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# Fractional Reserve Banking

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Introduction

﻿Fractional Reserve Banking 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: Bank Deposit Reserve Loan Bank #1 \$1,000 \$100 \$900 Bank #2 \$900 \$90 \$810 Bank #3 \$810 \$81 \$729 Bank #4 \$729 \$729 \$0 ...read more.

Middle

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 Deposit reserve loan Bank 1 x 0.2x 0.8x Bank 2 0.8x 0.16x 0.64x Bank 3 0.64x 0.128x 0.512x Bank 4 0.512x total 2.952x 0.488x 1.952x What did we find? 1. 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 ...read more.

Conclusion

complicacy, we assume in Round 1 the amount of money deposited in each bank is \$a, \$b, \$c Round2 deposit Reserve Loans Bank1 a 0.2a 0.8a Bank2 b 0.2b 0.8b Bank3 c 0.2c 0.8c Bank4 32000-(a+b+c) 6400-0.2(a+b+c) 25600-0.8(a+b+c) To reduce complicacy, we assume a situation as below Round3 deposit Reserve Loans Bank1 0.8b 0.16b 0.64b Bank2 0.8c 0.16c 0.64c Bank3 25600-0.8(a+b+c) 5120-0.16(a+b+c) 20480-0.64(a+b+c) Bank4 0.8a 0.16a 0.64a 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. deposit reserve Loans Bank1 in Round1 40,000 8000 32000 Bank2 in Round2 32000 6400 25600 Bank3 in Round3 25600 5120 20480 Bank4 in Round4 20480 Total 118080 19520 78080 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 ...read more.

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