(1) An insurance company is selling the one-year term insurance that pays an extra benefit in case of accidental death that is described on page 29. The company wishes to have at least a 95% probability that premiums with a relative security loading of 0.20 are adequate to cover claims. Using the normal approximation, determine the minimum number of policies that must be sold. (Ans 29,999.3, which rounds up to 30,000 policies).

(4) An insurance company has two classes of insured lives:

Class Claim Probability Claim Amount No. in Class

Smoker 0.6 1 100

Non-smoker 0.4 1 200

The company charges each smoker a relative security loading that is two times the relative security loading charged to each non-smoker. The company wants the total premium collected to equal the 95^th percentile of the aggregate claims distribution. Make a table like the one on page 41 for the two classes of insured lives. Then determine the relative security loading for non-smokers. (Ans 0.06979)

(5) An insurer offers group term insurance on 250 mutually independent lives for a premium of 285. The probability of a claim is 0.02 for each life. The distribution of the number of lives by benefit amount is:

Benefit Amount Number Covered

20 100

50 100

100 50

(a) Reinsurance is purchased which costs 120% of expected claims above a retention limit of 40 per life.

1. Calculate I, the total amount of insurance. (Ans 12,000)
2. Calculate I^R, the total amount of retained insurance.(Ans 8,000)
3. Calculate I', the total amount of reinsurance. (Ans 4000)
4. Calculate E(S'), the expected value of reinsured claim payments. (Ans 80)
5. Calculate the cost of the reinsurance. (Ans 96)
6. Using the normal approximation, determine the probability that the total of retained claims and reinsurance premiums will exceed the premium. (Ans 0.348)