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a. LKD's bond currently sells for $834, which gives it a yield to maturity of 8%. Suppose that if the yield increases by 50 basis points, the price of the bond falls to $820. What is the duration of the bond? (3 marks) b. Alan is managing a pension fund with obligations to make payments of $3 million, $4 million, and $5 million at the end of the next three years, respectively. The market interest rate is 6% per annum. i. Determine the duration of the fund's obligation. (6 marks) ii. Suppose Alan plans to fully fund the obligation using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds in market value) Alan will hold in the portfolio. (8 marks)