If a bank has $10 million of checkable deposits, a required reserve ratio of 10 percent, and it holds $2 million in reserves, then it will not have enough reserves to support a deposit outflow of:

Question

BlackTom AI · Accepted Answer

Required reserves = 10% × $10 million = $1 million, so the bank’s excess reserves = actual reserves − required reserves = $2 million − $1 million = $1 million.

1) Relevant knowledge points and concepts
- Required reserve ratio r means banks must hold r × deposits as reserves.
- A deposit outflow X reduces both reserves and deposits by X.
- After an outflow X, the bank can support it if remaining reserves ≥ new required reserves.

2) Complete reasoning process step by step
Let initial reserves R0 = $2,000,000, initial deposits D0 = $10,000,000, and r = 0.10. After a deposit outflow X:
- Reserves become R1 = R0 − X.
- Deposits become D1 = D0 − X, so required reserves become RR1 = r × D1 = r(D0 − X).

The bank can support the outflow as long as R1 ≥ RR1:
R0 − X ≥ r(D0 − X).

3) Calculations with intermediate steps
R0 − X ≥ rD0 − rX
Bring X terms to one side: R0 − rD0 ≥ X(1 − r)
Solve for X: X ≤ (R0 − rD0) / (1 − r)

Plug numbers:
R0 − rD0 = $2,000,000 − 0.10×$10,000,000 = $2,000,000 − $1,000,000 = $1,000,000
1 − r = 0.90
Maximum supported outflow Xmax = $1,000,000 / 0.90 = $1,111,111.11 (≈ $1.111 million)

4) Why the correct answer is correct
Any outflow up to about $1.111 million can be supported. An outflow of $1.2 million exceeds this maximum, so the bank will not have enough reserves to support a $1.2 million withdrawal.

5) Why other options are incorrect
- $1.1 million: below $1.111 million, so the bank can support it.
- $1.0 million and $0.9 million: both well below the maximum, so they are supportable.

6) Conclusion
Therefore the bank will not have enough reserves to support a deposit outflow of $1.2 million. This confirms answer (a) $1.2 million.

If a bank has $10 million of checkable deposits, a required reserve ratio of 10 percent, and it holds $2 million in reserves, then it will not have enough reserves to support a deposit outflow of:Single choice

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