Solve the following microeconomics questions.thanks

3.1 Evaluate (a) As and (b) As on the bases: (i) A1967-70 ultimate, 4% p.a. interest; (ii) E.L.T. No.12 . Males, 4% p.a. interest. 3.2 (i) Show that Ax = vqx + up,Ar+1 (ii) Given that poo = 0.985, per = 0.98, i = 0.05 and Acz = 0.6 , evaluate Aci and Aco 3.3 Consider n lives now aged 31, 12, ..., I', respectively. Let Z be the total present value of a contract providing the sum of fS, immediately on death of (r;), i = 1,2, ..., n. The n lives are subject to the same non-select mortality table, Table B, and the interest is taken to be fixed at rate i p.a. Show that E(Z) = SIA., + .. + S,Ax, on Table B with interest at rate i p.a. (ii) Assuming further that the future lifetimes 7(r;) of the lives are independent variables, show that Var( Z) = > SHIA; - (An,)] 1=1 where * refers to an interest rate of 2i tip.a. 3.4 Using commutation functions or otherwise calculate the values of the following: (i) A(to]:10 on A1967.70, 4% p.a. interest; (ii) 30:20 on A1967-70 Ultimate, 4%; (iii) A30:20 on A1967-70 Ultimate, 4%; (iv) A30:20 on A1967-70 Ultimate, 4%; (v) Aso:20 on English Life Table No.12 Males, 4%.Example 5.4.1. Consider n year endowment assurance without profits with sum assured fl issued to & select life aged a Expenses are & pur premium payment (including the first) plus / at issue date (so the total initial expense is / + e ). Find formulae for the level office annual premium, P".Net Annual Premium Net Annual Premium payable throughout duration of contract Limited to t payments Type of Assurance Symbol In terms of In terms of commutation Symbol In terms of In terms of commutation A and a Functions (n > 2) A and a Functions (n > 2 and t 2 2) A]:m MY - Mito A:m My - Mite Temporary a[x]:m No] - Nitn "[x]:71 No] - Nitt Deferred Motm - Mitt Metm - Metmth P (m|:m ) P ( m| App]:m ) Temporary No - Nitmen "[x]:21 No - Nitt M (x] M[=] Whole-life NI] - Nett Deferred Mr+m Whole-life P(m| 4[=]) No - Nett Endowment Me] - Mito + Pitn My - Mitt Pita Assurance No - Nitt