I assume you are using currency and money interchangably here. As you note, money is comprised of physical and digital money. A bunch of people here have commented on physical money, so that’s pretty simple.
Speaking for the USA, digital money comes in two forms: cash you have deposited at your bank (checking, savings, money market accounts, etc.) and cash the banks have at the US Federal Reserve (A.K.A. the Fed). Since it’s the Fed doing the counting, they know the second half already. As for cash held at banks, we have a multi-level regulatory system in the US. Banks reconcile their ledgers every day, and report their financial statements to regulators frequently (Typically quarterly, but it varies between the Fed, FDIC, OCC, and state regulators). These statements will report how much money they hold on behalf of depositors. Banks are regularly examined by the FDIC and others to ensure that their reporting is accurate.
You can go the FDIC’s Statistics on Depository Institutions (SDI) page right now to pull data on the total amount of deposits in the banking system.
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