This problem illustrates how banks create credit and can thereby lend out more m

Question

This problem illustrates how banks create credit and can thereby lend out more money than has been deposited. Suppose that $100 is deposited in a bank. Experience has shown bankers that on average, only 8% of the money deposited is withdrawn by the owner at any time. Consequently, bankers feel free to lend out 92% of their deposits. Thus $92 of the original $100 is loaned out to other customers (to start a business for example). This $92 will become someone else's income and, sooner or later, will be re-deposited in the bank. Then, 92% of $92 or $92(0.92) = $84.64, is loaned out and eventually re-deposited. Of the $84.64, the bank again loans out 92%, and so on. Find the total amount of money deposited in the bank as a result of these transactions. The total amount of money deposited divided by the original deposit is called the credit multiplier. Calculate the credit multiplier for this example and explain what this number tells us.

Explanation / Answer

From the given question,

a)Initial money deposited by first customer=$100

money deposited by second customer= 0.92*100=$92

money deposited by third customer= 0.922 *100=$84.64

This is an Geometric progression(GP) with first term(a)=$100 and common ratio(r)=0.92

Sum to infinity of a GP is a/(1-r)

=100/(1-0.92)

=$1250

Total money deposited in the bank as a result of these transactions is $1250.

b)credit multiplier=$1250/$100=12.5

credit multiplier is 12.5

This number tells us that bank gets 12.5 times initial money by lending out in loan.

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