Question

ACD Bank holds a total deposit of Rs. 256412. To expand the money supply in the economy during the COVID-19 pandemic period, the Reserve Bank of India reduces the cash reserve ratio (CRR) from 4.5% to 3.5%. Due to this policy change, the additional money supply generated by ACD Bank is Rs. ____ (in integer).

Answer 1

Correct Answer: 1628012

$\text{1. Define Variables and Formulas}$

Total Deposit Base ($D$): $\text{Rs. } 256412$

Initial CRR ($\text{CRR}_1$): $4.5\% = 0.045$

Final CRR ($\text{CRR}_2$): $3.5\% = 0.035$

The maximum money supply created by a deposit base in the banking system is determined by the Money Multiplier ($\text{MM}$):

$$\text{Money Multiplier } (\text{MM}) = \frac{1}{\text{CRR}}$$

The total money supply ($\text{MS}$) created from the deposit base ($D$) is:

$$\text{MS} = D \times \text{MM}$$

The additional money supply ($\Delta \text{MS}$) generated due to the change in $\text{CRR}$ is the difference between the maximum money supply possible under the new $\text{CRR}$ and the initial $\text{CRR}$.

$$\Delta \text{MS} = \text{MS}_2 - \text{MS}_1 = D \times \left(\frac{1}{\text{CRR}_2} - \frac{1}{\text{CRR}_1}\right)$$

$\text{2. Calculate Money Multipliers}$

$$\text{Initial Money Multiplier } (\text{MM}_1) = \frac{1}{0.045} \approx 22.2222$$

$$\text{Final Money Multiplier } (\text{MM}_2) = \frac{1}{0.035} \approx 28.5714$$

$\text{3. Calculate Additional Money Supply}$

$$\Delta \text{MS} = 256412 \times \left(\frac{1}{0.035} - \frac{1}{0.045}\right)$$

First, simplify the term in the parenthesis:

$$\frac{1}{0.035} - \frac{1}{0.045} = \frac{0.045 - 0.035}{0.035 \times 0.045} = \frac{0.01}{0.001575}$$

$$\frac{0.01}{0.001575} = \frac{10000}{1575} = \frac{400}{63} \approx 6.34920635$$

Now, multiply by the total deposit base ($D$):

$$\Delta \text{MS} = 256412 \times \frac{400}{63}$$

$$\Delta \text{MS} \approx 256412 \times 6.34920635$$

$$\Delta \text{MS} \approx 1628012.6984$$

$\text{4. Final Answer}$

Rounding the result to the nearest integer:

$$\Delta \text{MS} \approx 1628013$$

$$\text{The additional money supply generated by ACD Bank is } \mathbf{1628013}$$