You will be paying $$8,200$ a year in tuition expenses at th$$ end of the next two years. Bonds currently yield $9\%.$

Required:

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

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 $11\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond and that of your tuition obligation?

d$.$ What if rates fall immediately to $8\%?$