Your assumption of a 100% savings rate is not quite reality though. More realistically, suppose both people save 50%. Then in 20 years, the rentier is about 2x richer than the worker. https://www.wolframalpha.com/input/?i=sum+i+from+0+to+20+(50... vs https://www.wolframalpha.com/input/?i=sum+i+from+0+to+20+(50...