Question

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Posted 2 months ago

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Rous Bank's balance sheet is shown below. Assume that banks fully loan out and all money is held in banks. The reserve requirement is $10 \%$.
\begin{tabular}{ll}
Assets & Liabilities \& Equity \\
\hline Loans: $\$ 100,000$ & Deposits $\$ 100,000$ \\
Total reserves: $\$ 10,000$ & Owner's equity: $\$ 30,000$ \\
Bonds: $\$ 20,000$ & \\
Total Assets: $\$ 130,000$ & $\$ 130,000$
\end{tabular}
If Vizzini deposits $\$ 5,000$ into a demand deposit at Rous Bank, what is the maximum change in demand deposits in this banking system as a result of that deposit?
Choose 1 answer:
(A) $\$ 50,000$
(B) $\$ 40,000$
(C) $\$ 150,000$
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 1

Calculate the initial reserve ratio using the formula $\text{Reserve Ratio} = \frac{\text{Total Reserves}}{\text{Deposits}}$

step 2

Substitute the given values into the reserve ratio formula: $\text{Reserve Ratio} = \frac{\$10,000}{\$100,000} = 0.1$ or $10\%$

step 3

Determine the initial money multiplier using the formula $\text{Money Multiplier} = \frac{1}{\text{Reserve Ratio}}$

step 4

Calculate the money multiplier with the reserve ratio: $\text{Money Multiplier} = \frac{1}{0.1} = 10$

step 5

Calculate the maximum change in demand deposits using the formula $\text{Change in Demand Deposits} = \text{Money Multiplier} \times \text{Initial Deposit}$

step 6

Substitute the values into the change in demand deposits formula: $\text{Change in Demand Deposits} = 10 \times \$5,000 = \$50,000$

Answer

The maximum change in demand deposits in the banking system as a result of Vizzini's deposit is \( \$50,000 \).

A

Key Concept

Money Multiplier Effect

Explanation

The money multiplier effect describes how an initial deposit can lead to a larger increase in the total money supply due to banks lending out their excess reserves, while maintaining the required reserve ratio.

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