2. (25 points) Your friend has an obligation of paying $10,000 each year for the next three years (say for her student loans). To be able to meet her obligation, she is thinking about investing just enough money in a three year zero coupon bond (the present value of her bond portfolio is equal to the present value of her obligation). Assume YTM of all bonds is 5%. (a) What is the present value of your friend's obligation? What is the duration of her obligation? Show your work. (b) What is the duration of your friend's bond portfolio if she were to carry out her idea of investing in a three year zero coupon bond? (c) You have just learned in your Finc 335 class about interest rate risk of a fixed income portfolio and its duration. Explain to your friend why her idea of investing in a three year zero coupon bond does not immunize her net position by assuming a hypothetical case where YTM of all bonds were to increased by 10 basis points (1 basis point equals 0.01%)-That is, if YTM of all bonds were to increase by 10 basis points right after her investment in bond, is her obligation still fully funded by her bond portfolio? Explain. (d) Now that your friend is convinced that you are right, she wants you to find an immunization strategy for her. You plan to use a zero coupon bond as well. What maturity of zero coupon bond should you use? How much face value should you invest? Explain and show your work