1. An insurer issues 5,000 whole life insurance policies to select lives aged 51. The appropriate interest rate is i = 0.06. The company calculates A[51] = 0.111865 and 2A[51] = 0.0276334.
If the death bene t is $350,000, what annual premium should the company charge using the portfolio percentile method with a 98% probability of making a pro t?
2. Using the lifetable in Table 1, and interest rate i = 0.05, calculate the net annual premium for a 5-year term insurance policy with Death bene t $250,000, sold to a select life aged 32,
if:
(a) The life is an impaired life, and is treated as being 8 years older than she is [but is still treated as being select at the start of the policy].
(b) The life works in a hazardous environment, and has mortality 0.008 higher than normal.
3. An insurance company has a whole life insurance policy for a select individual aged 39. The death bene t of this policy is $800,000, and the interest rate is i = 0.07. Premiums are payable until age 80. The insurance company calculates A[39] = 0.0423697, and A[39]+41 = 0.353734.
Therefore, the net annual premium for the policy is $2,361.64. What is the policy value if the life survives to age 75? [Use the lifetable in Table 1. A[39]+36 = 0.286183.]
4. For the individual in Question 3, what is the policy value at age 75 if the individual is found to be select at age 75? [All other assumptions remain the same.]
5. For the individual in Question 3, what is the policy value at age 75 if the interest rate has increased to i = 0.09? [All other assumptions remain the same as in Question 3. At this interest rate, we have A80 = 0.281157 and A75 = 0.218262.]
6. A select life aged 48 takes out a 5-year endowment insurance with bene t $600,000. The initial cost of this insurance is $1000 plus 30% of the rst annual premium. The renewal cost is 2% of each subsequent premium. The interest rate is i = 0.04. Using the lifetable in
Table 1, we can calculate A[48]:5j = 0.8221934 .
(a) Calculate the gross premium for this policy.
(b) Calculate the gross policy value after 2 years.
7. An insurance company wants to develop a new policy with a variable death bene t, designed so that if the policy basis does not change, then the net policy value is 0 at all future times.
Assuming the policy has a constant annual premium, what should the death bene t be if the policyholder dies in the nth year of the policy?