At what frequency does monetary inflation compound?

M1 changes changes all the time, depending on activity and reporting intervals.

In the US, M1 consists of currency and notes in circulation, plus demand deposits/checking accounts (and other demand-deposit like arrangements).

• Whenever, a less liquid asset is sold/bought and the money for this transaction is put into/taken out of a checking account M1 changes (and, for example, M3 decreases).

• Banks/ATM operators will prepare for higher demand for notes (and coins) ahead of certain times, for example paydays for certain jobs paid in cash, or ahead of weekends by converting reserve money into currency which they then pay out. This increases M1. Conversely, when, for example, restaurants and bars bring their cash to the bank, M1 will fall to the extent that currency is converted back to less liquid forms of money.

• Whenever someone uses their credit (not debit) card to withdraw cash from an ATM this will increase M1 (as credit card money is not part of M1, but cash is, unless you have a positive balance).

Note that usually neither the Fed nor the government are actively intervening here, although they can. A recent example are the US government benefit checks.