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Modern banking
 
The goldsmith bankers were an early example of a financial intermediary.
A financial intermediary is an institution that specializes in bringing lenders and borrowers together.
A commercial bank borrows money from the public,crediting them whith a deposit. The deposit is a liability of the bank. It is money owed to depositors.It turn the bank  lends money to firms,households or govemments wishing to borrow.
Banks are not the only financial intermediaries,insurance companies,pension funds,and building societies also take money to relent them.
The payment,and are therefore part of the money stock.
Commercial banks are financial intermediaries whith a government  licence to make loans and issue deposits against
 which cheques can be written.
 In the UK,commercial bank system comprises about 600 registered banks,the National Girobank  operating through post offices,and a dozen trustee saving banks. Much of the most important single group is the London clearing banks. The clearing banks are so named because they have a central clearing house for handling payments by cheque.A clearing system is a set of arrangements in which debts between banks are settled to balance inter-bank accounts.
Suppose you bank whith "Barclays" but visit a supermarket that banks whith "Lloyds".
To pay for your shopping you write a cheque against your deposit at Barclays.
The  supermarket pays this cheque  into its account at Lloyds. In turn,Lloyds presents the cheque to Barclays,which will credit Lloyds account at Barclays and debit your account at Barclays by an equivalent amount.
Because you purchased goods from a supermarket using a different bank,a transfer of funds between the two banks is required. Crediting or debiting one bank's account at another bank is the simplest way of achieving this.
However on the same day someone else is probably writing a cheque on a Lloyds' deposit account to pay for some stereo aquipment from a shop banking with Barclays. The stereo shop pays the cheque into its Barclay's account,increasing its deposit. Barclays then pays the cheque into its  account at Lloyds where this person's account is simultaneously debited.Now the transfer flows from Lloyds to Barclays.


The clearing system calculates the net flows between the member clearing banks and these are the settlements they make between themselves.
Thus the system of clearing cheques represents another way society reduces the costs of making transactions.
The details of banking system vary from country to country but the general principle is much the same everywhere.