Suppose the banking system currently has $400 billion in reserves, the reserve requirement is 8 percent, and excess reserves amount to $5 billion. What is the level of deposits?

Question

BlackTom AI · Accepted Answer

Reserves equal required reserves plus excess reserves; required reserves are the reserve ratio times deposits. Use these relationships to find deposits.

1) Relevant concepts:
- Total reserves (R) = Required reserves (RR) + Excess reserves (ER).
- Required reserves = reserve requirement (rr) × Deposits (D). Therefore D = RR / rr.

2) Step-by-step reasoning:
Given R = $400 billion, ER = $5 billion, and rr = 8% = 0.08.
First find required reserves: RR = R − ER = 400 − 5 = $395 billion.
Then solve for deposits: D = RR / rr.

3) Calculations with intermediate steps:
RR = 400 − 5 = 395 (billion dollars).
D = 395 ÷ 0.08.
Since 1 ÷ 0.08 = 12.5, D = 395 × 12.5 = 395 × (10 + 2 + 0.5) = 3950 + 790 + 197.5 = 4,937.5 (billion dollars).

4) Why this is correct:
Required reserves are the portion of deposits banks must hold; excess reserves are additional reserves above that requirement. Only the required portion determines the level of deposits via the reserve ratio, so we must subtract excess reserves from total reserves before dividing by the reserve requirement.

5) Why common alternatives are incorrect:
- Dividing total reserves by the reserve ratio (400 ÷ 0.08 = 5,000) is wrong because it treats excess reserves as required reserves.
- Using only excess reserves (e.g., 5 ÷ 0.08 = 62.5) ignores the required reserves entirely.
Any method that does not first subtract excess reserves from total reserves will produce an incorrect deposit level.

6) Conclusion:
The level of deposits is $4,937.5 billion, which matches the provided correct answer.

Suppose the banking system currently has $400 billion in reserves, the reserve requirement is 8 percent, and excess reserves amount to $5 billion. What is the level of deposits?单项选择题

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