solution

a. The present value of the fund’s obligation is $800,000/.08 = $10 million. The duration is 13.5 years. Therefore, the fund should invest $10 million in zeros with a 13.5-year maturity. The face value of the zeros will be

b. When the interest rate increases to 8.1%, the present value of the fund’s obligation drops to 800,000/.081 = $9,876,543. The value of the zero-coupon bond falls by roughly the same amount, to The duration of the perpetual obligation falls to 1.081/.081 = 13.346 years. The fund should sell the zero it currently holds and purchase $9,876,543 in zero-coupon bonds with maturity of 13.346 years.