# Fractional Reserve Banking

Highly contrived example with 3% reserve ratio:

Lets say I deposit $$100 in a bank. Bank loans$$97 PersonA, keeps $$3 as reserve PersonA buys something from PersonB for$$97
PersonB deposits it in Bank, bank loans 97%of $$97 to PersonC, keeps 3% in reserves. PersonC buys something from PersonD for$$94
This cycle goes on until until 100/0.03=$$3333 is in deposits,$$3233 in loans and $100 in reserves.  Is it accurate to say, if a bank starts with $100 as reserves, they can loan out $3333 assuming reserve ratio is 0.03%? In the above example, if everyone repays the loan ($3233) can bank lend it again? That doesn't sound correct. Where am I going wrong here?

Yes with reserve requirement of $$0.03\%$$ the maximum amount of money that can be created will be given by $$\frac{100}{0.03} = {\\\}3333.33$$, with $${\\\} 100$$ reserves and $${\\\}3233.33$$ new money.
Yes if everyone repays the $${\\\}3233.33$$ and there is still demand for loans bank can lend it again. To be clear the $${\\\}3233.33$$ will not become new reserve, so the reserve ratio would still have to be maintained. If people start paying the loans back with no demand for new loans the money supply will start contracting.
However, with presently reserve requirements being set to zero by Fed the only constraint is the demand for loans. Furthermore, while in past banks tended to hold almost no excess reserves (see this graph from Fred), after 2008 they started holding excess reserves and in such situation the multiplier idea becomes less useful abstraction as banks can always borrow extra reserves from other banks that have extra reserves if they need to. For example, if system holds excess reserves when the $${\\\}3233.33$$ would be repaid (assuming all this is done through lending and borrowing with single bank) bank could just get extra reserves from other banks holding excess reserves, even when banking system as whole would not be allowed to create new reserve (without central bank agreeing to that). McLeay, Radia, & Thomas(2014), money creation in the modern economy is good source for explaining how fractional reserve system works in such situation.
• Meaning, bank can reserve 0.03% of $3222.33 =$97 and lend out \$3136.33 and start the cycle again and again? Each time increasing reserve by a bit – Jean Oct 27 '20 at 17:59