Question: Suppose you and your spouse have 2 children and each of them have two children, and so on into the future. At what date in the future will you and your spouse have more than 1 billion descendants?
Answer: By around 2600 AD you and your spouse will have generated 1 billion descendants. Rationale: 1 billion is approximately 2^30. In one generation, you will have 2 decendants; in two generations, you will have 4; in 3 generations, you will have 8 decendants; and so on. So, if your decendants double each generation, it will take 30 generations to generate 1 billion descendants. If a generation is around 20 years, that's five generations per century. Thirty generations will take approximately six centuries or 600 years.
Source: See Joseph Chang, Yale University, Recent Common Ancestors of All Present-Day Individuals, 1999: Given the assumptions in his model of population growth, all Europeans alive today are descended from a common ancestor who lived around 1400 AD.
Source: See Steve Olson "The Royal We", Atlantic Monthly, May 2002: "The mathematical study of geneology indicates that everyone in the world is descended from Nefertiti and Confucius, and everyone of European ancestry is descended from Muhammad and Charlemagne."
Source: See Matt Crenson (July 2006) We are all related: The ancestor of every one of the 6.5 billion people living today on Earth probably lived somewhere in East Asia around the time of King Tut (~ 1330 BC) or even during the golden age of Greece (~600 BCE).
Want to trace your genetic roots? See National Geographic's Genographic Project