adds up to $4,126.16 for every one of Ireland's 4.6 million population.

The EU said earlier Tuesday that Apple owed 13 billion euros plus interest, without quantifying what the total might amount to. But its agreement with the Irish government that allowed Apple to pay a tax rate of just 1 percent or even less -.0005 percent, in some years - according to the European Commission, following a two-year investigation. "It is about which government collects the money". Online retailer Amazon.com Inc and fast-food company McDonald's Corp face probes over taxes in Luxembourg, while coffee chain Starbucks Corp has been ordered to pay up to 30 million euros ($33 million) to the Dutch government.

Apple said in a statement: "The European Commission has launched an effort to rewrite Apple's history in Europe, ignore Ireland's tax laws and upend the worldwide tax system in the process".

However, the Irish tax authority agreed only 50 million euros of this was taxable in Ireland, the European Commission said. "It will have a profound and harmful effect on investment and job creation in Europe". Apple follows the law and pays all of the taxes we owe wherever we operate.

He has rejected findings that Ireland cut an especially generous tax-avoidance deal to boost Apple's investments in Ireland, where the company employs 5,500 and plans to expand further.

Either way, the EU's bold move risks fueling tensions with the USA, which complains that it is singling out American companies.

Facebook's tax relationship with Ireland could be disclosed by the company or by the EU.

Last week, the U.S. treasury department criticized the European Commission, arguing that if it overrides the established tax laws of its member states it could risk becoming a "supra-national tax authority". He said a successful appeal, which could take years, would "provide tax certainty to business".