Putting that into a table so that you can visualize it differently:
Iteration #
|
Deposited
|
=
|
Reserves
|
+
|
Available to Lend
|
Bank
Lends to
|
1. Adam
|
1,000.00
|
=
|
100.00
|
+
|
900.00
|
Anne
|
2. Brian
|
900.00
|
=
|
90.00
|
+
|
810.00
|
Brenda
|
3. Chris
|
810.00
|
=
|
81.00
|
+
|
729.00
|
Cathy
|
4. David
|
729.00
|
=
|
72.90
|
+
|
656.10
|
Dale
|
And the cycle continues…
| ||||||
How long can this cycle continue?
The following table illustrates how this happens over many iterations in the fractional reserve banking system:
Iteration #
|
Deposited
|
Held
in Reserve
|
Loan from Deposit
|
Loans
|
Reserves
|
Deposits
|
1
|
1,000.00
|
100.00
|
900.00
|
0.00
|
100.00
|
1,000.00
|
2
|
900.00
|
90.00
|
810.00
|
900.00
|
190.00
|
1,900.00
|
3
|
810.00
|
81.00
|
729.00
|
1,710.00
|
271.00
|
2,710.00
|
4
|
729.00
|
72.90
|
656.10
|
2,439.00
|
343.90
|
3,439.00
|
And a little while later (87% there)…
| ||||||
19
|
150.09
|
15.01
|
135.09
|
7,649.15
|
864.91
|
8,649.15
|
20
|
135.09
|
13.51
|
121.58
|
7,784.23
|
878.42
|
8,784.23
|
Closer towards those limits (97.5% there)…
| ||||||
34
|
30.90
|
3.09
|
27.81
|
8,721.87
|
972.19
|
9,721.87
|
35
|
27.81
|
2.78
|
25.03
|
8,749.68
|
974.97
|
9,749.68
|
36
|
25.03
|
2.50
|
22.53
|
8,774.72
|
977.47
|
9,774.72
|
And closer towards those limits…
| ||||||
115
|
0.01
|
0.00
|
0.01
|
8,999.95
|
999.99
|
9,999.95
|
116
|
0.01
|
0.00
|
0.00
|
8,999.95
|
1,000.00
|
9,999.95
|
And we hit those limits!
| ||||||
137
|
0.00
|
0.00
|
0.00
|
8,999.99
|
1,000.00
|
9,999.99
|
138
|
0.00
|
0.00
|
0.00
|
9,000.00
|
1,000.00
|
10,000.00
|
2 decimal places displayed — accurate to 28 decimal places
| ||||||
The examples above all use a 0.1 (10%) reserve requirement, but different countries can have different reserve requirements.
Looking at some of the equations above again:
Loans = ( Initial Deposit ÷ Reserve Requirment ) − Initial Deposit
Deposits = ( Initial Deposit ÷ Reserve Requirment )
The second equation there is formally called the "money multiplier". As the reserve requirement approaches zero, "Deposits" approaches infinity. Here’s a graph that shows reserve requirements from 0.1 up to 1:
Notice that as the reserve requirement becomes lower, the amount of money that a deposit can generate becomes higher and higher.
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