# Discount Rate in the Banking System

(a) Third National Bank is fully loaned up with reserves of $20,000 and demand deposits equal to $100,000. The reserve ratio is 20%. Households deposit $5,000 in currency into the bank. How much excess reserves does the bank now have, and what is the maximum amount of new money that can be created in the banking system as a result of this deposit? Show all work.

(b) What is the discount rate in the banking system, and explain how the Fed manipulates this rate in order to achieve macroeconomic objectives.

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#### Solution Preview

a. The bank has initial deposits of $100000, and the required reserve ratio is 20%. So the bank has to keep 20% of $100000 = $20000 in reserves. When households deposit an additional $5000, the demand deposits of the bank rise to $105000, and the bank is now required to keep 20% of $105000 = $21000 in reserves. It already has $20000, so the bank will need to add another $1000 to reserves and can loan another $4000 (= $5000 - $1000).

In the absence of currency drain the money multiplier is given by 1/RRR, where RRR stands for the required reserve ratio. Here it is 20%, or 0.2, and hence the money multiplier is 1/0.2 = 5. Thus a deposit of $5000 ...

#### Solution Summary

Calculations are shown for solving the increase in monetary supply due to new demand deposits. An explanation for why how these calculations are determined and what happens to the money supply is provided along with a discussion of the Federal Reserves manipulation of interest rates with regards to monetary policy. This solution is 455 words.