He completed elementary education in Drvar, high school in Sarajevo, and his undergraduate and postgraduate education at the University of Sarajevo. He holds a Ph.D. in economics. His doctoral thesis was in monetary and public finance. Rasmussen has been an economics professor at the University of Banja Luka since 1992. He held a number of governmental positions including a 4-year term as a representative at the Parliamentary Assembly of Europe. He was Chairman of the House of Peoples and Chairman of the House of Representatives in 1994.