Suppose, instead, we have a three year bond that will pay a constant rate of interest

during these three years given by r3t. Suppose, further, that we can purchase 3 consecutive one year (and hence short-term)bonds. The first bond pays a short-term

interest rate given by r1t. The second pays a short term expected interest rate given re . re .

by 1t1 Finally,the third pays a short-term expected interest rate given by 1t2

Show that the long-term interest rate is still the average of the short term rates. Make sure in your answer to explain the role that arbitrage and the inverse relationship between interest rates and bond prices play in deriving this relationship. Note that you will have to make use of one of the approximate relationships in deriving your answer.