An anonymous source was quoted:
“Peter is the perfect Doctor. He’s a life-long fan of the show and a great actor.
He wanted to do another series and the BBC wanted him back. Even before the premiere, no one at the BBC was in any doubt that Peter was going to be brilliantly received.
It’s hoped that he’ll play the role for years.”Given that this is an anonymous source, there is no guarantee on the reliability of this information. However, due to previous experience with other Doctors, it is highly unlikely that Capaldi will not stay on for at least a couple of series.