2) You are given the following information: at t = 0, the price of a 10?year zero coupon bond with FV = $10,000 is $7,000; the price of a 3-year zero coupon bond with FV = $5,000 is $4,300; f3,12 = 6%. A bank is offering the following product: for every $Z that you give the bank at t = 10, the bank will give you back $1 at t = 15, or for every $Z that you borrow from the bank at t = 10, you will have to pay back $1 at t = 15. (In other words, money gets multiplied once by (1/Z) going from t = 10 to t = 15.)

a) What should Z be if there is no arbitrage?

b) Suppose the bank is offering the product described above, but instead of Z being equal to your answer from part a, it is equal to 0.95 times your answer to part a. Describe how you would construct an arbitrage strategy. Assume that part of your strategy involves buying or selling $1 worth of the 10?year zero coupon bond, and also either buying or selling $1 worth of the 3?year zero coupon bond. Construct the arbitrage in such a way that your profit is realized at t = 15, and the net cash flows at all other points in time are 0. You must specify for f3,12 = 6% whether you are borrowing or lending at that rate, and how much. You must also specify how much you are borrowing or lending using the bank