Fractional Reserve Banking

by huigraceli (student)

AS and A Level Business Studies

By Grace Li

Materials online about fractional reserve banking pg1~2

My thinking about how the system really works pg 3

My thinking about Ms.Aimee’s simulation pg4~5

Fractional Reserve Banking

Fractional Reserve Banking refers to a banking system which requires the commercial banks to keep only portion of the money deposited with them as reserves. The bank pays interest on all deposits made by its customers and uses the deposited money to make new loans. In order to understand how fractional reserve banking works, let's look at the following example.

Somebody deposits $1,000 with Bank A. Bank A is obligated by law to keep 10% of the deposited money as a reserve, that's why the bank keeps $100 and lends out $900. Somewhere down the road the $900 loan is deposited in another chequing account (it might or might not be with the same bank). This second bank also wants to make money by giving out loans, that's why it keeps the required $90 and lends $810. Fast forward to a deposit with a fourth bank and you'll get the following:

As you can see from the table above, the banks created $2,439 based on the first $1,000 deposited. Talking about license to print money. The fractional reserve banking works for now, because the total amount of withdrawals is offset by deposits made at the same time. While the depositors are confident at the fractional-reserve banking system, a very small part of all deposits is withdrawn at the same time allowing the banks to handle the withdrawals through their minuscule reserves. However when people's confidence in the banks is shaken, bank runs are possible, and the entire banking and financial system can collapse.

Source: http://www.centralbanksguide.com/fractional+reserve+banking/

The expansion of $100 of central bank money through fractional-reserve lending with a 20% reserve rate. $400 of commercial bank money is created virtually through loans.

Although no new money was physically created in addition to the initial $100 deposit, new commercial bank money is created through loans. The 2 boxes marked in red show the location of the original $100 deposit throughout the entire process. The total reserves plus the last deposit (or last loan, whichever is last) will always equal the original amount, which in this case is ...

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Source: http://www.centralbanksguide.com/fractional+reserve+banking/

The expansion of $100 of central bank money through fractional-reserve lending with a 20% reserve rate. $400 of commercial bank money is created virtually through loans.

http://en.wikipedia.org/wiki/Fractional-reserve_banking#cite_note-24#cite_note-24

How does it work?

First, let’s analyze the model we saw last 2 pages.

Let initial deposit = x dollars, reserve requirement ratio is 20%

Note: After bank 4 receive the deposit money, the system would be ended and a loan would not be given out by bank4, so it would be no need for Bank4 to calculate their reserve that would be kept and loans that would be given out in the next round

What did we find?

0.512x+ 0.488x= 1x

Last deposit + reserve = initial deposit

Why it was the reserve + last deposit = initial deposit? Why did reserve keep these parts of initial deposit? Why reserve is not double counted?

Let’s look at fraction : Total reserve + last deposit = 1

=0.2 + 0.16 + 0.128 + 0.512

=0.2 + 0.2*(1-0.2) + 0.2*(1-0.2)2 + 0.83

=(0.2 + 0.2*0.8 + 0.2*0.82) + 0.83

= Total Reserve + last deposit

So, reserve is the sum of numbers that has taken the fraction20% of the deposit, but the last deposit is the number that had taken the fraction80% in every step, so total reserve is effected by all the 3 steps of being taken 20%fraction, and last deposit was effected by all the 3 steps of being taken 80%fraction, so these 2 numbers( total reserve and last deposit) actually makes up with each other and they add up to 100%

In the equation above((0.2 + 0.2*0.8 + 0.2*0.82) + 0.83=1), why do we add up the reserves but we cube the loans? (last deposit= loan made in the round before)

Because reserves in each round is static, it doesn’t go into the recycle, so it would not be double counted during the circulation of money, however, loans are recycled in the system, so we shouldn’t add up these 3 loan numbers because it is double counted.

1.952x + 0.488x + 0.152x = 2.952x

Loan + initial deposit = total deposit

Actually it was the loan that was recycled again and again, so it was the loans that was double counted, and it was the loans that created the extra money.

Ms.Amiee’s simulation

There are 4 banks in a town. Every bank has an initial deposit of 10,000. The reserve requirement ratio is 20%. In each round, everybody has to do their best to make a loan and deposit it into a different bank.

Let’s assume that all banks lent out all their loans in each round, all borrowers deposited all loaned money in each round.

Question: How much money would be created after 3 rounds?

To answer the question, we can first think about what would happen during the 3 rounds.

Table: deposit, reserbe and loans situations in each round

Note: Reserve= reserve that is saved in this round

Loans = Loans that are lent in this round

Deposit= the money people deposit in the next bank

So in the table Round2, the deposit was actually completed at the end of Round1 before Round2 started.

To reduce complicacy, we assume in Round 1 the amount of money deposited in each bank is $a, $b, $c

To reduce complicacy, we assume a situation as below

As we can see above, the Ms.Aimee’s simulation is equivalent to the model we first saw in the first page. We can assume that there’s only one bank in each round.

Note: In the table above, same color = things we have done in the same round. For example, at the end of round 2, all people made loans in bank2 and deposit it in Bank3, and in the end of round2, banks saved 20% reserve from the deposit they had before Round2 began( at the end of Round1), so 6400 reserve, 25600 Loans, 25600 deposit are in the same color: yellow.

The total money created would be 118080-40000=78080 dollars= total loans