SOA Exam ALTAM Sample Question 22

Study guide: Exam ALTAM

D and M are each aged 50, and have independent future lifetimes. They purchase a fully discrete last survivor whole life insurance of 100,000. You are given:

(i) Mortality for each life follows the Standard Ultimate Life Table (SULT).

(ii) $i = 0.05$

(iii) Premiums of $G$ per year are payable until the second death.

(iv) Premiums are payable semi-annually for the first 20 years, then annually thereafter.

(v) $G$ is calculated using the equivalence principle.

(vi) Commissions are 10% of each premium.

(vii) Other acquisition expenses, payable at issue, are 70% of $G$ .

(viii) The two-term Woolhouse formula is used to value single and joint life annuities.

Part a (1 point)

Show that the probability that exactly one of D and M survives 20 years, is 0.14 to the nearest 0.01. You should calculate the probability to the nearest 0.0001.

Part b (2 points)

Show that $\ddot{a}_{\overline{50:50}:\overline{20}|}^{(2)}$ is 12.92 to the nearest 0.01. You should calculate the value to the nearest 0.0001.

Part c (2 points)

Show that $G$ is 850 to the nearest 10. You should calculate the value to the nearest 0.1.

Part d (2 points)

(i) Show that the policy value at time 20, if both lives are alive, is 22,400 to the nearest 100. You should calculate the value to the nearest 1.

(ii) Calculate the policy value at time 20 if only one of the lives is alive at that time.

Part e (3 points)

Calculate the policy value at time 19.5 if both D and M are alive at that time. Assume a constant force of mortality between ages 69 and 70 for the individual lives.

(This is Question 4 from the Fall 2020 Written Answer exam.)

Answer this question and see the worked solution