Suppose that there is a bank that is offering to lend and/or borrow money at an interest rate of 8% (regardless of the time-to-maturity of the loan). Further suppose that there is a two-year coupon bond trading with a face value of $100 and a coupon rate of 5% trading in the market. Price the bond using an explicit no-arbitrage argument.

a. Now suppose that the bond is actually trading for $92. Show how you could exploit the mispricing to make an arbitrage profit.

b. Consider a gold mine that will produce annual cash flows of $100 (with certainty) for five years starting in two years, i.e. from t = 2 to t = 6. What is the arbitrage-free price of the gold mine?

c. Now suppose that the cash flows from the mine in the previous question are risky with a standard deviation of = $50. How would your answer change?