Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) Premium and Policy Value Calculation for Long-Term Insurance Coverages Practice Questions

Master premium and policy value calculations for long-term insurance on Exam FAM. Questions cover net and gross premiums, benefit reserves, Thiele's equation, and profit testing.

208 Questions
99 Easy
78 Medium
31 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
Which expression equals P(Ax)P(A_x)?
Solution
P=(1−da¨x)/a¨x=1/a¨x−dP=(1-d\ddot{a}_x)/\ddot{a}_x=1/\ddot{a}_x-d.

(A) adds dd. (C) reverses subtraction. (D) is too small. (E) is too large.

The answer is (B).
Question 2 Medium
For a fully discrete whole life insurance of 1 with 10V=0.18{}_{10}V=0.18, P=0.02P=0.02, qx+10=0.015q_{x+10}=0.015, i=0.06i=0.06, calculate 11V{}_{11}V.
Solution
(0.18+0.02)(1.06)=0.015+0.985⋅11V(0.18+0.02)(1.06)=0.015+0.985\cdot{}_{11}V. 0.212=0.015+0.985⋅11V0.212=0.015+0.985\cdot{}_{11}V. 11V=0.197/0.985=0.200{}_{11}V=0.197/0.985=0.200.

(A) assumes constant reserve. (B) ignores interest. (C) uses wrong qq. (E) uses q=0q=0.

The answer is (E).
Question 3 Hard
For a fully discrete whole life insurance of 1 on (x), you are given:

- Ax=0.25A_x = 0.25, i=0.06i = 0.06

If mortality increases so that A'_x = 0.35, calculate the change in the net premium PxP_x.
Solution
d=0.06/1.06=3/53d = 0.06/1.06 = 3/53.

Original: a¨x=0.753/53=0.75×533=39.753\ddot{a}_x = \frac{0.75}{3/53} = \frac{0.75 \times 53}{3} = \frac{39.75}{3} = 13.25
Px=0.2513.25=0.01887P_x = \frac{0.25}{13.25} = 0.01887

New: a¨x′=0.653/53=0.65×533=34.453\ddot{a}'_x = \frac{0.65}{3/53} = \frac{0.65 \times 53}{3} = \frac{34.45}{3} = 11.483
Px′=0.3511.483=0.03048P'_x = \frac{0.35}{11.483} = 0.03048

Change =0.03048−0.01887=0.01161= 0.03048 - 0.01887 = 0.01161.

0.011610.01161, closest to (C) 0.010000.01000. Not a great match.

The answer is (A).
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More Exam FAM Topics

Short-Term Insurance and Reinsurance Coverages Severity, Frequency, and Aggregate Models Parametric Estimation Introduction to Credibility Pricing and Reserving for Short-Term Insurance Coverages Option Pricing Fundamentals Long-Term Insurance Coverages and Retirement Financial Security Programs Mortality Models Present Value Random Variables for Long-Term Insurance Coverages

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