Suppose that initially $10,000 is deposited in a bank. Experience has shown bank

Question

Suppose that initially $10,000 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 Experience has shown bankers that on average only 8% of the money deposited is withdrawn by the owner at any time.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 $9200 of the original $10,000 is loaned out to other customers (to start a business, for example). This $9200 will become someone else’s income and, sooner or later, will be redeposited in the bank (in somebody else’s account). Then 92% of $9200, i.e. $9200(0.92) = $8464, is loaned out again and eventually redeposited. Of the $8464, the bank again loans out 92% and so on. a) Find the total amount of money deposited (including the original deposit of $10,000) in the bank as a result of these transactions. b) 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

[solution - a]

amount deposited = 10000 + 10000 x 92/100 + 10000 x (92/100)^2 + 10000 x (92/100)^3.....................

= 10000[ 1 + 92/100 + (92/100)^2 + (92/100)^3.....................]

= 10000[ 1/1-(92/100)] = (100/8) X 10000 = 125000 [use sum of infinite terms = a/1-r]

solution -(b) credit multiplier = total deposit / orginal deposit

= 125000/10000 = 12.5

It means bank lending and deposit is increasing at 12.5 %.

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