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for making this question clear let's create a simplified world when there are only 3 private banks (bank A, bank B, bank C) in the world, and 1 central bank. let's also assume that all the citizen in this simplified world have all their money saved in those 3 banks.

let's also assume each bank has this capital inside:

bank A : 50k dollars

bank B : 30k dollars

bank C : 70k dollars

now let's assume bank B ask for a loan to the central bank of 20k with an intrest rate of 0.7%.

logically bank B can only take money weather from bank A or C to pay back the loan to the central bank. and so it does.

but this takes the money out of the system, and back to the central bank with that 0.7% more.

now let's repeat this process over and over again, it will reach to a point where there will be no more money on the system..then what happens?

the central bank prints more money and make another loan to pay back the other loan?..

and over and over again?

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  • $\begingroup$ So essentially your questions are "1. does a single central bank loan with positive interest rate decrease money supply in the long-run?" and "2. If the answer to 1. is Yes, how does the money supply not contract?", right? $\endgroup$
    – Giskard
    Commented Jul 2, 2022 at 8:02
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    $\begingroup$ @Andrew Nic: your case might be a little oversimplified. I think you need to consider both sides of the balance sheet to investigate this properly. that is you need track both, flows of assets and liabilities. Also, when you say "capital" do you actually mean the size of the balance sheet or really bank capital? These are two different things. $\endgroup$
    – BrsG
    Commented Jul 7, 2022 at 15:15

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The main problem with this example is that banks usually don't take out loans from the central bank.

A bank usually only borrows money from a central bank for extremely short periods via repos in case they need liquidity (e.g. to meet legal requirements like the LCR).

The way banking works is that banks get deposits and issue bonds. They provide loans to the economy with the funds they have available through these, thereby affecting overall money supply.

A central bank mainly only steps in to make sure there is enough liquidity (by buying financial instruments) or to curb inflation (by selling financial instruments it owns).

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  • $\begingroup$ When a central bank buys financial instruments this is effectively a loan to whoever sells them. When the instrument matures the effect is a net transfer of money to the central bank. So do they have to keep buying more and more each year just to keep the money supply steady? $\endgroup$
    – user20574
    Commented Mar 27 at 10:37
  • $\begingroup$ @user253751, central banks usually only buy financial instruments in the secondary market. Assume you are a bank and the CB buys a US government bond from you. How is that effectively a loan to the bank? It is no different from the bank selling the bond to anyone else in the secondary market (apart from the CB being able to pay for it with money they just created). $\endgroup$
    – Alex
    Commented Apr 15 at 23:14
  • $\begingroup$ you end up with one less bond and one hundred more dollars, same as if you borrowed it with a bond as collateral. When the bond matures you still have one hundred dollars which is the same as you would have if you'd kept the bond, so the scenarios are no longer any different. $\endgroup$
    – user20574
    Commented Apr 15 at 23:23
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but this takes the money out of the system, and back to the central bank with that 0.7% more

It does not take money out of a system with "0.7% more". Central bank sends all net profits to the government. Hence central bank will either spend that money on its cost of operation (which means the money will circulate more as people spend it) or it will be send to the government and it will circulate further when government spends it. Hence the money supply only contracts by the amount of the money created by the loan (here I mean all money derived by the loan in case the money was previously lent further) not by the amount interest.

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