You manage a pension fund with perpetual annual obligations of $5M. The current YTM is 10%.(a) Create a strategy using zero-coupon bonds to immunize your portfolio from interest rate movements.(b) How many zero-coupon bonds with a par value of $1,000 will you need to purchase to meet your obligations?(c) If the convexity of a zero-coupon bond with a duration of 5 years and par value of $1,000 and YTM of 10% is 24.793, estimate the new price of the zero-coupon bond in part c if YTM decreases by 5% using the bond's duration and convexity. What is the difference between your estimated price and the actual new price?