This is rather straight forward... Pick any arbitrary interest growth factor, then compare to someone making thousands...Even tens of thousands...To someone who makes millions per year. There's simply no way for the poor to keep up; heck, suspect the poor do not even get to earn interest, but you can bet the rich do. Nothing short of a global disaster or depression can reset this. Your best chances to slow this is to simply STOP BUYING $&%# and endure a little sacrifice to bolster your next generation...Instead of fulfilling self-gratification at every corner.
I think it is very much proven that the global income gap between the rich and the poor will widen the more as years advance. The rich continue to amass, while the poor need to spend to live, so it's impossible for them to make savings, and social mobility seems to be more and more just a utopian concept.
The trends that we have been seeing over the past few decades indicates that the top 1% of the world are pulling away from the rest of the world significantly. In addition to this, the gulf between developing and developed nations is also growing. This is a natural effect of the consolidation of resources and capital in so few hands. As the political will to target inequality is absent in the developed world, the gap is only likely to grow further.
When the United States finally broke the last link from gold to its money supply, it was possible to simply "create" wealth by adjusting the amount of dollars in the system. Not surprisingly, the politically connected (typically in the financial industry) has taken advantage of that in numerous ways. The end result is that newly created money goes to the politically connected, typically for under market rates. This forces the value of each dollar lower, as there are more of them in existance. Without getting a handle on monetary policy of the country (and rest of the world), there's no way to tackle wealth inequality, as the politically connected will simply conjure what they want.
There is no middle class anymore. How can the income gap get any smaller? The short answer is that the government is bought and paid for by the rich, so there isn't any help there. Doctors and lawyers go to the highest bidder, so there isn't any help or justice there. The rich are powerful. They will stay that way. The poor are disorganized and distracted by pictures of cats. The gap will stay the same.