Question 1

A mortality table covers the age range 10 to 100, inclusive. The graduated rates have

been produced using the parametric formula method - a formula with 3 parameters has

been fitted to the crude rates. The deviations of the observed number of deaths from the

expected number of deaths at each age have been calculated. You have:

Number of positive deviations: 41

Number of groups of positive deviations: 16

Carry out a grouping of signs test on these graduated rates and state your conclusion. [6]

For each of the following expected present values, describe the payments involved and calculate the value assuming AM92 mortality and 6% pa interest. (i) (1@)[45]:201 (ii) (IA) 49:61 (iii) (la )(50]:10] Graham, aged 40, purchases a conventional with-profits whole life assurance with sum assured f2,000 plus attaching bonuses, payable at the end of the year of death. Assuming allowance for simple bonuses of 3% pa, which are added at the start of each policy year, calculate the expected present value of Graham's policy benefits. Basis: AM92 Ultimate mortality, 4% pa interest. A special term assurance policy is to be issued to a life currently aged 52 exact. The policy term is 8 years, and the sum assured is paid at the end of the year of death. The benefit is 120,000 in the first year, increasing by 10,000 at the end of each year, so that if death occurs in the final policy year 190,000 will be paid. Calculate the EPV of this policy benefit using the following basis: Mortality: AM92 Ultimate Interest: 4% pa The payments under a special deferred annuity are payable continuously from age 60 and increase continuously at the rate of 5% pa compound. The payment stream starts at the rate of f200 pa. Assuming AM92 Select mortality before age 60 and PFA92C20 mortality after age 60, calculate the expected present value of the annuity for a female life now aged 40, if interest is 5% pa effective. A life insurance company has issued a decreasing term assurance with a 20-year term to a person aged exactly 40. The sum assured is 100,000 in the first year, decreasing by 1,000 each year, so that the death benefit in the final policy year is 81,000. The benefit is paid at the end of the policy year of death. Calculate the EPV of this benefit assuming AM92 Select mortality and 4% pa interest