Question

Bank A has checking account deposits of \(\$ 20\) million, the reserve requirement is 10 percent, vault cash equals \(\$ 2\) million, and deposits in the reserve account at the Fed equal \(\$ 1\) million. What do required reserves equal? What do excess reserves equal?

Short answer

The required reserves equal \$2 million, and the excess reserves equal \$1 million.

Step-by-step solution

Calculating Required Reserves

First, calculate the required reserves by multiplying the total deposits (\$20 million) by the reserve requirement (10%). So, \( Required\, Reserves = 20\, million * 0.10 = \$2\, million \).

Summation of Available Cash

Next, sum up the available cash, which is the vault cash (\$2 million) plus the balance in the reserve account at the Fed (\$1 million). So, \( Available\, Cash = 2\, million + 1\, million = \$3\, million \).

Calculating Excess Reserves

Lastly, subtract the required reserves from the total available cash to determine the excess reserves. So, \( Excess\, Reserves = Available\, Cash - Required\, Reserves = 3\, million - 2\, million = \$1\, million \)

Key concepts

Required Reserves

Banks are obligated to hold a portion of their deposits as required reserves. This is a way to ensure they have enough funds on hand to meet some of their liabilities. Here's how it works: if a bank has total deposits and the reserve requirement is set at a certain percentage, then the required reserves are calculated by multiplying the total deposits by this percentage. For instance, if a bank has \(20 million in deposits and a 10% reserve requirement, multiplying 20 million by 0.10 gives \)2 million in required reserves.

• Definition: Required reserves are the minimum amount of reserves a bank must hold.
• Purpose: They ensure liquidity and stability in the banking system.
• Formula: \( Required\, Reserves = Total\, Deposits \times Reserve\, Requirement \)

Excess Reserves

Excess reserves refer to the funds that a bank holds over and above the required reserves. These extra funds offer flexibility and can be used for lending or other purposes. To find excess reserves, you simply deduct the required reserves from the bank's total available cash.

• Definition: Funds held beyond the required reserves.
• Purpose: Provide banks with safety and lending opportunities.
• Calculation: \( Excess\, Reserves = Available\, Cash - Required\, Reserves \)

In our example, with \(3 million in total available cash and \)2 million in required reserves, the excess reserves amount to $1 million.

Vault Cash

Vault cash refers to the physical currency a bank keeps in its vault. This amount is part of the total reserves a bank holds. While it might seem like just the cash on hand, it plays a crucial role in the bank's operations by meeting immediate withdrawal demands.

• Definition: Physical cash held in the bank’s vault.
• Purpose: Allows immediate cash withdrawal by customers.
• Part of Reserves: Vault cash is counted when calculating the bank's total reserves.

In our scenario, the bank has $2 million in vault cash, which is crucial for daily operations and meeting customer needs.

Reserve Requirement

The reserve requirement is a regulation that sets the minimum fraction of customer deposits that each bank must hold as reserves. It is crucial for maintaining the liquidity and health of the financial system by ensuring banks do not lend out all their deposits.

• Definition: The minimum percentage of deposits to be held as reserves.
• Purpose: Ensures bank stability and the soundness of the financial system.
• Application: Varies by country and is set by the central bank.

In our exercise, a 10% reserve requirement means the bank must hold $2 million if there are $20 million in deposits.