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Posted 2 months ago

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%10 \%.
\begin{tabular}{ll} 
Assets & Liabilities \& Equity \\
\hline Loans: $100,000\$ 100,000 & Deposits $100,000\$ 100,000 \\
Total reserves: $10,000\$ 10,000 & Owner's equity: $30,000\$ 30,000 \\
Bonds: $20,000\$ 20,000 & \\
Total Assets: $130,000\$ 130,000 & $130,000\$ 130,000
\end{tabular}

If Vizzini deposits $5,000\$ 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\$ 50,000
(B) $40,000\$ 40,000
(C) $150,000\$ 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 Reserve Ratio=Total ReservesDeposits \text{Reserve Ratio} = \frac{\text{Total Reserves}}{\text{Deposits}}
step 2
Substitute the given values into the reserve ratio formula: Reserve Ratio=$10,000$100,000=0.1 \text{Reserve Ratio} = \frac{\$10,000}{\$100,000} = 0.1 or 10% 10\%
step 3
Determine the initial money multiplier using the formula Money Multiplier=1Reserve Ratio \text{Money Multiplier} = \frac{1}{\text{Reserve Ratio}}
step 4
Calculate the money multiplier with the reserve ratio: Money Multiplier=10.1=10 \text{Money Multiplier} = \frac{1}{0.1} = 10
step 5
Calculate the maximum change in demand deposits using the formula Change in Demand Deposits=Money Multiplier×Initial Deposit \text{Change in Demand Deposits} = \text{Money Multiplier} \times \text{Initial Deposit}
step 6
Substitute the values into the change in demand deposits formula: Change in Demand Deposits=10×$5,000=$50,000 \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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