Answer the following questions

An annuity policy provides the following benefits: an annuity of $20,000 pa payable monthly in advance. It is guaranteed to last for 10 years and continuing thereafter until the first death out of the two policyholders (a woman aged 63 exact and her husband aged 66 exact); a reversionary annuity of $15,000 pa payable monthly in advance to the surviving spouse, commencing on the next payment date following the death of the first of the lives to die, or from the 10th policy anniversary if this is later. Calculate the net single premium for this policy assuming mortality follows that of the PA92C20 mortality tables (males or females as appropriate) rated down 3 years and using an interest rate of 4% pa. [11](i) An annuity is payable continuously throughout the lifetime of a person now aged exactly 60, but for at most 10 years. The rate of payment at all times / during the first 5 years is $10,000 pa, and thereafter it is $12,000 pa. The force of mortality of this life is 0.03 pa between the ages of 60 and 65, and 0.04 pa between the ages of 65 and 70. Calculate the expected present value of this annuity assuming a force of interest of 0.05 pa. [4] (ii) Assuming that mortality and interest are as in (i) above, calculate the expected present value of: (a) a 10-year term assurance issued to the life in (i), which pays $50,000 immediately on death (b ) a 10-year endowment assurance issued to the life in (i), which pays $50,000 on maturity or immediately on earlier death. [4] [Total 8]