In this paper, we study a sampling problem, where samples of a Markov source are taken and sent through a queue to a destination. We use the mutual information between the real-time source value and the delivered samples to characterize the freshness of the information at the destination. Hence, “aging of the delivered information" can be considered as a process that the above mutual information reduces as the age grows. We obtain the optimal-sampling policy that maximizes the time-average mutual information subject to a sampling rate constraint. The optimal sampling policy is proven to be a threshold policy, where the optimal threshold is obtained exactly. Numerical results are provided to compare different sampling policies.