Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) Present Value Random Variables for Long-Term Insurance Coverages Practice Questions
Present value random variables on SOA Exam FAM test insurance and annuity present values, variance of future loss, and the mathematical relationship between whole life insurance and whole life annuity functions.
157 questions87 easy43 medium27 hard2026 syllabus
Sample Questions
Question 1
Easy
Which of the following correctly describes Ax:n∣?
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Correct Answer: A
Solution
A is correct.
No bar means discrete. No superscript 1 means the benefit pays on the first of death or survival to n. This is an endowment insurance: Ax:n∣=Ax:n∣1+nEx.
Question 2
Medium
You are given Ax=0.35, Ax:10∣1=0.05, and 10Ex=0.45. Calculate Ax+10.
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Correct Answer: E
Solution
E is correct.
The deferred insurance is:
10∣Ax=Ax−Ax:10∣1=0.35−0.05=0.30
Also 10∣Ax=10Ex⋅Ax+10, so:
Ax+10=10Ex10∣Ax=0.450.30=32=0.667
Question 3
Hard
You are given: Aˉx:n∣=0.60, nEx=0.35, and Aˉx+n=0.50. Calculate Aˉx.
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Correct Answer: C
Solution
C is correct.
First: Aˉx:n∣1=Aˉx:n∣−nEx=0.60−0.35=0.25.
The deferred insurance: n∣Aˉx=nEx⋅Aˉx+n=0.35×0.50=0.175.
The whole life insurance: Aˉx=Aˉx:n∣1+n∣Aˉx=0.25+0.175=0.425.
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