  In the article we consider accumulated values of annuities-certain with
yearly payments with independent random interest rates. We focus on annuities
with payments varying in arithmetic and geometric progression which are
important basic varying annuities (see Kellison, 1991). They appear to be a
generalization of the types studied recently by Zaks (2001). We derive, via
recursive relationships, mean and variance formulae of the final values of the
annuities. As a consequence, we obtain moments related to the already discussed
cases, which leads to a correction of main results from Zaks (2001).
