Alpha Insurance Company is obligated to make payments of $2 million, $3 million, and $4 million at the end of the next three years, respectively. The market interest rate is 8% per annum. i. Determine the duration of the companys payment obligations. (10 marks) ii. Suppose the companys payment obligations are fully funded and immunized using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds the company will hold in the portfolio. (7 marks )