> Actually in classical macro theory, lower interest rates (which amounts to the Fed increasing the money supply) ... hence price inflation.
If the money supply is increased (more dollar bills are printed), you'll need more to pay for the same thing: and that is directly price inflation. You can ignore the expected effects in the middle. (In fact, there's no direct correlation to cheaper credit and greater investment.)
4% is stated core inflation. The true inflation number is much higher, but it's hard to know because there's a lot of effort put into diminishing it, for obvious reasons. Sure we're not in hyperinflation yet, but the idea is that it could get there quickly. While it seems impossible from the comfort of growing up in the second half of the 20th century, America is in much more trouble than it realizes.