SOA Exam ALTAM Spring 2026, Question 5
Study guide: Exam ALTAM
You are developing a Type A last survivor universal life policy of 1,000,000 on a couple, Xiaobai and Yvette. At the issue date Xiaobai is 51 and Yvette is 61. You are given:
(i) The death benefit is paid at the end of the year of the second death.
(ii) Premiums are payable at the start of each year.
(iii) Account values are calculated annually; AV_t denotes the account value at t.
(iv) Xiaobai and Yvette have independent future lifetimes.
(v) The cost of insurance (COI) is based on 100% of the mortality in the Standard Ultimate Survival Model (SUSM).
(vi) The interest rate for calculating the COI is i_q = 0.03.
(vii) Initial expense charges are 200 plus 40% of the first premium.
(viii) Renewal expense charges for the second and subsequent policy years are 50 plus 10% of the premium.
Part a (1 point)
Show that 1000 \times q_{\overline{51:61}} = 0.005 to the nearest 0.001. You should calculate the value to the nearest 0.00001.
Part b (3 points)
The couple pays a premium of 14,400 at the start of the first year. The crediting rate in the first year is 5%.
(i) Calculate AV_1 if both insureds remain alive at the end of the first year.
(ii) State with reasons whether AV_1 would be larger, smaller, or the same, if only Yvette survives to the end of the first year.
Part c (2.5 points)
You are given that AV_6 = 92{,}000, a premium of 14,400 is paid at t = 6, and the crediting rate in the 7th year is 5%.
(i) Calculate AV_7 if both lives are alive at t = 6.
(ii) Calculate AV_7 if only Xiaobai is alive at t = 6.
Part d (3.5 points)
The policy has a no lapse guarantee. At the end of year 10, based on this policy's premium history, it cannot lapse before the end of year 20. The reserve for the no lapse guarantee is based on the following assumptions:
- Mortality follows the SUSM.
i = 0.05
You are given that AV_{10} = 127{,}000.
(i) Show that A^{\;1}_{\overline{61:71}:\overline{10}|} = 0.008 to the nearest 0.001. You should calculate the value to the nearest 0.0001.
(ii) Determine the reserve for the no lapse guarantee at the end of year 10 if both lives are alive at time 10.
(iii) Determine the reserve for the no lapse guarantee at the end of year 10 if only Yvette is alive at time 10.
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