2. In cla we showed that the modified duration of any asset equals minus the derivative of its price with respect to its yield, divided by its price: modified duration = -(dP/dY)/P. a) Use this formula to calculate the modified duration of a perpetuity that promises to pay a coupon C forever. b) Does your answer to part a) depend on the coupon C? Why or why not? c) Is it possible for bonds with finite maturities to have greater duration than perpetuities? Explain. d) The same formula can be applied in the Gordon growth model, where you may interpret the steady-state return / of the model as equivalent to yield. Calculate the modified duration of a stock with current dividend D, steady-state return R, and steady-state growth rate G. e) Consider a disruption in financial markets that leads investors to increase the steady- state return they require from stocks, driving down stock prices. Which type of stocks, growth stocks or value stocks, are likely to have the greatest percentage price declines? Explain