You will be paying $$18,000$ a year in tuition expenses at the end of the next three years. Bonds currently yield $5\%.$

What is the present value of your tuition expenses?

What is the duration of the tuition expenses?

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

What if rates rises to $5\mathrm{.}5\%?$

Please show work through a photo or a Word document.