You will be paying $$10,800$ a year in tuition expenses at the end of the next two years. Bonds currently yield $9\%.$

Required:

a$.$ What are the present value and duration of your obligation? $($Do not round intermediate calculations. Round "Present value" to $2$ decimal places and "Duration" to $4$ decimal places.$)$

$\backslash$table$[[$Present value,$],[$Duration$,$years$]]$

b$.$ What is the duration of a zero$-$coupon bond that would immunize your obligation and its future redemption value? $($Do not round intermediate calculations. Round "Duration" to $4$ decimal places and "Future redemption value" to $2$ decimal places.$)$

$\backslash$table$[[$Duration$,,$years$],[$Future redemption value,,$]]$

c$.$ Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to $10\%.$ What happens to your net position, that is$,$ to the difference between the value of th

c$.$ Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to $10\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond and that of your tuitic obligation? $($Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Net position changes by

d$.$ Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately fa $8\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond and that of your tuition obligation? $($Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Net position changes bye bond and that of your tuition