Annan's term ends when Bill Clinton's term begins. I would not be in a big hurry...
From Wikipedia:
"UN Secretaries General normally spend two terms in office; however sometimes they will serve only one if there is significant member state disapproval of their performance. That is what happened to Boutros Boutros-Ghali. The position of UN Secretary General is supposed to rotate by geographic region, but that rule is often broken. Since Boutros Boutros-Ghali served only one term, his successor (Kofi Annan) had to come from Africa as well. When Kofi Annan had finished his first term, the position should have gone to an Asian by the custom of rotation. The member states were very impressed with Annan's performance, and so they appointed him to a second term anyway."
Apparently, it is a four year term. It implies that his second term started in 2001.