It is mainly to study the mathematical expectation and variance of the present value of some annuities about the calculation under stochastic interest rates. In this paper, we give the present values of some annuities whose payments are of the flatheaded rainbow, the rainbow,the reverse flatheaded rainbow and the reverse rainbow and derive the simplified formulas under stochastic interest rates. The simplified formulas of the moment of the present values of the annuities are derived, and the expectation and variance of these annuities are obtained.