When a bank accepts or collects deposits they keep some of the deposit as reserves (0.r is the reserve ratio) and advance the rest. As this money is spent it comes back into the banking system as someone else’s deposits. Some of this new deposit is kept as reserves and the rest advanced. This process continues until the new deposit becomes so small it can be ignored.
The value credit creation multiplier is an indicator of the final change in bank deposits which will stem from the initial change. We can calculate this as 1 / 0.r, where 0.r is the reserve ratio.
In the example below the credit creation multiplier equals 4 (that is, 1 / 0.25). Further we can work out the growth in the money supply (eventual increase in money supply), using the following formula: Eventual increase equals 1 / 0.r multiplied by the initial deposit in the money supply. In our example it is 4 times $100m equals $400m. The example below shows that loans given by one bank then become a deposit in another bank. Of that $75m deposited 25% must be kept in reserve ($18.75) and the remainder can be lent out ($56.25). This process continues through the banking system. We can also calculate the secondary expansion or credit created using this formula: Credit created equals (1 / 0.r multiplied by the initial deposit) minus the initial deposit.In our example it is $400m – $100m equals $300m.
The change in the money supply may not be as high as calculated because of leakages or withdrawals from the credit creation process. Banks tend to lose reserves as the public will not deposit the whole of the loans back. The public may retain some of the loan in the form of cash, or banks may be unable to find creditworthy customers to make advances to, or funds may get diverted into government securities.
Reserves may also be lost to taxation and imports (under a fixed exchange rate). The reasons for the initial increase in bank reserves could be the public banking more notes and coins than they withdraw, or public debt maturing. If a Central Bank buys back (purchases) government securities or other financial assets from the public or financial institutions, then there will be an increase in bank reserves.