The Never-Say-Die Insurance Company has asked you to develop a premium for its new 10 year life insurance policy. Insureds will pay a single premium at the beginning of the 10 year period. While the policies will be sold at various ages and to both males and females, you have been asked to determine the premium for a policy that will be issued to a 45 year old female. The information on probability of death is provided below. To qualify for the policy, the insureds are all non-smokers and in good health. NSD assumes that it can earn 13% on the cash that it has available to invest. The policy carries a $10,000 death benefit and NSD assumes that it will sell 10,000 of these policies to this group. All death benefits are paid out at the end of the year in which the deaths occur. While NSD has said that the premium charged will include a 25% load to account for operating expenses and profit, they have asked you to base your calculations solely on the expected losses. The probability of dying for females ages 45-54 is as follows (Note: the number of deaths in a given year is calculated by multiplying the probability of death in a given year by the number of indidividuals living at the beginning of that year):
Beginning of Year Age Probaility of Death During Year
1 45 0.0044
2 46 0.0047
3 47 0.0052
4 48 0.0058
5 49 0.0064
6 50 0.0071
7 51 0.0079
8 52 0.0088
9 53 0.0097
10 54 0.0102
Questions:
(1) What is the single premium that NSD will charge to each insured? [Show that the premium calculation is correct (i.e., value at the begninning of year 10 = death benefits to be paid)]
(2) NSD wants to assume 13% interest rate. Does this seem like a reasonable assumption? What happens if the rate of return that NSD actually earns is lower or higher than 13%? What happens if this group of insureds experiences higher than expected losses (e.g., they have collective mid-life crises at age 55 and turn to extreme sports and unfiltered cigarettes for excitement)?