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
100% Free

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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