JohnD, here’s the way I see it:
If the Fed creates money out of thin air by purchasing assets, banks acquire deposit accounts at the Fed and have increased reserves. Now that their reserves have increased, they can lend out more money and increase the number of loans they can make. The supply of loanable money increases which causes the price (interest rate) to borrow money to fall (if demand stays the same). Thus monetary inflation (increase in the money supply) can lead to lower interest rates.
At some point the money created out of thin air pushes up prices which is called price inflation. As you said: “A decrease in the purchasing power of money brings about a higher interest rate, since lenders must take into account what the money they will be paid with will be worth in the future.”
I hope this helps. If I happen to be wrong, please correct me Dr Herbener!