Assume that a pension fund is fully funded and that the manager plans to invest all money in a single-maturity zero to immunize the fund. The yield curve is flat at 6% and the pension fund has the following obligations:

Time in years. 0 1 2 3 4 5 6 7 8 9 10

Obligation (in $MM) $5 7 10 12 15 18 20 25 30 35

c. How much needs to be invested in the zero coupon bond to immunize the fund?

d. What is the Macaulay duration of the funds obligations?

e. What maturity zero coupon bond should be purchased to immunize the fund?

f. Instead of investing in a single zero coupon bond, say you have access to a 2 year zero coupon bond and a 10 year zero coupon bond. What percentage of your investment should be invested in the 2 year and what percentage in the 10 year?