b) An individual buys an annuity from an insurance company for a single lump sum premium. The annuity wiH pay RM10,000 annually at the end of each year for 15 years. The insurance company invests the premium in a bond which pays annual coupons at the rate of 6% per annum and is redeemable at par in exactly nine years. (i) Calculate the Macaclay duration of the annuity at an interest rate of 5% per annum effective. (ii) Calculate the Macaulay duration of the bond at an interest rate of 5% per annum effective. (iii) Explain whether the insuranice company will make a profit or a loss if interest rates decrease slightly at all terms. (2 marks)