Step 1: Understanding the Concept:
The Cash Reserve Ratio (CRR) is the specific percentage of total deposits that commercial banks are legally required to keep as reserves with the Central Bank.
Banks are prohibited from using this reserve amount for lending or investment activities.
The amount a bank can lend in the first round is the surplus remaining after setting aside the required reserve from the initial deposit.
Step 2: Key Formula or Approach:
The calculation follows these logical steps:
1. Determine the Required Reserve: \[ \text{Required Reserve} = \text{Initial Deposit} \times \text{CRR} \]
2. Determine the Loanable Amount: \[ \text{Loanable amount} = \text{Initial Deposit} - \text{Required Reserve} \]
Step 3: Detailed Explanation:
According to the problem:
Initial Deposit = 100
CRR = 20%
First, calculate the reserve amount:
\[ \text{Required Reserve} = 100 \times 20% = 100 \times \frac{20}{100} = 20 \]
Next, subtract this reserve from the initial deposit to find the lending capacity:
\[ \text{Loanable amount} = 100 - 20 = 80 \]
Thus, the bank keeps 20 units as a safety net with the Central Bank and utilizes the remaining 80 units for providing loans.
Step 4: Final Answer:
The bank is authorized to lend 80 units in the first round.