NEED HELP ONLY FOR PART B, but imformation in a is important.

a) You are a financial consultant and an expert on contingent immunization strategies. A client has asked you to make sure that her portfolio has a value of at least $500,000 at the end of six years. The current value of her portfolio is $390,000. The bonds that you have at your disposal currently yield an effective annual rate of 5%.

1. Given the current interest rate, what amount would need to be invested today to achieve the requested goal? [1 mark]

2. Suppose that four years have passed, and the interest rate is 9%. What is the trigger point of your clients portfolio currently? That is, how low can the value of the portfolio get before you are forced to immunize your strategy in order to achieve the requested goal? [2 mark]

3. If the portfolio's value after four years is $405,811 (i.e., there are two years left to meet the original goal) what should you do? What effective annual rate is required to meet the original goal? [2 marks]

b) Youare about to purchase a 10-year par bond with a 5% coupon rate paid annually.

i. What are the duration and the convexity of this bond? [4 marks]

2. Assume that right after you purchase the bond an economic announcement drives the YTM to 7%. What is the new price of the bond? [1 mark]

3. What price would be predicted by the duration rule after the YTM increases to 7%? Is this answer the same as the one reported in part (ii)? Why? [2 marks]

4. What price would be predicted by the duration-with-convexity rule after the YTM increases to 7%? Is this answer the same as that reported in part (ii)? Why? [2 marks]