1. Today is period 0. Consider the following default-free securities. A two year zero coupon bond, which pays $1000 in period 2, currently costs $869.36. A three-year annuity that pays $1000 at the end of period 1, 2, and 3, and has a current price of $2,604.94.
   1. A forward contract that matures in period 2 is also available. As you know, the current price is zero, but the buyer of the contract must pay $1837.02 at the maturity of the contract and in return receives a certain amount in period 3. What is the continuously compounded forward rate implicit in this contract if you know that _{01 ,0} = 7.5%? What will be the payoff at period 3?
   2. A growing bond G pays $1000 in period 1, $2000 in period 2, and $3000 in period 3. The cost of this bond is $5100. Provide an investment strategy that will let you make an arbitrage profit of $28.67 at period zero. Provide a different strategy that will give you an arbitrage profit of $32.98 at period 2.