You will be paying $$9,400$ a year in tuition expenses at the end of the next two years. Bonds currently yield $7\%.$

a$.$ What is 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 $8\%.$ 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 $6\%?$