$(10$ pts$)$ You will be paying $$35,000$ tuition a year at the end of the next $4$ years. Bonds currently yield $5\%.$

$2.$A What are the present value and duration of your obligation?

$2.$B What maturity zero$-$coupon bond would immunize your obligation?

C Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to $6\%.$ What happens to your net position? That is$,$ what happens to the difference between the value of the bond and that of your tuition obligation?

$2.$D Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately decrease to $4\%.$ What happens to your net position? That is$,$ what happens to the difference between the value of the bond and that of your tuition obligation?