Adrienne Arsht, the chairman of Miami-based TotalBank until she sold it last year for $300 million, plans to donate $30 million to the city's performing- arts center. In return, Miami's Carnival Center for the Performing Arts, named for Carnival Corp., the cruise-ship operator, will be renamed the Adrienne Arsht Center for the Performing Arts of Miami-Dade County. The center is home to four resident companies: Florida Grand Opera, Miami City Ballet, the New World Symphony and the Concert Association of Florida. "A performing-arts center is the heart of a community," Arsht, 65, said in a telephone interview. "Dance and music are about as essential as your DNA." Arsht plans to spread the donation over three years. In the first year, $7 million will pay off a bank loan and $4 million will be used to fund programming, according to a press release from the performing-arts center. It will return $2 million to Carnival Corp. that was part of a 10-year $10 million commitment. Carnival, which agreed to relinquish the naming rights, thanked Arsht for the donation. "Carnival's interest has always been in doing what is best for the Performing Arts Center and the community," Carnival Chief Operating Officer Howard Frank said in a statement. Arsht said she has no plans to "meddle" in programming at the center. She said the name change wasn't her idea, and she didn't know its duration. "The lawyers are still trying to figure that out," she said. Banco Popular Espanol SA completed its purchase of privately held TotalBank in November.