Bank A receives a demand for the $1000 in FRNs from checking-account owners who want cash and expect to get it in exchange for face-value payment from their checking accounts. Bank A's asset entry 'vault cash reserves' is debited by the face value of the FRNs provided to the customer, and the demand-deposit liability account is debited by an equal amount, and lo, the assets and liabilities are in balance.
The customers now have possession of the cash, and everybody's happy. Here, again, the FRNs are exchanged at face value and the FRNs are backed by the FR Bank's FRN collateral-liability account as required by US law.
Return to the FR system
When any commercial bank, say, Bank A, decides it has too much cash on hand and/or FRNs damaged beyond further usefulness, it tenders these FRNs to the FR Bank in exchange for a credit of the face value of the FRNs tendered. The commercial bank's vault-cash reserves asset account decreases by the face value of the tendered FRNs, say, $1000 in face value, and its reserves account on deposit at the FR Bank (an asset account of Bank A) increases by the same amount. Thus, there is no change in assets or liabilities, and Bank A's balance sheet is balanced.
At the FR Bank, the received FRNs are placed in the vault at $0 value, and their face value ($1000) is subtracted from the FRN collateral-liability account tracking the FRNs issued by the bank into circulation. Since Bank A's reserve account is credited for the return of the FRNs at their face value, the FR Bank's Reserves on deposit: Bank A liability account is increased by $1000. The assets and liabilities on the balance sheet are now in balance.
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