1. A corporation has an obligation to pay $50M in 12 years. The current interest rate is 8% at all maturities.
   1. What is the current value that the fund must have now to cover the obligation in 12 years?
   2. Unfortunately, they cannot find 12-year bonds and must instead purchase 5-year and 20-year zero-coupon ($1000) bonds. What are the prices of each of these bonds today?
   3. How many 5- and 20- year ZCBs should the company buy to be immunized against interest rate changes?
   4. If the interest rate changes to 6% in 5 years permanently, what will the value of the immunized bond portfolio be in 12 years?