Question 3 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:
Period 
Time until payment 
Payment 
Payment discounted at 4% 
weight 
Time x weight 
(t) 
(CF_{t}) 
PMT/(1 + y/m)^{t} 
(w_{t} = discounted pmt/P) 
(t)(w_{t}) 

1 
1.0 
$10,000 
9615.3846 
0.5098 
0.5098 
2 
2.0 
$10,000 
9245.5621 
0.4902 
0.9804 
Column Sums 
$18,860.95 
1 
1.4902 

(1) What is the present value and duration of your obligation? (2) What maturity zerocoupon bond would immunize your obligation? (3) Suppose you buy a zerocoupon 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%? 