Officials of the University Medical Center of Princeton at Plainsboro promise they will open the new hospital as planned May 22. Hospital president and CEO Barry Rabner said that physically, just about everything is done at the hospital's new location, some three miles from its old site in Princeton. Setting the price of all costs in building the hospital and financing it at $522.7 million, he expects that figure to swell to between $1.2 billion and $1.5 billion over the years as the campus is built out. The hospital raised $147 million for the project and spent another $50 million in savings, along with the money from the sale of the old Witherspoon Street hospital, he said. To market the hospital's opening, another $2 million is being spent.