Final answer:
The question as posed contains a discrepancy. If a bank has excess reserves of $4,000 and makes new loans of $70,000 without acquiring additional reserves, it cannot just meet reserve requirements—unless the reserve ratio is 0% as adopted since March 2020.
Step-by-step explanation:
The student has asked to find out what the required reserve ratio must be if the commercial banking system has excess reserves of $4,000 and then makes new loans of $70,000, ending up just meeting its reserve requirements. To determine the required reserve ratio, we use the following relationship:
Required Reserves = Required Reserve Ratio x Total Deposits
In this case, the total reserves needed after lending $70,000 would be the initial excess reserves plus the new loans made, which equals the initial excess reserves plus the required reserves for the new loans:
$4,000 (excess reserves) + Required Reserves = $4,000 + $70,000
Which means:
Required Reserves = $70,000 (since the system ends up just meeting its reserve requirements, the excess reserves are fully utilized)
Now, using the formula for required reserves, if we let r represent the required reserve ratio, we get:
$70,000 = r x $70,000
Dividing both sides by $70,000 gives us:
r = $70,000 / $70,000
r = 1 or 100%
However, this is not a feasible or logical reserve ratio as banks do not hold 100% reserves. Therefore, there must be a mistake in the question's premises since an excess reserve of $4,000 would not allow for new loans of $70,000 if the bank ends up just meeting its reserve requirements. As such, without additional information or a correction in the question's figures, we cannot accurately determine the required reserve ratio. It is important to note that as of March 2020, reserve requirements for all depository institutions have been reduced to 0%, effectively eliminating the reserve requirement.