There is no absolute low limit, but the extra costs of taking advice, opening new bank acocunts, phone communication at a distance, etc, etc mean that offshore investment is unlikely to be worthwhile for less than say $25,000. Still, costs are coming down all the time because of the Internet. Offshore banks will take deposits down to $1,000, but for a personalised 'private banking' service, you will need to deposit $100,000 or more.
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