An example of how $100 of currency could create $1000 of money in the form of deposits in bank accounts if banks hold 10% of all deposits as reserves

Table 16 provides an example of how $100 of currency could create $1000 of money in the form of deposits in bank accounts if banks hold 10% of all deposits as reserves and create loans that equal 90% of the value of each deposit.

Table 16.
Loan number
Loan amount
(dollars)
Total value of the loans
(dollars)
Total value of deposits
(dollars)
Loan number
Loan amount
(dollars)
Total value of the loans
(dollars)
Total value of deposits
(dollars)
0
0
0
100
49
0.57
894.83
994.83
1
90
90
190
50
0.52
895.35
995.35
2
81
171
271
51
0.46
895.81
995.81
3
72.9
243.90
343.90
52
0.42
896.23
996.23
4
65.61
309.51
409.51
53
0.38
896.61
996.61
5
59.05
368.56
468.56
54
0.34
896.95
996.95
6
53.14
421.70
521.70
55
0.30
897.25
997.25
7
47.83
469.53
569.53
56
0.27
897.52
997.52
8
43.05
512.58
612.58
57
0.25
897.77
997.77
9
38.74
551.32
651.32
58
0.22
897.99
997.99
10
34.87
586.19
686.19
59
0.20
898.19
998.19
11
31.38
617.57
717.57
60
0.18
898.37
998.37
12
28.24
645.81
745.81
61
0.16
898.53
998.53
13
25.42
671.23
771.23
62
0.15
898.68
998.68
14
22.88
694.11
794.11
63
0.13
898.81
998.81
15
20.59
714.70
814.70
64
0.12
898.93
998.93
16
18.53
733.23
833.23
65
0.11
899.04
999.04
17
16.68
749.91
849.91
66
0.10
899.14
999.14
18
15.01
764.92
864.92
67
0.09
899.23
999.23
19
13.51
778.43
878.43
68
0.08
899.31
999.31
20
12.16
790.59
890.59
69
0.07
899.38
999.38
21
10.94
801.53
901.53
70
0.06
899.44
999.44
22
9.85
811.38
911.38
71
0.06
899.50
999.50
23
8.86
820.24
920.24
72
0.05
899.55
999.55
24
7.98
828.22
928.22
73
0.05
899.60
999.60
25
7.18
835.40
935.40
74
0.04
899.64
999.64
26
6.46
841.86
941.86
75
0.04
899.68
999.68
27
5.81
847.67
947.67
76
0.03
899.71
999.71
28
5.23
852.90
952.90
77
0.03
899.74
999.74
29
4.71
857.61
957.61
78
0.03
899.77
999.77
30
4.24
861.85
961.85
79
0.02
899.79
999.79
31
3.82
865.67
965.67
80
0.02
899.81
999.81
32
3.43
869.10
969.10
81
0.02
899.83
999.83
33
3.09
872.19
972.19
82
0.02
899.85
999.85
34
2.78
874.97
974.97
83
0.02
899.87
999.87
35
2.50
877.47
977.47
84
0.01
899.88
999.88
36
2.25
879.72
979.72
85
0.01
899.89
999.89
37
2.03
881.75
981.75
86
0.01
899.90
999.90
38
1.82
883.57
983.57
87
0.01
899.91
999.91
39
1.64
885.21
985.21
88
0.01
899.92
999.92
40
1.47
886.68
986.68
89
0.01
899.93
999.93
41
1.33
888.01
988.01
90
0.01
899.94
999.94
42
1.20
889.21
989.21
91
0.01
899.95
999.95
43
1.08
890.29
990.29
92
0.01
899.96
999.96
44
0.97
891.26
991.26
93
0.01
899.97
999.97
45
0.87
892.13
992.13
94
0.01
899.98
999.98
46
0.79
892.92
992.92
95
0.01
899.99
999.99
47
0.70
893.62
993.62
. . .
0.01
900
1000
48
0.64
894.26
994.26

Fractional Reserve Banking: Using T-accounts to Illustrate How Banks Create Money

Using T-accounts to Illustrate How Banks Create Money

Suppose the only currency in our simple economy is the 100 dollar-bills that Tracy deposited in the Dolphin Bank. If the required reserve ratio is .10 and all banks choose to hold no excess reserves, how large can the money supply become? If banks hold no excess reserves, then the reserve ratio is the same as the required reserve ratio. The monetary base is the amount of currency in circulation or held as reserves. Thus, this simple economy has a monetary base of $100. The money multiplier is 10 because it is the inverse of the reserve ratio (.10). Since the money supply is the monetary base multiplied by the money multiplier, the money supply in this economy is $1000.

To illustrate how a bank creates money, return to the previous example. Suppose a new bank, the Dolphin Bank, is created. Suppose the first depositor, Tracy, deposits 100 dollar bills in the Dolphin Bank and these are placed in the bank’s vault. At the end of this transaction, Tracy has a $100 deposit at the Dolphin Bank (which are liabilities for the bank) and the Dolphin Bank has $100 of reserves (cash in the vault, which are assets for the bank).

Table 9.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 100
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)


The Dolphin Bank will not earn any profit if it leaves the $100 in its vault. Banks earn profits by creating loans. Suppose the Dolphin Bank keeps $10 as required reserves and lends $90 to Brenda. It takes 90 dollar bills from the vault and gives them to Brenda as a loan. The Dolphin Bank now has $10 cash in the vault and its $90 loan to Brenda as assets.


Table 10.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 10
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)
Loans $ 90
(owed to the bank by Brenda)



When people borrow money, they usually spend it. Suppose Brenda uses the $90 loan to buy a guitar from Carlos. Suppose Carlos deposits the $90 in an account at the Dolphin Bank. The bank now has $190 in deposits, $100 in vault cash, and $90 in loans.


Table 11.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 100
(cash in the bank’s vault)
Deposits $ 190
($100 owed to Tracy by the bank)
($90 owed to Carlos by the bank)
Loans $ 90
(owed to the bank by Brenda)



The Dolphin Bank now has excess reserves that can be used to create more loans. Since the bank is only required to keep $19 as reserves (10% of $190 is $19), it can create an $81 loan. Suppose the Dolphin Bank lends $81 to Jasmine.

Table 12.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 19
(cash in the bank’s vault)
Deposits $ 190
($100 owed to Tracy by the bank)
($90 owed to Carlos by the bank)
Loans $ 171
($90 owed to the bank by Brenda)
($81 owed to the bank by Jasmine)



Suppose Jasmine uses the $81 to buy a painting from Vincent. Suppose Vincent deposits the $81 in an account at the Dolphin Bank. The bank now has $271 is deposits, $100 in vault cash, and $171 in loans.


Table 13.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 100
(cash in the bank’s vault)
Deposits $ 271
($100 owed to Tracy by the bank)
($90 owed to Carlos by the bank)
($81 owed to Vincent by the bank)
Loans $ 171
($90 owed to the bank by Brenda)
($81 owed to the bank by Jasmine)



Once again, the Dolphin Bank has excess reserves that can be used to create additional loans. Since the bank is only required to keep $27.10 as reserves (10% of $271 is $27.10), it can create a $72.90 loan. Suppose the Dolphin Bank lends $72.90 to August.


Table 14.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 27.10
(cash in the bank’s vault)
Deposits $ 271
($100 owed to Tracy by the bank)
($90 owed to Carlos by the bank)
($81 owed to Vincent by the bank)
Loans $ 243.90
($90 owed to the bank by Brenda)
($81 owed to the bank by Jasmine)
($72.90 owed to the bank by August)




Suppose August uses the $72.90 to buy a book from Maya. Suppose Maya deposits the $72.90 in an account at the Dolphin Bank. The bank now has $343.90 in deposits, $100 in vault cash, and $243.90 in loans.


Table 15.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 100
(cash in the bank’s vault)
Deposits $ 343.90
($100 owed to Tracy by the bank)
($90 owed to Carlos by the bank)
($81 owed to Vincent by the bank)
($72.90 owed to Maya by the bank)
Loans $ 243.90
($90 owed to the bank by Brenda)
($81 owed to the bank by Jasmine)
($72.90 owed to the bank by August)



This process can continue until the entire $100 currency becomes required reserves. In this case, $1000 of deposits will have been created by issuing $900 in loans.


Table 16 provides an example of how $100 currency could create $1000 of money in the form of deposits in bank accounts if banks hold 10% of all deposits as reserves and create loans that equal 90% of the value of each deposit.

Fractional Reserve Banking: The Relationships Between the Monetary Base, the Reserve Ratio, and the Money Supply

The Relationships Between the Monetary Base, the Reserve Ratio, and the Money Supply


The total amount of money in an economy depends on two things: the monetary base and the reserve ratio. The monetary base is the amount of currency in circulation or held as reserves. Reserves are the currency commercial banks hold in their vaults plus deposits in their accounts at the Fed.

The reserve ratio (R) is the fraction of deposits that banks hold as reserves. The reserve ratio (R) equals the required reserve ratio (rr) only if banks hold no excess reserves. The reserve ratio (R) is larger than the required reserve ratio (rr) when banks hold excess reserves.

The money multiplier is the amount of money the banking system generates with each dollar of reserves. It is the reciprocal of the reserve ratio.


money multiplier = 1/R where R = reserve ratio


The money supply can be calculated as the monetary base multiplied by the money multiplier. If the reserve ratio is .10, for example, then the money multiplier is (1/.10) = 10. If the monetary base is $1 billion, then the money supply is $10 billion.

Fractional Reserve Banking: How Required Reserves Keep the Banking System Solvent

How Required Reserves Keep the Banking System Solvent


Reserves are deposits that banks have received but not loaned out. Instead they are kept as currency in the vault of the bank (vault cash) or deposited in the bank’s accounts at the Federal Reserve System.

Banks do not earn a rate of return on reserves. Reserves can be divided into two categories: reserves that the Fed requires banks to hold (required reserves) and any additional reserves the banks choose to hold (excess reserves).

The Federal Reserve System established and controls the required reserve ratio. The required reserve ratio (rr) is the fraction or percentage of deposits that commercial banks are required to hold in the form of reserves. This money can be kept in the vault of the commercial banks (as vault cash) or deposited with the regional Federal Reserve Banks that serve the commercial banks. In the absence of a required reserve ratio, commercial banks might not hold enough reserves. This might cause consumers to lose confidence in the banking system.

To illustrate how the required reserve ratio helps maintain the solvency of the banking system, consider the following example. Suppose a new bank, the Dolphin Bank, is created. Suppose the first depositor, Tracy, deposits 100 dollar bills in the Dolphin Bank and these are placed in the bank’s vault. At the end of this transaction, Tracy has a $100 deposit at the Dolphin Bank (which is a liability for the bank) and the Dolphin Bank has $100 of reserves (cash in the vault, which is an asset for the bank).
Table 3.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 100
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)

The Dolphin Bank will not earn any profit if it leaves the $100 in its vault. Banks earn profits by creating loans. Suppose the Dolphin Bank lends the $100 to Brenda. It takes all 100 dollar bills from the vault and gives them to Brenda as a loan. The Dolphin Bank now has no cash in the vault, but its loan to Brenda is an asset for the bank.

Table 4.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves 0
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)
Loans $ 100
(owed to the bank by Brenda)


This is not a good situation, however. Suppose Tracy decides to withdraw $10 from her account. Since the bank has no reserves, it does not have any currency in the vault to give Tracy. The bank is now insolvent. A bank is insolvent if it does not have enough cash to provide to the depositors who wish to withdraw their funds. To avoid this situation, the Federal Reserve System requires banks to keep a fraction of their deposits as reserves (vault cash and deposits at the Fed). If the required reserve ratio is .10 (i.e., 10 percent), then the maximum loan the Dolphin Bank could create from a $100 deposit would be $90. Ten dollars would be required to be kept as reserves. The balance sheet of the Dolphin Bank is now illustrated in Table 5.

Table 5.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 10
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)
Loans $ 90
(owed to the bank by Brenda)


If Tracy goes to withdraw $10 from her account, the bank will have the currency in the vault. If Tracy withdraws $10, the balance sheet of the Dolphin Bank is:

Table 6.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves 0
(cash in the bank’s vault)
Deposits $ 90
(owed to Tracy by the bank)
Loans $ 90
(owed to the bank by Brenda)



In this scenario, the bank is able to give Tracy the $10 she requests, but the bank no longer has 10% of deposits as reserves. Thus it is normal for banks to hold excess reserves.

Consider again the example of Tracy making an initial $100 deposit at the Dolphin Bank. Suppose the bank keeps $30 of this deposit as reserves and creates loans of $70. Of the $30 in reserves, $10 are required reserves (because 10 percent of $100 is $10) and the remaining $20 are excess reserves. In this case, the balance sheet of the Dolphin Bank is:

Table 7.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 30
(cash in the bank’s vault)
Deposits $ 100
(owed to Tracy by the bank)
Loans $ 70
(owed to the bank by Brenda)


Suppose Tracy now withdraws $10 from her account. The bank takes $10 of currency out of the vault and gives it to Tracy and reduces the balance in Tracy’s account to $90. The balance sheet of the Dolphin Bank is now:

Table 8.
Balance Sheet for the Dolphin Bank
ASSETS
LIABILITIES & NET WORTH
Reserves $ 20
(cash in the bank’s vault)
Deposits $ 90
(owed to Tracy by the bank)
Loans $ 70
(owed to the bank by Brenda)


The bank now has $90 of deposits and $20 of reserves. Of the $20, $9 are required reserves (because 10 percent of $90 is $9) and the remaining $11 are excess reserves.

By holding excess reserves, the Dolphin Bank avoided falling short of reserves when Tracy withdrew part of her deposit.

Fractional Reserve Banking - An Introduction

Fractional Reserve Banking

Fractional-reserve banking is a banking system in which banks hold only a fraction of deposits as reserves. Reserves are a commercial bank’s deposits in accounts at a Federal Reserve Bank plus its vault cash. Vault cash is the currency held in the commercial bank’s vault. When banks hold only part of their deposits as reserves, they are able to create money by making loans. If banks held all deposits as reserves, banks would not influence the money supply because they would not be able to issue loans. The money supply increases when banks create new loans. The money supply decreases when banks reduce the amount of money loaned to the public.

Banks are businesses that make profits by accepting deposits of funds and lending a portion of them to businesses and households. Banks pay depositors little or no interest, but charge moderate to high interest rates to borrowers. The difference in the interest rates charged to borrowers and paid to depositors allows banks to cover their costs of operation and make a profit.

When a customer deposits currency in a bank, the bank does not write the customer’s name on it and place it in the vault until the customer returns to withdraw it. Only a small fraction of all the money deposited in banks is kept in the bank's vault or on account with the Fed. The majority of the money deposited in banks is loaned to businesses or households or otherwise invested by the bank.

To illustrate how fractional reserve banking works, it helps to examine a simplified bank balance sheet.



Table 2. A simplified balance sheet for a commercial bank.
Balance Sheet of the First National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,000)
(excess = $ 400,000)
$1,400,000
Deposits
$10,000,000
Loans
$7,500,000


Government Securities
$ 900,000


Property & other assets
$600,000
Net Worth
$ 400,000




Total Assets
$10,400,000
Total Liabilities
& Net Worth
$10,400,000


The left side of the balance sheet lists the assets of the bank. An asset is a financial claim or piece of property that is a store of value. Assets are what the bank owns or is owed. The right side of the balance sheet lists the bank’s liabilities and net worth. Liabilities are debts. Liabilities represent what the bank owes someone else. Net worth is the difference between a firm’s assets and its liabilities. In the sample balance sheet above, the bank’s assets include reserves, loans, government securities, and property & other assets. Reserves are the bank’s deposits in accounts with the Fed plus currency that is held in the bank’s vault. Required reserves are the vault cash and deposits at the Fed that commercial banks hold to meet the Fed’s requirement that for every dollar of deposits at a bank, a certain fraction must be kept as reserves. Excess reserves are the vault cash and deposits at the Fed that commercial banks hold is addition to those held to meet the Fed’s requirement that for every dollar of deposits at a bank, a certain fraction must be kept as reserves. Thus, excess reserves are the reserves that banks hold in excess of the required reserves. U.S. government securities are long-term debt instruments (such as bonds) issued by the U.S. Treasury to finance the budget deficits of the federal government. They are the most widely traded bonds in the United States and are thus the most liquid security. Liquidity is the relative ease and speed with which an asset can be converted into cash. Loans are assets for banks because they represent money that the borrowers owe to the bank. Deposits are liabilities for banks because they represent money that the bank is obligated to pay back to the depositors. By definition, net worth is assets minus liabilities.