In this research, we investigated the burnup characteristics and the conversion of fertile $^{232}Th$ into fissile $^{233}U$ in the core of a Sodium-Cooled Fast Reactor (SFR). The SFR fuel assemblies were designed for burning $^{232}Th$ fuel (fuel pin 1) and $^{233}U$ fuel (fuel pin 2) and include mixed minor actinide compositions. Monte Carlo simulations were performed using Serpent Code1.1.19 to compare with CRAM (Chebyshev Rational Approximation Method) and TTA (Transmutation Trajectory Analysis) method in the burnup calculation mode. The total heating power generated in the system was assumed to be 2000 MWth. During the reactor operation period of 600 days, the effective multiplication factor (keff) was between 0.964 and 0.954 and peaking factor is 1.88867.