Gary Barnett’s Extell Development sold a sponsor unit of the Central Park Tower at 217 West 57th Street nearly 50 percent below its asking price.

The 7,984-square-foot, four-bedroom unit was offered on the market at $95 million and sold for $49.7 million—the mystery behind the buyer, who protected his identity behind an LLC.

The residence with a 2,000-square-foot terrace and an outdoor pool was the building’s most expensive until it was surpassed by an 11,535-square-foot duplex created by the merger of two apartments ...