The present interest rates on money in your checking account in terms of value is negative 5-20%.  If you could earn 5% interest your money would be shrinking.  All you have to do is look at change in m1 money supply.  money supply chasing goods is the value of money.  m1 is the closest factor to loose spendable money in the economy.  m3 such as 5 year cds is locked up and does not effect the money supply as much.   There will be inflation the lag has not hit yet.

If interest rates are zero, their money will not grow in the present dollar world.  However, in cryptocurrencies their will be some deflation.  From 1840-1914 there was basically deflation overall.  When you get a job, you don't get a raise but your money is worth more with time.

Savers money can only grow if interest exceeds inflation, or there is deflation.  If interest is zero, bitcoin will far exceed dollar deflation due to lost coins.