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Difficulty: MediumCommercial Banks: Functions and Credit Creation

A commercial banking system operates under a cash reserve ratio of 10%10\%. If a new cash injection into the system leads to a total net credit creation (new loans issued) of ₦450,000₦450,000, what was the value of the initial cash deposit, assuming commercial banks maintain no excess reserves and there are no cash leakages?

  1. A
    ₦45,000₦45,000
  2. ₦50,000₦50,000Answer
  3. C
    ₦405,000₦405,000
  4. D
    ₦500,000₦500,000

Answer

The initial cash deposit required is ₦50,000₦50,000.
The total credit multiplier (mm) is 1CRR=10.10=10\frac{1}{\text{CRR}} = \frac{1}{0.10} = 10. Total deposits created equal 10×D010 \times D_0. Since Net Credit Created equals Total Deposits minus Initial Deposit (10D0−D0=9D010 D_0 - D_0 = 9 D_0), we have 9D0=₦450,0009 D_0 = ₦450,000, which gives D0=₦50,000D_0 = ₦50,000. Thus, ₦50,000₦50,000 is the correct initial cash deposit.

Step-by-Step Solution

1
Determine the credit multiplier and total deposit expansion formula
Credit Multiplier (mm) = 1Cash Reserve Ratio (CRR)=10.10=10\frac{1}{\text{Cash Reserve Ratio (CRR)}} = \frac{1}{0.10} = 10. Total Deposits (DtotalD_{\text{total}}) = 10×Initial Deposit(D0)10 \times \text{Initial Deposit} (D_0).
Commercial banks expand deposits up to the reciprocal of the cash reserve ratio.
2
Express Net Credit Creation in terms of the initial deposit
Net Credit Creation = Total Deposits - Initial Deposit = 10D0−D0=9D010 D_0 - D_0 = 9 D_0.
Net credit created represents the secondary loan deposits generated minus the primary initial deposit.
3
Solve for the initial cash deposit (D0D_0)
9D0=₦450,000  ⟹  D0=₦450,0009=₦50,0009 D_0 = ₦450,000 \implies D_0 = \frac{₦450,000}{9} = ₦50,000.
Dividing the net credit created by the net credit multiplier (m−1=9m - 1 = 9) yields the original primary deposit.

Key Concept

Credit Creation and Net Credit Expansion by Commercial Banks
Estimated Time:1m 15s
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Topics

Commercial Banks: Functions and Credit Creation