1. An insurance firm needs to make a payment of $10000 in 3 years, the market interest rate to discount this obligation is 1%. The insurance firm funds this obligation with a 4-year zero-coupon bond and a 2-year coupon bond with a coupon rate of 10% (The coupon payments are made annually). Both bonds have a face value of $1000 and a yield of 1%.
   1. What is the price of the 2-year coupon bond?
   2. What is the duration of the 2-year coupon bond?
   3. What is the portfolio weight on the 2-year coupon bond to immunize the insurance firms obligation?
   4. How much money should the firm invest in the 2-year coupon bond?

Assume one year has passed, the firm needs to rebalance its portfolio to make sure its obligation is still immunized. Assume the market interest rate and the yields do not change.

5. What is the duration of the 2-year coupon bond?
6. What is the portfolio weight on the 2-year coupon bond to immunize the insurance firms obligation?
7. How much money should the firm invest in the 2-year coupon bond?