Chapter 12: Problem 423

Suppose a commercial bank has deposits of $\$ 400,000$ and has made loans and investments of $\$ 315,000 .$ Assume also that deposits are its only source of reserves. If the required reserve ratio is $20 \%$, how much are its excess reserves?

Short Answer

Expert verified

The excess reserves of the bank are $-\$235,000$, indicating a shortfall of $\$235,000$ in reserves. The bank needs to raise additional reserves to meet the required reserve ratio.

Step by step solution

Find the Total Reserves of the Bank

To find the total reserves of the bank, we need to multiply its deposits by the required reserve ratio. The formula to calculate total reserves is: $Total\ Reserves = Deposits * Required\ Reserve\ Ratio$ Given the deposits are $\$400,000$ and the required reserve ratio is $20\%$, we plug in these values into the formula: $Total\ Reserves = \$400,000 * 20\%$

Convert Required Reserve Ratio to Decimal

Before we move further, let's convert the required reserve ratio from percentage to decimal. To convert 20% into decimal, divide it by 100: $20\% = \frac{20}{100} = 0.2$ Now we can continue the calculation using the decimal value of the required reserve ratio.

Calculate the Total Reserves

With the required reserve ratio converted to decimal, we can now multiply it by the deposits to find the total reserves: $Total\ Reserves = \$400,000 * 0.2 = \$80,000$ The total reserves of the bank are $\$80,000$.

Calculate the Excess Reserves

To find the excess reserves of the bank, we need to subtract the loans and investments from the total reserves. The formula to calculate excess reserves is: $Excess\ Reserves = Total\ Reserves - Loans\ and\ Investments$ Given the loans and investments are $\$315,000$ and the total reserves are $\$80,000$, we plug in these values into the formula: $Excess\ Reserves = \$80,000 - \$315,000$

Find the Excess Reserves

Now we can perform the subtraction: $Excess\ Reserves = -\$235,000$ The excess reserves of the bank are $-\$235,000$, which means the bank has a shortfall of $\$235,000$ in reserves. In this case, the bank needs to raise additional reserves to meet the required reserve ratio.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Required Reserve Ratio

To effectively manage a bank's liquidity and ensure it remains financially stable, regulatory authorities set a 'required reserve ratio' – a mandatory percentage of depositors' balances that banks must hold and not lend out. This ratio is expressed as a percentage.

To convert the required reserve ratio from a percentage to a decimal for calculation purposes, simply divide the ratio by 100. For instance, a 20% required reserve ratio becomes 0.2 when divided by 100. This step is critical in determining the total reserves the bank needs to maintain.

Bank Reserves Explained

Bank reserves are the currency deposits that are not lent out to the bank's clients and are held in the bank's reserve account to fulfill withdrawal requests and other financial obligations. These reserves are composed of two types: 'required reserves' based on the required reserve ratio and any 'excess reserves', which are funds exceeding this minimum threshold. Calculating total reserves requires us to multiply the bank's deposits by the required reserve ratio in decimal form. The concept of bank reserves is central to maintaining a stable banking system and preventing insolvency.

The Deposit Multiplier Effect

The deposit multiplier is a key concept in banking which illustrates how banks can amplify the initial deposits they receive through the lending process. The multiplier effect refers to the ability of a bank to increase the money supply in the economy. It is inversely related to the required reserve ratio: a lower ratio means banks can lend out more, thus creating a higher deposit multiplier.

However, this calculation needs to be approached with caution. It doesn't take into account other factors like currency drain or banks choosing to hold excess reserves, hence in the real-world scenario, the multiplier effect can be less pronounced than the theory suggests.

Suppose a commercial bank has deposits of \(\$ 400,000\) and has made loans and investments of \(\$ 315,000 .\) Assume also that deposits are its only source of reserves. If the required reserve ratio is \(20 \%\), how much are its excess reserves?