Originally, they had the rights through 2020. That agreement cost $4.4 billion when it was signed just 3 years ago in 2011. The price tag for this 12-year extension: $7.75 Billion.
http://www.usatoday.com/story/sports/olympics/2014/05/07/nbc-olympics-broadcast-rights-2032/8805989/
http://www.usatoday.com/story/sports/olympics/2014/05/07/nbc-olympics-broadcast-rights-2032/8805989/