Complete the following problems from chapters 4 and 5 in the textbook:

1. 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?

2. 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?

3. A bank has $110 million in deposits and holds $10 million in vault cash.
a. If the required reserves ratio is 10 percent, what dollar amount of reserves must be held at the Federal Reserve Bank?
b. How would your answer in Part (a) change if the required reserves ratio was increased to 12 percent?

4. Assume that Banc One receives a primary deposit of $1 million. The bank must keep reserves of 20 percent against its deposits. Prepare a simple balance sheet of assets and liabilities for Banc One
immediately after the deposit is received.

5. The SIMPLEX financial system is characterized by a required reserves ratio of 11 percent; initial excess reserves are $1 million, and there are no currency or other leakages.
a. What would be the maximum amount of checkable deposits after deposit expansion, and what would be the money multiplier?
b. How would your answer in (a) change if the reserve requirement had been 9 percent?

6. Challenge Problem ABBIX has a complex financial system with the following relationships: The ratio of required reserves to total deposits is 15 percent, and the ratio of noncheckable deposits to checkable deposits is 40 percent. In addition, currency held by the nonbank public amounts to 20 percent of checkable deposits. The ratio of government deposits to checkable deposits is 8 percent.
Initial excess reserves are $900 million.
a. Determine the M1 multiplier and the maximum dollar amount of checkable deposits.
b. Determine the size of the M1 money supply.
c. What will happen to ABBIX’s money multiplier if the reserve requirement decreases to 10 percent while the ratio of noncheckable deposits to checkable deposits falls to 30 percent?
Assume the other ratios remain as originally stated.
d. Based on the information in (c), estimate the maximum dollar amount of checkable deposits, as well as the size of the M1 money supply.
e. Assume that ABBIX has a target M1 money supply of $2.8 billion. The only variable that you have direct control over is the required reserves ratio. What would the required reserves ratio have to be to reach the target M1 money supply amount? Assume the other original ratio relationships hold.
f. Now assume that currency held by the nonbank public drops to 15 percent of checkable deposits and that ABBIX’s target money supply is changed to $3.0 billion. What would the required reserves ratio have to be to reach the new target M1 money supply amount? Assume the other original ratio relationships hold.