Kemper was born into an influential banking and railroading family in Kansas City, Missouri. His father was R. Crosby Kemper. He attended Southwest High School in Kansas City, then transferred to Phillips Academy in Andover, Massachusetts where he graduated in 1945. After returning from service in World War II, Mr. Kemper enrolled in the University of Missouri and became a member of the Zeta Phi chapter of Beta Theta Pi.
In 1950, Kemper went to work for the United Missouri Bank, which later became UMB Financial Corporation. He later became president in 1959. He ran for the U.S. Senate in 1962 on the Republican ticket and in the same year chaired the Kansas City Industrial Committee. He was active in the running of the Kemper Museum of Contemporary Art, which was named for him. He retired as chairman of UMB in 2004.