A small state bank currently has reserves equal to $300,000.If the state reserve requirement is 20%,but the bank currently maintains a 30% reserve,what amount of reserves would the bank need if it met the reserve requirements exactly?
A) $200,000
B) $100,000
C) $300,000
D) $1,000,000
E) None of the above.

Question

Quizplus · Accepted Answer

The state reserve requirement is 20% of the bank's deposits. Since we do not know the bank's deposits, we cannot calculate the exact amount of reserves required to meet the reserve requirement. However, we do know that the bank currently maintains a 30% reserve, which is higher than the required 20% reserve.

To find out the amount of reserves needed to meet the reserve requirement exactly, we can use the following formula:

Reserves needed = Deposits x Reserve requirement percentage

Let R be the required reserves and D be the deposits.

We know that the current reserves, R, is equal to 30% of the deposits, so we can write:

R = 0.3D

We also know that the required reserves is 20% of the deposits, so we can write:

0.2D = R

Substituting the first equation into the second equation, we get:

0.2D = 0.3D
D = 0.2/0.3 x R
D = 0.67R

So, the deposits needed to meet the reserve requirement exactly is 0.67 times the required reserves.

Substituting the current reserves into the first equation, we get:

R = 0.3D
R = 0.3 x 300,000
R = 90,000

So, the current reserves of $300,000 is equivalent to a deposit of $900,000 ($300,000/0.3).

Therefore, the reserves needed to meet the reserve requirement exactly is:

R = 0.2 x $900,000
R = $180,000

So, the bank needs reserves of $180,000 to meet the reserve requirements exactly.

Subtracting the current reserves from the required reserves, we get:

$180,000 - $300,000 = -$120,000

This means that the bank has excess reserves of $120,000, which is 10% of the required reserves.

Therefore, the best choice is A) $200,000.

A Small State Bank Currently Has Reserves Equal to $300,000