Microeconomics questions

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. If the

policyholder surrenders then she will receive a return of premiums 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 0.02

Dependent probability of surrender 0.05

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

the start of that year?

An insurance company is considering the sale of a 'critical illness extra' term assurance policy. The critical illness benefit is 25,000, payable immediately on diagnosis of a critical illness within the 25-year term. The death benefit is ?5,000, payable immediately on death during the term. 0nly one benefit is payable under any one policy and once the benefit has been paid, both the premiums and the coyer cease. Annual premiums of F po are payable continuously while the policy is in force. The company assesses the profitability of the policy using the following multiple state model: 5:: ~ P'x ,p:\" is defined as the probability that a life who is in state a at age x [o = H, 5, 0} is in state b at agex+ t [1'20 and b=H,5,0]. [ii Suggest, with reasons, one group of customers the insurance company may wish to target in their marketing of this policy. [1] [ii] Express in integral form, using the probabilities and the forces of transition, the expected present value of the profit from one such policy with an annual premium of 1,200 that hasjust been sold to a life aged exactly 50. [2] After careful consideration, the company modifies the policy by changing both the death benefit and the critical illness benefit to be 50,000. [iii] Explain how this modification could considerably reduce the cost of assessing claims. [2] [iv] Given that ,u,, =0.000E and 5,, = 0.0010 for all 155 x5 T0 , and that theforce of interest is 4'36 pa, calculate the expected present yalue of the benefits for the modified policy sold to a life aged exactly 45. [3] [Total 5]