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Suppose there is one depositor who earns an income of $100 in each period.She spends $50 for consumption and the remainder goes to her savings account.Assume that a bank doesn't do anything with this money except safeguards it.The bank charges $5 for safeguarding fee.
-A known fraction of 0.4 of the depositors will withdraw at t = 1.How much will they receive?
A)$45
B)$90
C)$98
D)$135
E)$196

Question

Use the following information for questions 
Suppose there is one depositor who earns an income of $100 in each period.She spends $50 for consumption and the remainder goes to her savings account.Assume that a bank doesn't do anything with this money except safeguards it.The bank charges $5 for safeguarding fee.
-A known fraction of 0.4 of the depositors will withdraw at t = 1.How much will they receive?
A)$45
B)$90
C)$98
D)$135
E)$196

Quizplus · Accepted Answer

In the first period, the depositor saves $50 ($100 income - $50 consumption) and pays $5 as a safeguarding fee. Thus, the total amount saved is $45. 
Since 0.4 of the depositors will withdraw in the first period, the bank must have kept (1-0.4)=0.6 of the total savings, which is $27. 
The withdrawing depositors will share this $27 equally. Therefore, each of them will receive $27/0.4 = $67.5 in the first period. However, since they only saved $45, they can only receive $45. Thus, the correct answer is $45.

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