Confusion about the effect of an increased expected inflation on the price level In Mankiw's Macroeconomics 7th edition, on page 99, there is the following equation, which states that "the price level depends not only on today’s money supply but also on the money supply expected in the future":

$$M/P=L(r+E_{\pi},Y)$$

where $L$ stands for the demand for real money balances and $r$ for the real interest rate. The author then poses the following thought experiment:


  Suppose the Fed announces that it will increase the money supply in
  the future, but it does not change the money supply today. This
  announcement causes people to expect higher money growth and higher
  inflation. Through the Fisher effect, this increase in expected
  inflation raises the nominal interest rate. The higher nominal
  interest rate increases the cost of holding money and therefore
  reduces the demand for real money balances. Because the Fed has not
  changed the quantity of money available today, the reduced demand for
  real money balances leads to a higher price level.


My question is: I understand that, by the above equation, considering that $M$ is fixed, a decrease in the demand for real balances should lead to an increase in $P$. However, what exactly happens in the real world that causes the price level to rise as a result of people trying to get rid of the excess money they are holding? I can see that, if they were spending those "extra" balances on consumption, that would increase the demand for goods and services, which in turn would lead to higher prices. But since the reduction in $L$ was motivated by a rise in the interest rate, it is savings that is increasing, and not consumption. So, what is going on here? Thanks in advance.
From what I understand, everything here has been expressed in real terms. With the announcement, people now expect higher money growth and 'higher inflation'. True that the nominal interest rate rises, they earn greater return on savings, yet it is of no use to them if price level rises. Note that, here, only real rise in interest rate would induce people to save more. Thus now, according to the author, consumption tends to rise and how that might lead to rise in price level is clear.