Question

Suppose a commercial bank has \(\$ 100,000\) in deposits and has made loans of \(\$ 65,000 .\) If the required reserve ratio is \(20 \%\) (a) how much additional money can the bank lend, and (b) how much can the banking system as a whole add to the money supply as a result of the loan?

Short answer

The bank can lend an additional \( \$15,000\) and the banking system as a whole can add a maximum of \( \$75,000\) to the money supply as a result of the additional loan capacity.

Step-by-step solution

Calculate the Required Reserves

Required reserves are calculated as a percentage of the total deposits according to the reserve ratio. Here, the reserve ratio is 0.20 (20%). Required Reserves \(= \) Total Deposits × Reserve Ratio Required Reserves \(= \$100,000 × 0.20 = \$20,000\)

Calculate the Available Reserves

To find the available reserves, subtract the loans made from the total deposits. Available Reserves \(= \) Total Deposits - Loans Available Reserves \(= \$100,000 - \$65,000 = \$35,000\)

Calculate the Additional Loan Capacity

Now, subtract the required reserves from the available reserves to find out the additional loan amount the bank can lend. Additional Loan Capacity \(= \) Available Reserves - Required Reserves Additional Loan Capacity \(= \$35,000 - \$20,000 = \$15,000\) The answer to part (a) is that the bank can lend an additional \( \$15,000\).

Calculate the Money Multiplier

The money multiplier is calculated as the inverse of the reserve ratio. Money Multiplier \(= \frac {1}{Reserve\, Ratio} = \frac {1}{0.20}\) Money Multiplier \(= 5\)

Calculate the Maximum Increase in the Money Supply

The maximum increase in the money supply due to additional lending is calculated by multiplying the money multiplier by the additional loan capacity. Maximum Increase in Money Supply \(= \) Money Multiplier × Additional Loan Capacity Maximum Increase in Money Supply \(= 5 × \$15,000 = \$75,000\) The answer to part (b) is that the banking system as a whole can add a maximum of \( \$75,000\) to the money supply as a result of the additional loan capacity.

Key concepts

Commercial Bank

Commercial banks play a vital role in the modern economy. These institutions are financial intermediaries that accept deposits from the public and provide loans to individuals and businesses.
The primary goal is to earn profits through interest differentials, where they charge higher interest on loans than they pay on deposits.
This profit-making function helps in circulating money within the economy and enabling individuals and businesses to invest or consume more. The banking operations rely heavily on the concept of reserves. These banks are required by law to hold a certain percentage of their deposits as reserves, primarily to ensure stability and liquidity.
Reserves are held in the form of cash in the bank’s vault or deposits with the central bank. These reserves help maintain confidence in the banking system as they ensure that the bank has enough money to meet customers' withdrawal needs.

Money Multiplier

The money multiplier is a crucial concept in understanding how the banking system creates money.
It is a factor that quantifies the amount of money that the banking system generates with each dollar of reserves.
In essence, it shows the potential for the entire banking system to expand the money supply through the process of making loans.To calculate the money multiplier, use the formula:

• The inverse of the Required Reserve Ratio: \[ Money\ Multiplier = \frac{1}{Required\ Reserve\ Ratio} \]

For instance, if the required reserve ratio is 20%, the money multiplier will be 5. This means that for every dollar of reserve, banks can potentially create five dollars in the money supply.
This process magnifies an initial deposit through a chain of additional borrowing and lending events.

Money Supply

Money supply refers to the total amount of monetary assets available in an economy at a particular time. It encompasses all the currency in circulation and the balances held in checking and savings accounts.
Central banks, like the Federal Reserve, monitor and control the money supply to stabilize the economy. The money supply is influenced by various factors, including the money multiplier and the activity of commercial banks.
When banks lend money, they create new money within the economy, adding to the money supply. Conversely, when loans are paid back, the money supply decreases as the money returns to the bank as reserves. Understanding money supply is crucial for insight into economic indicators like inflation and interest rates. A larger money supply can lead to lower interest rates, making borrowing more attractive, but if uncontrolled, it might result in inflation.

Required Reserve Ratio

The required reserve ratio is a regulatory measure that determines the minimum amount of reserves a bank must hold in relation to customer deposits.
It is a powerful tool for central banks to control money supply within the economy. For example, if a bank has $100,000 in deposits and the reserve ratio is 20%, the bank must keep $20,000 in reserve and can lend the remaining $80,000. The impacts of the reserve ratio include:

• A higher reserve ratio reduces the amount banks can lend and thus contracts the money supply.
• A lower reserve ratio increases bank lending, potentially expanding the money supply.

This reserve requirement stabilizes the banking system by ensuring that banks have enough liquid assets to cover a certain proportion of withdrawals.
It ensures banks remain solvent, preventing bank runs where too many depositors withdraw money at once, risking a bank's cash reserve.