You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 4%. In order to compute the present value and the duration of the obligation, we conduct the following calculations.

(1) What is the present value and duration of your obligation?

(2) What maturity zero-coupon bond would immunize your obligation?

(3) Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 5%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? What if rates fall to 3%?

Time until Payment Period payment Payment discounted at 4% 1.0 $10,000 9615.3846 $10,000 2.0 9245.5621 Column Sums $18,860.95 weight (wt discounted pmt/PI 0.5098 0.4902 Timex weight 0.5098 0.9804 1.4902