A commercial banking system generates a total deposit expansion of ₦600,000 from an initia… — JAMB UTME

A commercial banking system generates a total deposit expansion of $₦600,000$ from an initial cash injection of $₦150,000$ . If the central bank subsequently raises the cash reserve ratio by $5\%$ , what is the new total deposit expansion that the banking system can generate from the same initial cash injection?

$₦500,000$ Answer
B
$₦350,000$
C
$₦570,000$
D
$₦45,000$

Answer

₦500,000

The option specifying

₦500,000

is correct because the initial reserve requirement of

25\%

(

0.25

), derived from

\frac{150,000}{600,000}

, increases by

5\%

30\%

(

0.30

). Dividing the primary cash injection of

₦150,000

0.30

yields a new total deposit capacity of

₦500,000

Step-by-Step Solution

Determine the initial credit multiplier and cash reserve ratio

Credit Multiplier =

4

, Cash Reserve Ratio =

25\%

The initial credit multiplier is

\frac{\text{Total Deposit Expansion}}{\text{Initial Cash Injection}} = \frac{₦600,000}{₦150,000} = 4

. Since

\text{Credit Multiplier} = \frac{1}{\text{Cash Reserve Ratio}}

, the initial Cash Reserve Ratio is

\frac{1}{4} = 0.25

25\%

Calculate the updated cash reserve ratio

New Cash Reserve Ratio =

30\%

(

0.30

)

The central bank increases the reserve requirement by an additional

5\%

, making the new ratio

25\% + 5\% = 30\%

Compute the new total deposit expansion

₦500,000

Using the credit expansion formula,

\text{New Total Deposits} = \frac{\text{Initial Cash Injection}}{\text{New Cash Reserve Ratio}} = \frac{₦150,000}{0.30} = ₦500,000

Key Concept

Credit Creation and the Credit Multiplier Formula

Estimated Time:2m 0s

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