Currency and checkable deposits?

Question

A question regarding currency and checkable deposits:

Refer to the following information about a banking system: new currency deposited in the system = $40 billion; legal reserve ratio = 0.20; excess reserves prior to the currency deposit = $0.

The $40 billion deposit of new currency will support total checkable deposits of:

a. $160 billion

b. $200 billion

c. $40 billion

d. $128 billion

Any help would be greatly appreciated. Thank you!

Answer 1

$40 billion new currency deposited with the banking system create both a deposit liability of $40 billion and Assets of Cash (or deposit Reserves with the Central bank) of $40 billion. With  $40 billion of reserves, the banking system can support a maximum of $40billion/0.2= $200 billion of total deposits inculding the first $40 billion deposits made with new currency.

Answer 2

First wave it will be only $40 billions

Secondary and further initiated deposits by this $40 deposit will be $40/0.2=$200

So answer "C" is right if they hold excess reserves and "B" is right if they continue to lend further and there is no excess and drains cash-on-hand.