Answer the following questions in clear and concise explanation

Question 1.2 A whole life annuity is payable continuously to a life now aged 60. The rate of payment at time / is: p(1) = 10,000(1.02) (/>0) (i) Write down an expression for the present value of the annuity in terms of annuities-certain. [2] (ii) Write down expressions for the expected present value and variance of the present value of the annuity. [2] (iii) Calculate the expected value and the variance of the annuity assuming AM92 Ultimate mortality and 6.08% pa interest. [4] (iv) Simplify your expressions for the present value and its expectation assuming that i =0.02. [2] (v) Calculate the expected present value of the annuity assuming AM92 Ultimate mortality and 2% pa interest. [1] [Total 11] Question 1.3 Consider the following assertions relating to a mortality model that assumes uniform decrement rates between consecutive integer ages, where x is an integer and OS/