(a) What is the present value of these payments? (b) To fund these payments the fund manager must invest in the four bonds described in Question 8. Assume that she is trying to minimize transaction costs; use the figures in QUESTION 8 to write the equations that would need to be satisfied to immunize the annuity described in this question. Note that the fund manager is concerned that the application of these conditions could result in only one or two different types of bonds being held. As this is considered risky she introduces a diversification condition whereby she must hold a minimum of five of each of B1, B2, B3 and B4. Note; these conditions will need to be considered in your equations. (2 marks) QUESTION 10 (use Excel to do this question) For the portfolio described in QUESTIONS 8 and 9 and the methods outined in the course notes on Mathematical Programming; that is, using the solver in excel, find the portfolio of bonds that the fund manager must invest in to immunize the portfolio. Although you need to apply the diversification conditions, there is no need to apply the second order condition of Convexitypayments > Convexityreceipts. Therefore, all that is required is for the two streams of payments and receipts to have the same present value, their Macaulay Durations must be equal and for the diversification conditions need to be satisfied. Submit you answer and sensitivity reports and write a brief paragraph explaining how much of each bond the fund manager should buy. (3.5 marks)