Question 1

An actuary is profit testing a 15-year endowment assurance policy. The sum assured is 25,000

payable on survival or at the end of the year of earlier death. On surrender, a return of premiums

is paid without interest at the end of the year of surrender.

A level premium of 1,500 pa is payable annually in advance.

For a policy in force at the start of the eighth year the remaining details are as follows:

()

Renewal expenses 35

Claim expenses on death or surrender 75

Reserve at the start of year, 7V 8,000

Reserve at end of year per survivor, 8V 9,300

Rate of interest 8% pa

Dependent probability of death during 8th year 0.02

Dependent probability of surrender during 8th year 0.05

Calculate the profit expected to emerge at the end of the eighth year, per policy in force at the

start of that year.

A unit-linked policy issued to lives aged 50 has a minimum death benefit of 3,000 (payable at the

end of the year). Write down an expression for the expected death cost in the non-unit fund for

Year 2 for a policy in force at the start of the year, expressed in terms of i F , the size of the unit

fund at the end of year i

Amit aged 60, invests 100 at the beginning of each month in an account earning interest at the

rate of 1% per month. Amit requires a guaranteed amount of 3,000 at the end of the month of

his death. To provide this guarantee, he buys a decreasing term assurance with a sum assured

payable at the end of the month following death equal to the difference between the balance in

the account and 3,000. The office premium for the assurance is 10 per month. The office

incurs initial expenses of 25 and renewal expenses of 5 per month. The mortality basis for

premium calculations is AM92 Ultimate and a uniform distribution of deaths over each year of age

is assumed.

Determine the expected net outgo for the 18th month of the assurance contract as at policy

outset. (Ignore interest earned by the life office.)

A life insurance company sells five-year-term, single-premium, unit-linked policies each for a

premium of 10,000. There is no bid/offer spread and the allocation percentage is 100%. The

only charge is a 2% annual management charge. The maturity, death and surrender benefits are

equal to the value of the units at maturity, or at the end of the year of death or surrender, as

appropriate, after deduction of the annual management charge in each case

(i) Define in words the following single figure indices: the crude death rate . . the directly standardised mortality rate the standardised mortality ratio. [4] (ii) Two states, A and B, of a particular country have produced the following mortality data for a given time period: State A Age last birthday Deaths Central exposed to risk 0 - 19 75 40,000 20 -59 1,175 80,000 60 - 100 2,600 60,000 Total 3,850 180,000 State B Age last birthday Deaths Central exposed to risk 0- 19 150 30,000 20 - 39 300 20,000 40 - 59 375 15,000 60 - 100 600 10,000 Total 1,425 75,000 (a) Calculate the crude death rates and the standardised mortality ratios for the two areas, using ELT15 (Males) as the standard mortality basis, where appropriate. (For this purpose, you can assume that all lives in a particular age band are subject to the force of mortality applicable to the average age of that band.) (b) Comment on your results. [7] [Total 11]