Sirjana Finance Company is facing the problem of liquidity. So Nepal Rastra Banks lent Rs. 20 million under repurchase agreement. The required reserve is 10 percent. a. What is the total demand…

a. Total Demand Deposit Created by Rs. 20 Million Injection

The injection of Rs. 20 million by Nepal Rastra Bank (NRB) under a repurchase agreement (repo) increases the excess reserves of Sirjana Finance Company. Banks use excess reserves to create new loans, which in turn generate demand deposits in the banking system.

Step 1: Calculate Initial Excess Reserves

• Reserve Requirement Ratio (RRR) = 10% = 0.10
• New Reserve Injection (ΔR) = Rs. 20 million
• Required Reserves (RR) = RRR × Total Deposits
• Excess Reserves (ER) = ΔR – RR

However, since the injection is new reserves (not created from deposits), the entire Rs. 20 million becomes excess reserves that can be lent out.

Step 2: Money Creation Process

When a bank lends out excess reserves, the borrower deposits the loan amount in another bank, creating new demand deposits. This process continues until the system’s excess reserves are fully utilized.

The maximum demand deposit (ΔD) created is given by: $$\Delta D=\frac{\Delta R}{RRR}$$ $$\Delta D=\frac{20,000,000}{0.10}=\text{Rs. }200\text{ million}$$

Final Answer: Rs. 200 million of new demand deposits will be created in the banking system.

---

b. Money Multiplier

The money multiplier (k) determines how much money the banking system can create from a given increase in reserves. It is calculated as: $$k=\frac{1}{RRR}$$ $$k=\frac{1}{0.10}=10$$

Final Answer: The money multiplier is 10.

---

c. New Level of Money Supply

The initial money supply (M₀) is Rs. 1,500 billion. The increase in money supply (ΔM) due to the Rs. 20 million injection is: $$\Delta M=k\times \Delta R=10\times 20,000,000=\text{Rs. }200\text{ million}$$

The new money supply (M₁) is: $$M_1=M_0+\Delta M=1,500,000,000,000+200,000,000=\text{Rs. }1,500,200\text{ million (or Rs. }1,500.2\text{ billion)}$$

Final Answer: The new money supply will be Rs. 1,500.2 billion.

---

d. Interpretation of the Money Multiplier (k = 10)

The money multiplier indicates how much the money supply expands for every unit increase in high-powered money (reserves) injected into the banking system.

Key Insight: The multiplier of 10 implies that the Rs. 20 million injection can potentially expand the money supply by Rs. 200 million, assuming no leakages. However, in practice, bank behavior, public cash demand, and regulatory constraints may reduce the effective multiplier.

---

# Python code to calculate money multiplier and new money supply
RRR = 0.10  # Reserve Requirement Ratio (10%)
new_reserves = 20_000_000  # Rs. 20 million injection
initial_money_supply = 1_500_000_000_000  # Rs. 1,500 billion

# Calculate money multiplier
money_multiplier = 1 / RRR

# Calculate new money supply
increase_in_money = money_multiplier * new_reserves
new_money_supply = initial_money_supply + increase_in_money

print(f"Money Multiplier: {money_multiplier:.1f}")
print(f"Increase in Money Supply: Rs. {increase_in_money / 1_000_000:.1f} million")
print(f"New Money Supply: Rs. {new_money_supply / 1_000_000_000:.1f} billion")

How it works: The code calculates the money multiplier using the inverse of the reserve ratio, then computes the new money supply by multiplying the multiplier with the reserve injection and adding it to the initial supply. The output matches the manual calculations above.