Question

A bank borrows \(\$ 100,000\) from the Fed, leaving a \(\$ 100,000\) Treasury bond on deposit with the Fed to serve as collateral for the loan. The discount rate that applies to the loan is 4 percent and the Fed is currently mandating a reserve ratio of 10 percent. How much of the \(\$ 100,000\) borrowed by the bank must it kecp as required reserves? LO36.3 a. \(\$ 0\) b. \(\$ 4,000\) c. \(\$ 10.000\) d. \(\$ 100,000\)

Short answer

The bank must keep $10,000 as required reserves.

Step-by-step solution

Understanding Reserve Requirement

The problem states that the bank has borrowed $100,000, and a reserve ratio of 10% is mandated by the Fed. This means the bank must keep 10% of its borrowed amount as reserves.

Calculating Required Reserves

To calculate the required reserves, multiply the total borrowed amount ($100,000) by the reserve ratio (10%). Use the formula: \[\text{Required Reserves} = \text{Total Amount Borrowed} \times \text{Reserve Ratio}\]Substitute in the given values: \[\text{Required Reserves} = 100,000 \times 0.10 = 10,000\]

Result Verification

The calculated required reserves are $10,000. This means the bank must keep $10,000 of the $100,000 borrowed as required reserves per the Fed's mandate.

Key concepts

Federal Reserve

The Federal Reserve, often just called "the Fed," is the central bank of the United States. It plays a crucial role in the nation's economy by controlling the supply of money and credit. The Fed is responsible for setting monetary policy, overseeing and regulating banks, and ensuring the stability of the financial system.
The Federal Reserve influences the economic environment through:

• Monetary Policy Decisions: It sets interest rates to either stimulate or cool down the economy.
• Regulation of Banks: Ensures banks follow rules and maintain adequate reserves.
• Operating the Payments System: Facilitates the exchange of payments between banks.

The Fed's role is vital, as it aims to maintain low inflation, full employment, and a stable economy.

Discount Rate

The discount rate is the interest rate the Federal Reserve charges banks when they borrow money. This rate influences how much banks lend to businesses and consumers because it affects the banks' costs to obtain funds.
When the Fed sets a low discount rate:

• Banks borrow more readily, increasing the money supply.
• Interest rates for loans typically decrease, encouraging spending and investments.

Conversely, a higher discount rate does the opposite, restraining bank borrowing and lending. This is a tool used by the Fed for controlling inflation and stabilizing the economy.

Treasury Bond

Treasury bonds are long-term, fixed-interest government securities issued by the U.S. Department of the Treasury. They are used to finance government spending as well as to regulate the economy.
Key features of Treasury bonds include:

• Maturity Period: Typically 10 to 30 years, offering steady interest payments every six months until maturity.
• Security: Considered low-risk since they are backed by the government's credit.
• Investment Tool: Often used by financial institutions as a safe investment and sometimes as collateral, as seen when a bank deposits them with the Fed.

Treasury bonds are an integral part of the financial strategies employed by both individual investors and large financial institutions.

Monetary Policy

Monetary policy involves the processes by which a central bank, like the Federal Reserve, manages the supply of money and credit to achieve macroeconomic objectives like controlling inflation, consumption, growth, and liquidity.
There are two primary types of monetary policy:

• Expansionary Policy: Involves lowering interest rates and increasing the money supply to stimulate economic activity.
• Contractionary Policy: Involves raising interest rates and decreasing the money supply to curb inflation.

The Fed uses tools such as adjusting the discount rate, conducting open market operations (buying or selling government securities), and setting reserve requirements to implement its monetary policy. Efficient monetary policy is essential for maintaining economic stability and growth.