17) If a bank has $100,000 of checkable deposits, a required reserve ratio of 20 percent, and it
holds $40,000 in reserves, then the maximum deposit outflow it can sustain without altering its
balance sheet is
A) $30,000.
B) $25,000.
C) $20,000.
D) $10,000.

To solve this problem, we need to figure out how much deposit outflow the bank can sustain without altering its balance sheet, given the following information:

- Checkable deposits: $100,000
- Required reserve ratio: 20%
- Reserves held: $40,000

### Step 1: Calculate required reserves
The required reserve ratio is 20%, which means the bank must hold 20% of its checkable deposits in reserves.

\[
\text{Required reserves} = 0.20 \times 100,000 = 20,000
\]

So, the bank needs to hold at least $20,000 in reserves.

### Step 2: Calculate excess reserves
The bank holds $40,000 in total reserves, but it only needs $20,000 to meet the reserve requirement. The excess reserves are:

\[
\text{Excess reserves} = 40,000 - 20,000 = 20,000
\]

### Step 3: Determine maximum deposit outflow
The bank can afford to lose deposits until it has only the required amount of reserves left. For every dollar of deposits that flows out, 20% of that amount will be freed from the required reserve.

Let $ x $ be the maximum deposit outflow. When deposits flow out, the required reserves will decrease by 20% of that amount. Therefore, the reduction in required reserves is $ 0.20 \times x $, and the bank can sustain this outflow until the reduction in required reserves matches the excess reserves of $20,000.

Thus, we can set up the equation:

\[
0.20 \times x = 20,000
\]

Solving for $ x $:

\[
x = \frac{20,000}{0.20} = 100,000
\]

### Conclusion
The maximum deposit outflow the bank can sustain is **$100,000**, which corresponds to answer choice **C) $20,000**.

Would you like further details or have any other questions?

Here are 5 related questions to deepen your understanding:
1. What would happen if the bank's excess reserves were zero?
2. How does changing the reserve requirement ratio affect the bank's ability to handle deposit outflows?
3. What is the role of the Federal Reserve in determining the required reserve ratio?
4. If the reserve requirement increases to 30%, how would that affect the maximum deposit outflow?
5. How do banks manage liquidity to prevent balance sheet alterations during significant deposit outflows?

**Tip:** Understanding the concept of excess reserves is crucial for determining a bank's liquidity and its ability to withstand withdrawals.

If a bank has $100,000 of checkable deposits, a required reserve ratio of 20 percent, and it holds $40,000 in reserves, then the maximum deposit outflow it can sustain without altering its balance sheet is A) $30,000. B) $25,000. C) $20,000. D) $10,000.

Learn how to calculate the maximum deposit outflow a bank can sustain with $100,000 checkable deposits, a 20% required reserve ratio, and $40,000 reserves. This problem involves reserve ratios, excess reserves, and linear equations, suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation