[knn]

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...

[noego]

Your numbers are off. If both people save $50k each from their investment/wage income, then both of them will earn 10% returns on that $50k of savings. Hence why they cancel each other out. You've only given the worker 3% returns on his savings, not 10%