Calculations of Special Annuities under Random Rates of Interest

We consider the calculation of present value of some annuities over a period of years in which the rate of interest is a random variable under some restrictions. We aim at the expected value and variance of the present value. In this paper, the special pattern of annuity changes whose payments are of the rainbow is studied and beginning value is given. Meanwhile, we find recursive relationships for the variance of the present value and solve these relationships.