How much does it affect you? You might be surprised: The FBI estimates that insurance fraud costs the average U.S. family between $400 and $700 a year in increased premiums.And the FBI's $40 billion annual cost estimate doesn't even count health insurance scams.Furthermore, the problem appears to be getting worse.ow much does it affect you? You might be surprised: The FBI estimates that insurance fraud costs the average U.S. family between $400 and $700 a year in increased premiums.