This question is about bond duration. Youll need to use derivatives. Remember your calculus: The chain rule tells you that the derivative of ln(P(YTM)), with respect to YTM, is P(YTM)/P(YTM). a. Consider a zero-coupon bond which pays off $F in T years. What is its duration when its yield to maturity (YTM) is zero? Show your work. b. Now consider a T year bond which pays a coupon of $C each year. (It makes no final face payment.) What is its duration when its YTM is zero? Show your work. (Hint: (1 + 2 + 3 + + T)/T is (T+1)/2.) c. Finally, consider a T year bond which pays a coupon of $C each year and a final face payment of $F in T years. What is its duration when its YTM is zero? How is its duration related to your answers in parts (a) and (b)? Show your work