There are three bonds selling at par with an annual coupon rate of 3%, and 10, 20, and 30 years to maturity. The term structure of interest rates is flat. a. Which of the three bonds will have the largest price impact if the rates increase from 3% to 5%? Why? b. An investor buys a 20 year bond at par (3%). One year after, just after the first coupon payment, the term structure increases from 3% to 5%. Assuming that the investor reinvests the coupon payments at the new interest rate, how many years would the investor have to wait to recover its original investment, i.e. coupon reinvestments plus bond price is larger or equal to the principal