Enrollment in U.S. government-backed Medicare plans run by insurers led by UnitedHealth Group Inc. rose 10 percent to a record this year as lower premiums enticed people to sign up, a study shows. The average monthly charge for the 13.1 million people on Medicare Advantage fell $4 to $35, and is down from $44 in 2010, the Kaiser Family Foundation said today in a report. The Menlo Park, California-based nonprofit also attributed membership increases to less access to supplemental coverage from former employers and more comfort with managed care than previous generations.