Assume a bank has $5 million in deposits and $1 million in vault
cash. If the bank holds $1 million in excess reserves and the required
reserves ratio is 8 percent, what level of deposits are being held?
To determine the level of deposits being held, we need to understand how excess reserves and the required reserves ratio affect the deposit levels.
First, let's calculate the required reserves. The required reserves represent the minimum amount of reserves that the bank is required to hold based on the deposits it receives. The required reserves are calculated as a percentage of the bank's deposits, which is given as 8 percent in the question.
Required Reserves = Required Reserves Ratio * Deposits
Given that the required reserves ratio is 8 percent and the bank holds $5 million in deposits, we can calculate the required reserves:
Required Reserves = 8% * $5 million
Required Reserves = $0.08 * $5 million
Required Reserves = $0.4 million
Next, we need to calculate the excess reserves. Excess reserves are the reserves that banks hold above the required reserves. In this case, the bank holds $1 million in excess reserves.
Excess Reserves = Total Reserves - Required Reserves
Given that the vault cash is $1 million and the required reserves are $0.4 million, we can calculate the total reserves:
Total Reserves = Vault Cash + Required Reserves
Total Reserves = $1 million + $0.4 million
Total Reserves = $1.4 million
With the total reserves and the excess reserves known, we can find the level of deposits that the bank is holding:
Deposits = Total Reserves + Excess Reserves
Deposits = $1.4 million + $1 million
Deposits = $2.4 million
Therefore, the bank is holding $2.4 million in deposits.
To determine the level of deposits being held, we need to calculate the total reserves.
Reserves include both required reserves and excess reserves.
Required reserves = Deposits * Required reserves ratio
Given that the required reserves ratio is 8 percent and deposits are $5 million:
Required reserves = $5 million * 0.08 = $400,000
Total reserves = Required reserves + Excess reserves
Total reserves = $400,000 + $1 million = $1,400,000
Finally, to determine the level of deposits being held:
Deposits = Total reserves + Vault cash
Deposits = $1,400,000 + $1 million = $2,400,000
Therefore, the bank is holding $2,400,000 in deposits.
$5 million x 8%= $0.4 million
$5 million- ($1 million+ $1 million + $0.4 million)= $2.6 million