Question 1

Craig, aged 40, buys a four-year unit-linked endowment policy under which level annual

premiums of 1,000 are payable. 75% of the first premium and 105% of each subsequent

premium is invested in units. There is a bid/offer spread in unit values, the bid price being 95% of

the offer price.

A fund management charge of 0.75% of the value of the policyholder's fund is deducted at the

end of each policy year.

The death benefit, which is payable at the end of the year of death, is 3,000 or the bid value of

the units if greater. The maturity value is equal to the bid value of the units.

The insurance company incurs expenses of 150 at the start of the first year, 75 at the start of

the second year, and 25 at the start of each of the third and fourth years.

The mortality probability ( x q ) is assumed to be 0.01 at each age and withdrawals may be ignored.

(i) Assuming that the growth in the unit value is 5% pa, the non-unit interest rate is 5% pa,

and the insurance company holds unit reserves equal to the value of units and zero

non-unit reserves, calculate the expected profit emerging in each policy year.

(ii) Calculate the revised profit emerging each year assuming that the office sets up non-unit

reserves to ensure that the expected profit emerging in the second and subsequent policy

years is non-negative.

A life table with a select period of 2 years is based on rates of mortality, which satisfy the following relationship: 9 x-]+r= Xqx (for all values of x , and r = 0,1 ) 3-r 460 = 0.0195 , 461 = 0.0198, 962 = 0.0200 and /63 =100, 000 (i) Calculate: (a) 162 (b) 460]+1 (c) [60] [4] (ii) A select life aged 60 subject to the mortality table described in (i) above purchases a 3-year endowment assurance with sum assured f10,000. Premiums of f3,000 are payable annually throughout the term of the policy or until earlier death. The death benefit is payable at the end of the year of death. Calculate the expected value of the present value of the profit or loss to the office on the contract, assuming an effective rate of interest of 6% pa, and ignoring expenses. [4] [Total 8]