Five years today your firm is going to have to start making a series of four payments that look like this:

Year                      Payment

5                          $1 million

6                       $1.5 million

7                       $2.0 million

8                       $2.5 million

Today you are putting together an investment plan to make sure that your company will have that money it needs to cover this liability. Your plan is to invest in some combination of 4-year bonds and 10-year bonds such that the liability is immunized. The 4-year bonds pay a 5% coupon and the 10-year bond pay a 2% coupon. You may use a discount rate of 3.5% throughout this problem. How many of each type of bond do you need to buy?