A continuous-time homogeneous irreducible Markov chain {X(t)}, tϵ [0; ∞), taking values on N ={1,..., k}, k<∞, is considered. Matrix λ= (λij) of the intensity of transition λijfrom state ito state jis known. A unit of the sojourn time in state igives reward βiso the total reward during time tis . The reward rates {βi} are not known and it is necessary to estimate them. For that purpose the following statistical data on robservations are at our disposal: (1) t, observation time; (2) i, initial state X(0); (3) j, final state X(t); and (4) y, acquired reward Y(t).Two methods are used for the estimation: the weighted least-squares method and the saddle-point method for the Laplace transformation of the reward. Simulation study illustrates the suggested approaches.