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 keep as required reserves? \(L O 34.3\) 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

Understand Reserve Requirements

The reserve ratio is the percentage of deposits a bank must keep as reserves, either in the bank's vault or with the central bank. In this case, the required reserve ratio is 10%.

Calculate Required Reserves

Find the amount that must be kept as reserves from the borrowed amount. To do this, multiply the total borrowed amount by the reserve ratio. Amount to keep = Borrowed Amount $ imes$ Reserve Ratio = $ ext{100,000} imes 0.10$ = $ ext{10,000}$.

Conclusion

The bank must keep $ ext{10,000}$ as required reserves from the $ ext{100,000}$ it borrowed. Hence, option (c) is correct.

Key concepts

Understanding Reserve Ratio

The reserve ratio is a crucial component in monetary policy, acting as a stabilizer for the economy. It refers to the percentage of deposits that banks are required to keep in reserve and not lend out. This reserve can be held as cash in the bank vault or lodged with the central bank. The aim is to ensure that banks do not overextend themselves and can meet the demand of customers wanting to withdraw funds. For instance, if a bank has $1,000,000 in deposits and the reserve ratio is 10%, the bank must hold $100,000 and cannot lend this amount. The reserve ratio affects how much money a bank can create through its lending activities and ultimately impacts the money supply in an economy. A higher reserve ratio means less money available for banks to lend, which can restrict economic activity, whereas a lower reserve ratio encourages more lending and spending.

Required Reserves Demystified

Once the reserve ratio is established, banks must calculate their required reserves from their total deposits. Required reserves are essentially the specific amount a bank needs to set aside as dictated by the reserve ratio. Let's clarify this with an example: If a bank borrows \(100,000 and the reserve ratio is 10%, the required reserves would be calculated by multiplying the borrowed amount by the reserve ratio, that is \(100,000 imes 0.10\), resulting in \)10,000. These required reserves ensure that the bank maintains an adequate buffer, preventing liquidity shortages which can impact both the bank's stability and the wider financial system. This requirement promotes confidence in the banking system by ensuring that banks can handle unexpected withdrawals or economic downturns without significant risk.

Understanding the Discount Rate

The discount rate is set by the central bank (the Federal Reserve, in the case of the U.S.) and is the interest rate charged to commercial banks and other financial institutions on the loans they receive from the Fed's discount window. When a bank needs short-term funds to meet reserve requirements or manage liquidity issues, it can borrow these funds from the central bank at the discount rate. A higher discount rate makes borrowing more expensive, which can slow down borrowing and, in turn, dampen economic activity. Conversely, a lower discount rate encourages more borrowing by banks, which can stimulate the economy. In our example, the discount rate applied to the loan is 4%, meaning the bank must pay this interest on the amount it borrowed from the Fed.

The Role of the Federal Reserve

The Federal Reserve, often referred to as the Fed, serves as the central bank of the United States and plays a significant role in shaping monetary policy. It helps manage the country's money supply and aims to provide a stable and flexible financial system. The Fed is responsible for setting reserve ratios, discount rates, and other regulations that influence economic stability and growth. By adjusting these tools, the Fed can either stimulate the economy by making borrowing easier or control inflation by making it harder for banks to lend money. Its actions are crucial for maintaining balanced economic conditions and safeguarding the financial system from potential risks. The Federal Reserve's interventions aim to guide the economy towards full employment and stable prices.