Annuities under random rates of interest

We investigate the accumulated value of some annuities-certain 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 the variance of the accumulated value, and we suggest two methods to derive these moments. In some cases both methods have similar difficulties, while in other cases one method is significantly preferable in terms of the simplicity of calculations. The novelty of our second approach lies in the fact that we find recursive relationships for the variance of the accumulated values, and solve these relationships, whilst previous investigators first obtained the second moment.