Tiffany, you should try to count your tree rings. It will be easier than tapla's example because (I assume) you tree had a much easier life. I have done it a couple times on stumps of pine trees. It gets a little dizzying but fun to try. You know its less than 123 years old.
BTW, your question: "Do all trees have rings to count?" Trees living at the equator don't grow rings because they aren't subjected to seasons.
