The way that economists discuss low interest rates and the problems of savers seems to imply that they think we are saving by holding deposits at the central bank or, more realistically, at our commercial bank of choice. This idea was dispelled long ago by Keynes (1937), who wrote in his article in the Quarterly Journal of Economics:
Money, it is well known, serves two principal purposes. By acting as a money of account it facilitates exchanges without its being necessary that it should ever itself come into the picture as a substantive object. In this respect it is a convenience which is devoid of significance or real influence. In the second place, it is a store of wealth. So we are told, without a smile on the face. But in the world of the classical economy, what an insane use to which to put it! For it is a recognized characteristic of money as a store of wealth that it is barren; whereas practically every other form of storing wealth yields some interest or profit. Why should anyone outside a lunatic asylum wish to use money as a store of wealth?
Good point. Sadly, modern economics has returned to a state in which knowledge lost long ago becomes practically relevant. People have invested their savings in real estate, stocks, bonds, etc. The returns of these assets diverge quite significantly from interest rates set by the central bank (for instance, Chinese real estate performs quite well this year). So, neoclassical models with only one interest rate fall way short to make sense of our complex world.