Answer all 4 questions well.thanks

Example 8.4.1. A certain life office's premium basis for lives accepted at normal rates is as follows: Mortality: A1967-70 ultimate Interest: 4% per annum Expenses: none A certain impaired life, aged 50, is considered to be subject to the office's normal mortality rates for a life 10 years older. This life requires a contract providing the following benefits: (i) 430,000 at the end of the year of death, if within 10 years; (ii) on survival for 10 years, the sum of / (30, 000 + S). The impaired life finds that the level annual premium for this policy is the same for a policy providing identical benefits for a life his age accepted at normal rates. Find S.Example 8.5.1. A life office calculates annual premiums for without profits endowment assurances using the following basis: Mortality: A1967-70 select Interest: 4% Initial expenses: 50% of the first premium Renewal expenses: 5% of each premium after the first (i) Calculate the annual premium payable for a 25 year endowment assurance taken out by a male life aged exactly 45 for a sum assured of 650.000. The death benefit is payable at the end of the year of death. (ii) A man aged exactly 45 effects a policy identical to that in (i) above but rated up 7 years. (a) Calculate the level extra premium, payable throughout the term of the policy. (b) Alternatively, the life office offers to charge the standard premium but to impose a level debt. Calculate the amount of the debt.(i) Use the figures in the following table to calculate the marginal utility (expressed in $s) Sanjay obtains by consuming Good X and comment on your answers. Consumption of Total utility (5) Good X 1 30 2 55 3 76 4 95 5 113 (ii) Suppose that the market price of Good Xis $20. Determine the number of units of Good X Sanjay should consume and calculate his resulting consumer surplus.The following table shows the total utility that Peter receives from consuming various quantities of Good X and Good Y. Units of Total utility Marginal utility Total utility Marginal utility good from units of from each unit from units of from each unit consumed Good X of Good X Good Y of Good Y consumed consumed consumed consumed 1 10 12 2 18 22 3 25 30 4 30 36 5 34 40 6 37 43 (i) Complete the columns for the marginal utility of Good X and the marginal utility of Good Y. (ii) If Good X costs $2 and Good Y costs $4, list the possible combinations of goods that would satisfy the condition for the optimum combination of goods consumed and calculate the total utility of each combination. (iii) Assuming that Peter has 16 to spend on the two goods (and that there are no other goods available), identify the combination of Good X and Good Y that he will consume. (iv) If Peter's income now increases to E20, determine the combination of goods he will now buy