WASHINGTON — The Federal Housing Administration is shutting the door on too many potential homebuyers by charging high and unaffordable mortgage insurance premiums, according to several industry groups.

In a letter to the agency, the National Association of Realtors argued that between 125,000 and 375,000 renters would have been able to buy a home in 2013 had they not been priced out of the market by the FHA's policies.

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