Hafiz buys an annuity-immediate from an insurance company for a single lump sum premium. The annuity will pay RM10,000 annually for 15 years. The insurance company invests the premium in a fixed-interest bond which is redeemable at par in exactly 9 years. It pays coupons at the rate of 6% per annum at the end of each year.

(i) Calculate the duration of the annuity at an interest rate of 5% per annum effective. (4 marks)

(ii) Calculate the duration of the bond at an interest rate of 5% per annum effective. (4 marks)

(iii) Explain whether the insurance company will make a profit or a loss if interest rates increase slightly at all terms. (3 marks)