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The modern banking system was developed from fractional reserve banking of the early days. Goldsmiths had safes for gold and precious metals, which they often kept for consumers and merchants for a fee. They issued receipts for these deposits. Later on, the receipts came to be used as money in place of gold for their convenience, and goldsmiths became aware that much of the stored gold was never redeemed. Goldsmiths realized they could loan gold by issuing receipts to borrowers, who agreed to pay back gold plus interest. The actual gold in the vaults became only a fraction of the receipts held by borrowers and owners of gold. Fractional reserve banking is significant because banks can create money by lending more than the original reserves on hand.

Creation of money:

Individual banks are not allowed to print their own money. But, banks may create money by creating checkable deposits, which are a part of the money supply.

Suppose the Fed prints $100 and decided to deposit it in Bank X. Bank X sets aside a portion of that $100 that is required reserves (a specific amount that banks must hold as reserves on all deposits), say 10%. The remaining 90%, $90 becomes excess reserves. Bank X can lend that $90 to Customer A, who deposits into his account in Bank Y. At this step, the original $100 remains in the system, and we can now add Customer As $90. Bank Y sets aside 10%, and lends out the rest. This process continues until no new excess reserves can be created.

The money multiplier is the number by which a change in the monetary base is multiplied to find the resulting change in the quantity of money.

Change in quantity of money = Money multiplier X Change in monetary base.

The money multiplier is determined by the required reserve ratio (r) and by the currency drain (c). c: an increase in currency held outside the banks,  tells us the portion of currency which people will hold as cash for their expanses after they borrowed from the banks.  r is the required reserve ratio which determined by the Federal Reserve. Banks are required to hold r portion of their total deposit as their required reserve.

RR: Required Reserve = Total deposit x r

ER: Excess Reserve = Actual reserve - Required Reserve

Maximum new loan amount of the banks is equal to the excess reserve held by the banks.

Money multiplier = 1/ {1- (1-r)(1-c)}

Maximum change in checkable deposits = Money multiplier X Change in reserves from the initial injection

For example, A deposits $1000 in Bank X. The current required reserve ratio (r) is 10%, c is 25%

Money multiplier = 1 / {1- (1-10%)(1-25%)} = 3

Maximum change in checkable deposits = 3 X $1000 = $3000

Federal deposit Insurance Corporation (FDIC)

Deposits at banks are insured by the FDIC. Such insurance guarantees deposits in amounts of up to $100,000 per depositor before the 2008 recession. Since then, the amount is increased to $250,000. This guarantee gives financial institutions the incentive to make risky loans, and gives depositors confidence for their funds.

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