10. (a) Show that the present value of an annuity of 1 per annum payable annually in arrears, am, is given by am 1-0" where v is the discount factor from time 1 to time 0, and i is the effective rate of interest per annum. [4 marks] (b) Find the present value for an annuity of 200 per annum payable annually in arrears for 8 years assuming the force of interest is 2% per annum. [3 marks] (c) Find the present value for an annuity of 100 per annum payable at the end of every three years for 60 years, assuming the rate of interest is 6% per annum effective. [Total: END OF PAPER [4 marks] 11 marks]