You are given the following survival model: 2=5.510t1.122r,50x100 Choose a rate of interest i between 2% and 7% per anmum effective. State this value clearly in your report and use the same interest rate throughout the assignment. (a) Without using any approximations, calculate the following for n=30, 50 at your chinen interest rate, i: (i) 115 marks /A100nm and the standard deviation of the corresponding randam variable (b) Using numerical integration, calculate the following for n=30,50 at your-chosen interst rate, i : (i) [10 marks }A100n1m (ii) [10 marks ](Ia)imnin (iii) [10 marks] Comment briefly on the numerical values of the EPV s calculated in parts (a)(i),(a)(i),(b)(i) and (b)(ii). these with your findings in part (b)(i), and comment on thern bricfly. (d) Santa, aged exnctly 70, has made a proposal to a life office for a 30 -year term insurance wieh premiums, P per year payable anmally throughout the term. The sum insured of f250,000 payable at the end of the year of death within the term. The life alfice nses the following pricing basis: Mortality: Survival model as above Interest: 1% pai effective Initial Expensess 2500 Renewal Expenses: 5% of all preninus (t) 10 marks Calculate P. (ii) 120 marks] Calculate the groes preanium policy value immodiately after cach preminus payment (including the fint premium payzuent) during the contract, oa the pricing baves on the result. (iii) [10 marks] The underwriters of the life office consider Santa to bave a higher than tarmal mortality riak, because of his dangerous occupatiou of driving an overlonded sleigh at hrights they consider Santais risk of mortality is equivalent to a comstant addition of 0 03215 to the normal force of mortality al all ages. Using mumerical integration, and souming -100 calculate the complete lifo expectancy of Sant a. Brietly comument ca this result