Suppose a commercial bank's required reserves are \(\$ 100,000\), and the required reserve ratio is \(162 / 3 \% .\) What must its deposits be?

Understanding how commercial bank reserves work is fundamental to grasping why banks can lend money and how they contribute to the overall economy. Reserves are a portion of a bank's deposits that are not lent out to borrowers but are kept either as vault cash or on deposit with the central bank. This reserve acts as a safety net, ensuring that the bank can meet its customers' demands for cash and regulate the amount of money in the economy.

Reserves come in two varieties: required and excess. Required reserves are the minimum amount of funds that a commercial bank must hold, dictated by the central bank's reserve ratio. Excess reserves are any funds that a bank holds over the minimum requirement. Although reserves do not earn much interest for the banks, they play a critical role in the stability of the banking system and the execution of monetary policy.

Banking reserve calculations determine how much a commercial bank needs to hold back from its deposits as reserves. The required reserve ratio, which is the percentage of deposits that a bank is required to hold in reserve, is set by the central bank. To calculate the required reserves, you multiply the total deposits by the reserve ratio.

In the given exercise, the process involved converting the percentage into a decimal by dividing by 100 and then applying the following formula:
Total Deposits = Required Reserves / Required Reserve Ratio (decimal).

It's important to ensure that you use the correct form of the reserve ratio when doing this calculation. Otherwise, you could end up with a skewed understanding of a bank's reserve requirement, which is a vital component of its liquidity and ability to meet customer demands.

Monetary policy is the process by which the central bank manages the supply of money and the rate of interest to achieve specific economic objectives. One of the tools for this policy is the manipulation of the required reserve ratio. By adjusting the ratio, the central bank can control the amount of money banks can lend. A higher reserve ratio means banks have less money to lend, which can slow down economic growth; a lower ratio can increase lending and stimulate the economy.

Monetary policy decisions have far-reaching implications, including influencing inflation, unemployment rates, and overall economic growth. By understanding how reserve ratios fit into the broader scope of monetary policy, students can better appreciate the interconnectedness of banking systems and the economy at large.