By Andrew Mills, Maha El Dahan and Parisa Hafezi DUBAI, June 16 (Reuters) - A $300 billion private fund designed to trigger investment into Iran is outlined in the U.S.-Iran framework agreement and more than half that sum has already been committed, a source with direct knowledge of the deal told Reuters. The fund is designed to give both sides an economic incentive to conclude a final deal, said the source, who spoke on condition of anonymity because the plan has not yet been announced as Washington and Tehran prepare to sign on Friday.