An insurance company is obligated to pay $2200 in 1 years time and $2662 in 3 years time. In order to provide for these obligations, they plan to purchase a combination of 1-year and 2-year zero coupon bonds. The yield on the bonds is 10% annual effective.

a) Find the face values of each bond that should be purchased to satisfy the present value and duration conditions for Redington's immunization at an annual effective rate of interest of 10%.

b) Is the convexity condition also satisfied. What does this mean for small changes in the interest rate? Justify your answer.