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Suppose there is a financial asset, a bond ABC, which is the underlying asset for a futures contract with settlement six months from now.

Suppose there is a financial asset, a bond ABC, which is the underlying asset for a futures contract with settlement six months from now. You know the following about this financial asset and the futures contract:
-In the cash market ABC is selling for $80.
-ABC pays $8 per year in two semi-annual payments of $4, and the next semi-annual
  payment is due exactly six months from now.
-The current six-month interest rate at which funds can be loaned or borrowed is 6%.
Respond to these questions:
a. What is the theoretical (or equilibrium) futures price?
b. What action would you take if the futures price is $83?
c. What action would you take if the futures price is $76?
d. Suppose that ABC pays interest quarterly instead of semiannually. If you know that you can
    reinvest any funds you receive three months from now at 1% for three months, what would
    the theoretical futures price for six-month settlement be?
e. Suppose that the borrowing rate and lending rate are not equal. Instead, suppose that the
    current six-month borrowing rate is 8% and the six-month lending rate is 6%. What is the
    boundary for the theoretical futures price?

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