You will be paying $$11,000$ a year in tuition expenses at the end of the next two years. Bonds currently yield $8\%.$

Required:

What are the present value and duration of your obligation?

Note: Do not round intermediate calculations. Round "Present value" to $2$ decimal places and "Duration" to $4$ decimal places.

What is the duration of a zero$-$coupon bond that would immunize your obligation and its future redemption value?

Note: Do not round intermediate calculations. Round "Duration" to $4$ decimal places and "Future redemption value" to $2$ decimal places.

Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to $9\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond and that of your tuition obligation?

Note: Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to $2$ decimal places.