Answerallquestions:

Attachments.,,

The following diagram shows the aggregate expenditure schedule for the economy and the equilibrium condition on the 45 degree line. Round all answers to the nearest whole number. (36 34X 287 4 20-D AE C +1+ X - IM 167 1B 12 Y = AE K H J 12 15 18 21 24 27 30 33 36 39 Real GDP and Income6 Calculate are on the following basis: Mortality: 70-year-old: PMA92C20 60-year-old: PFA92C20 Interest: 4% pa 7 Two lives, aged 40 and 44, purchase a policy from an insurance company that pays 50,000 in 20 years' time, if at least one of them is still alive at that time. Assuming that the mortality of each life follows the AM92 Select table, and the annual effective interest rate is 6%, calculate the expected present value of the benefits from this policy. Two lives aged x and y take out a policy that will pay $15,000 immediately on the death of (x) yle provided that (y) has died at least 5 years earlier and no more than 15 years earlier. (i) Express the present value of this benefit in terms of the random variables denoting the future lifetimes of (x) and (v) . (2] (ii) Write down an integral expression (in terms of single integrals only) for the expected present value of the benefit. [3] (iii) Prove that the expected present value is equal to: 15,000 VS SPX Antsy -V13 15Px Ax+15:y [3] (iv) Describe the appropriate premium payment term for this policy, assuming premiums are to be paid annually in advance. [2] [Total 10]Express each of the following symbols: in terms of the random variables 7, and Ty , and as an integral. to 9xy xy (iii Two lives, each aged x, are subject to the same mortality table. According to this mortality table, and at a certain rate of interest, A, =0.4 and Axx =0.6. Calculate the value of Ax based on this mortality table and interest rate. Given that: 1 Hx for 0 5 x