SOA Exam ALTAM Sample Question 24

Study guide: Exam ALTAM

ABC Insurance issues a 10-year endowment insurance policy to Person A who is 60 and Person B who is 50. The sum insured is 200,000 payable at the earliest of the end of the year of the first death and the end of 10 years. Premiums are paid annually in advance.

You are given:

(i) Mortality follows the Standard Ultimate Life Table.

(ii) $i = 0.05$

(iii) Person A and Person B have independent future lifetimes.

(iv) Gross premiums are calculated using the equivalence principle.

Part a (1 point)

Show that the net premium is 15,780 to the nearest 10. You should calculate the value to the nearest 1.

Part b (2 points)

Show that ${}^2A_{50:60:\overline{10}|} = 0.39$ to the nearest 0.01. You should calculate the value to the nearest 0.0001.

Part c (1 point)

Calculate the standard deviation of the net Loss at Issue random variable.

Part d (1 point)

Expenses are 25% of the first year's premium plus 10% of all renewal premiums. Calculate the gross premium using the equivalence principle.

Part e (2 points)

Following a major economic upheaval, the interest rate has increased to 10.25% per year. Note that $1.05^2 = 1.1025$ .

(i) Calculate the percentage reduction in the gross premium, as a result of the change in the interest rate.

(ii) State with reasons whether the percentage reduction in the premium for a 10-year term joint life insurance on Person A and Person B would be greater or less than the change in (i) above.

(This is Question 5 from the Fall 2021 Form A Written Answer exam.)

Answer this question and see the worked solution