Abstract: The actuarial calculation of annuities is closely related to the interest rate model. In standard annuities, the interest rate for each period is a fixed constant. In practice, the interest rate for each period can be a variable or even a random variable. These random variables constitute a stochastic process of interest rate. In many cases, the stochastic process of interest rate is a Markov process. This article studies the actuarial calculation of annuities under the Markov stochastic interest rate model. It is proved that if the interest rate process is a time-homogeneous Markov chain, then the discounting process is also a time-homogeneous Markov chain, and they have the `same' initial distribution and the `same' one-step transition probability matrix. With the help of the interest rate discounting process, the expectation and variance of the present value of annuities under the Markov stochastic interest rate model are calculated. This article introduced annuity polynomials, operators, and annuity operator polynomials. It makes the expressions of expectation and variance for annuities very concise, and easy to program and calculate.