SOA Exam ALTAM Fall 2023, Question 5

An insurer sells both Type A and Type B universal life insurance policies to lives age 75.

You are given the following information about these policies:

(i) The cost of insurance rates for the policy are 100% of the mortality rates in the Standard Ultimate Mortality Model.

(ii) The interest rate used to discount the cost of insurance charge is 4%.

(iii) The expense charges at the beginning of each policy year are 100 plus 10% of premium.

(iv) The credited interest rate during all policy years is 7%.

(v) The corridor factor in all years is 1.05.

Part a (1 point)

Explain why Type A universal life policies are more commonly affected by corridor factors than Type B universal life policies.

Part b (1 point)

Consider a Type B universal life policy, with a death benefit of 100,000 plus the account value. The premium paid at the beginning of the first policy year is 10,000.

Show that the cost of insurance charge for the first policy year is 1800 to the nearest 100. You should calculate the value to the nearest 1.

Part c (1 point)

Calculate the account value of the policy at the end of the first policy year.

Part d (2 points)

Now consider a Type A universal life policy with a face amount of 100,000. The premium paid at the beginning of the first policy year is 10,000.

Calculate the account value of this policy at the end of the first policy year.

Part e (3 points)

The account value at the end of the 8th policy year for the Type A policy is 81,618.64. The policyholder pays a 10,000 premium at the beginning of the 9th policy year. Calculate the account value at the end of the 9th policy year.

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