A new bank has vault cash of $1 million and $5 million in deposits

held at its Federal Reserve District Bank.
a. If the required reserves ratio is 8 percent, what dollar amount
of deposits can the bank have?
b. If the bank holds $65 million in deposits and currently holds
bank reserves such that excess reserves are zero, what
required reserves ratio is implied?

To answer both of these questions, we need to understand the concept of required reserves and how they are calculated.

Required reserves are the minimum amount of funds that banks must hold in reserve against their deposits. These reserves are typically held in the form of vault cash or held at the Federal Reserve District Bank.

a. To determine the dollar amount of deposits a bank can have based on the required reserves ratio, we multiply the required reserves ratio by the total deposits held at the Federal Reserve District Bank.

In this case, the required reserves ratio is 8 percent (or 0.08) and the deposits held at the Federal Reserve District Bank are $5 million.

So, the formula to calculate the dollar amount of deposits is:
Dollar amount of deposits = Deposits held at the Federal Reserve x Required reserves ratio
Dollar amount of deposits = $5 million x 0.08
Dollar amount of deposits = $400,000

Therefore, the bank can have $400,000 in deposits.

b. To determine the required reserves ratio based on the given information, we need to first calculate the total reserves of the bank.

The total reserves of a bank can be calculated by adding the vault cash and the deposits held at the Federal Reserve District Bank.

In this case, the total reserves are zero because the excess reserves are stated to be zero.

So, we have vault cash (VC) + deposits held at the Federal Reserve (DR) = Total reserves (TR)

$0 + $65 million = $65 million

Now, we can calculate the implied required reserves ratio.

The required reserves ratio can be calculated by dividing the required reserves by the total deposits.

In this case, the required reserves are the total reserves, which is $65 million.

So, the formula to calculate the required reserves ratio is:
Required reserves ratio = Total reserves / Deposits

Required reserves ratio = $65 million / $65 million
Required reserves ratio = 1

Therefore, the implied required reserves ratio is 100% or 1.

a. To determine the dollar amount of deposits the bank can have, we need to calculate the required reserves.

Given that the required reserves ratio is 8 percent, we can calculate the required reserves as follows:

Required reserves = Deposits * Required reserves ratio
Required reserves = $5,000,000 * 0.08
Required reserves = $400,000

The bank must hold $400,000 in reserves for every $5,000,000 in deposits.

To find the maximum dollar amount of deposits the bank can have, we subtract the required reserves from the vault cash:

Maximum deposits = Vault cash - Required reserves
Maximum deposits = $1,000,000 - $400,000
Maximum deposits = $600,000

Therefore, the bank can have a maximum of $600,000 in deposits.

b. If the bank holds $65 million in deposits and the excess reserves are zero, we can calculate the implied required reserves ratio.

Given that excess reserves are zero, we can determine the required reserves by subtracting the vault cash from the total reserves.

Total reserves = Vault cash + Deposits at Federal Reserve District Bank
Total reserves = $1,000,000 + $65,000,000
Total reserves = $66,000,000

Required reserves = Total reserves - Excess reserves
Required reserves = $66,000,000 - $0
Required reserves = $66,000,000

Now, we can calculate the implied required reserves ratio by dividing the required reserves by the deposits:

Implied required reserves ratio = Required reserves / Deposits
Implied required reserves ratio = $66,000,000 / $65,000,000

The implied required reserves ratio is approximately 1.015 or 101.5%.

a. 1/A = 0.08

0.08A = 1
A = $12.5 Million.

b.