I think the deep linkages between demographics, saving and investment behavior, and interest rate dynamics are not yet adequately understood or even discussed a sufficient extent to allow for understanding. Karl Smith and Edward Hugh have done some writing on this issue, but more people need to start thinking about it.
Here's the issue. In a very abstract sense, the way "savings" happens is that you build something expensive that lasts a long time—a building or an airplane or a really large boat—and then you rent it out to future people. This gets very hard to do if the quantity of people alive in the future is going to be shrinking. An equivalently costly-to-construct building earns a lower rental income in a lower population growth dynamic. That means that unless future old people want to accept lower incomes, they need to start investing in increasingly lavish and expensive to build structures. That means that saving rates need to get really high. In the short term, an open economy facing demographic decline can try to deal with this by externalizing the savings and buying foreign assets. That's part of the story with Germany, Japan, and persistent current account surpluses. But as the world as a whole shifts to a more Japan-esque demographic, there's no "abroad" to invest in. Given such overwhelming desire to save for the future, the economy will either fall into a state of permanent recession, permanently negative real interest rates, or both (see again Japan). Particularly during the transition period it's going to be psychologically tempting for savers to see this as a case of wicked malfeasance by central bankers. We've all been raised on stories about ants and grasshoppers and the moral praiseworthiness of savers. The idea that virtuous ants should be financially penalized seems upside down, so we'll hear that "loose money" is "punishing" savers in a problematic way when in fact it's a case of straightforward demographics. Part of the problem is that unlike the ant, an aging person can't just stockpile food for a temporary seasonal shortfall.
And global population doesn't need to be strictly declining for a similar dynamic to take place. If all the world's net population growth is happening in economic and institutional basketcases like Nigeria then absent a radical shift in the politics of immigration you get the same problem.
People often look at a particular window of this problem—the Social Security Trust Fund or the Italian debt:GDP ratio—without recognizing that it's a perfectly general issue. We are accustomed to living in a world where tomorrow holds more people than today, such that slowly-depreciating goods earn positive real returns over time and individuals face a tradeoff between more consumption today and even more consumption tomorrow. But that's an empirical regularity, not a law of nature.