Consider a mutual savings bank (depositors are the owners of the bank) with 1000

Question

Consider a mutual savings bank (depositors are the owners of the bank) with 1000 depositors. In the beginning of a year, each depositor makes $100,000 deposit. The bank holds 10% of the total deposit in vault cash. The remaining deposit is invested in a project with a 10% rate of return at the end of the year. However, if the bank liquidates it investment, it only gets 50% of its initial investment back. For simplicity, we assume that this mutual saving bank does not have to comply to any reserve requirement.

a. Suppose the bank does not have to liquidate its investment project, what is the return after a year on each deposit account?

Suppose 10 depositors decide to withdraw all their deposit after a month. What is the return after a year on each remaining deposit account?

Suppose every depositor thinks that more than 20% of depositors will withdraw after a month, what should a depositor do? What is the return on each deposit account in this case?

Explanation / Answer

a. In case the bank does not liquidate, the return on an annual basis per deposit = $ 100,000 X 10% = $ 10,000.

b. 10 depositors withdraw their deposits after a month

Hence, the balance deposits will be $ 100,000 X (1000-10) = $ 100,000 X 990 = $ 99,000,000

The return on these deposits after a year will be $ 99,000,000 X 10% X 11/12 = $ 9,900,000 X 11/12 = $ 9,075,000

Hence, the return per deposit will be $ 9,075,000/990 = $ 9166.67

The last question is incomplete. In the absence of the exact number of depositors withdrawing their amounts each month, the same cannot be answered.

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