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Republican presidential candidate Mitt Romney keeps at least $30 million, probably more, in the tax-free Cayman Islands, Vanity Fair reported on Tuesday.

The Romney campaign claims that the candidate has not exploited offshore havens to avoid paying necessary U.S. taxes, but the Vanity Fair report detailed how Romney continues to have interests in at least 12 of the 138 funds, organized by his company Bain Capital, in the Cayman Islands.

Cayman Islands investments are hidden behind confidentiality disclaimers, making the total amount of Romney's true wealth virtually impossible.

Romney also holds a Swiss bank account, with $3 million in it, according to 2010 tax returns, and other money in tax havens such as Bermuda, according to the report in the August issue of Vanity Fair.

In 2010 he reported income of $21.7 million, mostly from investments, and paid just over $3 million in taxes, a rate of just 13.9 percent, far lower than the rate for most Americans.

The Romney campaign released a statement on the article, saying: "As job growth slows, manufacturing activity stalls, and our economy continues to sputter, President Obama knows he can't make a legitimate argument for another term in office, so instead he is trying to tear down his opponent."

In response, the Obama campaign quoted Vice President Joe Biden on Twitter: "We need to choose someone who invests in America, not in a Swiss bank account."

The Obama campaign also linked to a map where Mitt Romney has reportedly kept money, including: Ireland, Switzerland, Luxembourg, Bermuda and the Cayman Islands, reports the New York Daly News.