Bank Runs and FDIC

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?

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

c) 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?

d) Now the bank becomes a member of FDIC, which guarantees that any deposit account up to $250,000. Answer the question in c.