SOA Exam ALTAM Spring 2024, Question 6

Study guide: Exam ALTAM

A policyholder age 70 purchases two policies:

A Type B Universal Life (UL) policy with an additional death benefit of 100,000.
A 10-year equity-linked (EL) insurance policy with a guaranteed minimum death benefit equal to the value of the premiums accumulated at 5% interest, and a guaranteed minimum maturity benefit of the total premiums paid.

You are given the following information about the policies.

UL policy information:

The policyholder pays premiums of 20,000 at the start of each year.
The death benefits are paid at the end of the year of death.
The policy uses a COI rate of 150% of the Standard Ultimate Mortality Model, and an interest rate $i_q = 0\%$ for calculating the cost of insurance.
Expense charges of 1.5% of the account value (before the premium) plus 2% of the premium are payable at the start of each year.
There is a level corridor factor of 1.5.
Each year the insurer sets an anticipated rate that it expects to earn on its EL funds. The credited rate for the UL policy is set at 65% of this anticipated rate, with a minimum credited rate of 2.5%.
Account values are calculated annually.

EL policy information:

The policyholder pays premiums of 20,000 at the start of each year.
The death benefits are paid at the end of the year of death.
Management charges of 2% of the fund value (before the premium) plus 2% of the premium are payable at the start of each year.
An additional management charge of 4,000 is payable at the start of the first year.

Part a (2 points)

The anticipated rate earned and actual rate earned on the EL funds in the first year are both 9%.

(i) Calculate the account value at time 1 for the UL policy.

(ii) Calculate the fund value at time 1 for the EL policy.

Part b (3 points)

The policyholder survives to time 9. You are given:

The account value for the UL policy at time 9 before the premium payment is 196,840.
The fund value for the EL policy at time 9 before the premium payment is 212,000.
The anticipated rate and the actual rate earned on the EL funds in the 10th year are both 3%.

(i) Show that the account value at time 10 for the UL policy is 214,000 to the nearest 100. You should calculate the value to the nearest 1.

(ii) Show that the fund value at time 10 for the EL policy is 234,200 to the nearest 100. You should calculate the value to the nearest 1.

Part c (2 points)

Calculate the payout from each policy if the policyholder dies during the 10th year.

Part d (2 points)

Describe two advantages and two disadvantages of the UL policy compared with the EL policy, from the perspective of the policyholder.

Part e (2 points)

The policyholder decides to annuitize the EL proceeds at policy maturity (calculated in (b)(ii)). The policy has a Guaranteed Minimum Income Benefit (GMIB) option, allowing the policyholder to annuitize the Benefit Base amount at time 10, at a guaranteed annuitization rate of 11.2% for a life age 80. The Benefit Base is the value of the premiums accumulated at 5% interest.

(i) Calculate the annual annuity payout under the GMIB.

(ii) Explain why the policyholder might choose to annuitize the policy proceeds without exercising the GMIB.

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