At current interest rates, an individual will lose purchasing power in their savings account if there is even an inkling of inflation. A common assumption is that the Fed has done this (i.e. pushed interest rates to historic lows) to increase aggregate demand (i.e. if you are earning nothing, you might as well spend it) or to move investors to riskier investments that might provide better momentum for the underlying economy (i.e. an investment in a corporate bond that makes it cheaper for corporations to borrow).

But what if low to negative interest rates in fact causes the opposite... an increase in the savings rate and derisking by investors? This post is based on a very quick and dirty framework I've been thinking about and focuses on the savings rate, but the same framework could (in my opinion) justify why investors may choose to derisk as well. Any feedback would be greatly appreciated.

**Getting to $100 Saved**

Let's assume our saver knows that in ten years they will need to have $100 saved (for retirement, college education for their kids, a new car, etc...). Earning 0% on their savings, they would need to save $10 / year. If they were to earn a rate of return on that $10 saved each year, by the tenth year they would have excess savings (i.e. the blue and yellow lines).

As a result, if an investor can earn more than 0%, they do not need to save $10 / year, but a smaller amount. The chart below shows how much that $10 can be reduced based on various rates of return on their savings.

Assuming the individual earned $200 / year, the original $10 was 5% of their income (i.e. a 5% savings rate). The various amounts needed to save each year is converted to a savings rate below. It clearly shows that if a saver can earn a rate of return greater than 0% (i.e. if interest rates were higher), they can save less to get to their goal.

Unfortunately, savers aren't currently able to earn 0% on their checking / savings accounts. With any inflation, an investors is faced with negative interest rates. So, to get to a $100 real level of savings, an investors will need to save more than the $10 / year.

I know some readers will point out that an individual can always choose to add more risk to increase their returns, but what happens if that investment doesn't work out? An even higher level of savings, which they may not be willing or able to do.

So there's the very basic framework. What am I missing?