How do interest rates, on local and global scales of an economy, affect the distribution of wealth?
Good question! But difficult to answer.
A) Typically, economists think of most interest rates as being set by markets. Under that assumption, you can't change rates by themselves because the market would bring them back to a value that equilibrates demand and supply of savings. Economists try to model how everything is in equilibrium with "general equilibrium" models. Of course, in reality, the fed does set an interest rate...
B) In the "life cycle model" of an individual's life, people borrow when they are young and need to study and create businesses, save when they are middle aged and draw down their savings when they are old. In that context, young people suffer from a high rate and old people gain from a high rate. However, its often the case that people invest in long-term bonds and so it's not really clear that they benefit from an increase in interest rates, because it pushes down the price of their bonds (and their houses too).
C) If instead the idea is to figure out what happens when the equilibrium interest rate is low, then it's good to try to imagine the scenarios when it is indeed low. Economists think that the real interest rate is low when economic growth is low and when there is little demand for capital from firms or a lot of supply of capital by savers. These two things have happened together many times, but they don't have to. For example, a disaster that wipes out a very productive asset, like port infrastructure, will lead to a lot of investment but not a lot of net growth. Similarly, an extra supply of savings should lead firms to invest more and should lead the economy to grow. But now in 2016, we are in a low growth, relatively low investment scenario.
D) It doesn't seem like the interest rate is the biggest determinant to the wealth distribution out there. Some evidence to think this way is that capital markets have become very open, making interest rates very similar everywhere, but inequality remains very different across countries: Commonwealth + Europe+ Japan (low) vs. Russia,+ US +China + Latin America +Africa(high). The distribution of income seems to depend more on the link between political power and economic power that is the norm in many countries, some because of corruption, others by design. It also seems to be more dependent on the quality public education and other public services.
Some similar ideas are discussed in a sort of reasonable Forbes article here: http://www.forbes.com/sites/jeffreydorfman/2015/05/12/the-feds-low-interest-rates-are-increasing-inequality/2/#65fdfe4679cc