Deposit multiplier is the numerical measure of change in the total deposits of a bank due to a change in the primary deposits. Thus, if the initial primary deposits increase by ΔDP and total deposits (both the primary as well as the derivative deposits) change by ΔDT, then the deposit multiplier
k = ΔDT / ΔDT
The limit of credit creation or the extent to which total deposits will increase with the primary deposits of a given sum and a given reserve ratio can be found out by the deposit multiplier whose value is calculated by the following formula
k = 1/X
Where k is the deposit multiplier and X is the reserve ratio. Thus, when reserve ratio Rr is 20 per cent of the deposit money, the deposit multiplier k will be
k = 1/20% = 1/20/100 = 5
ΔDT = k.DP
where DP is the initial or primary deposit. In our example, with an initial deposit of $1000, the increase in total deposits will be
DT = $1000 X k
= $1000 X 1/x
= $1000 X 1/20%
= $1000 X 5
= $5,000
It should be clear from the above example that lower the cash reserve requirements and hence lower the value of x, higher shall be the value of deposit multiplier k and larger shall be the amount of total additions to deposits. Thus, with a x of 10%, k will be $10000. On the other hand, if x is 40 per cent, k will be 2.5 and an initial deposit of $1000 will result in total additional deposits of $2500 only. Thus, with high x the deposit multiplication is smaller.
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