Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) Pricing and Reserving for Short-Term Insurance Coverages Practice Questions

Practice pricing and reserving for short-term insurance coverages on Exam FAM. Questions involve loss development triangles, case reserves, IBNR estimation, and ratemaking fundamentals.

117 Questions
49 Easy
40 Medium
28 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
Which is NOT typically a variable expense in ratemaking?
Solution
Variable expenses vary with premium: commissions, taxes, contingent commissions, assessments. Rent is fixed.

(A), (B), (D), (E) are variable. The answer is rent.
Question 2 Medium
Reported \$500K; CDF 1.50; EP \$1,200K; ELR 65%. Calculate the BF ultimate.
Solution
% reported =1/1.50=66.7%= 1/1.50 = 66.7\%. Unreported =33.3%= 33.3\%. Expected ult =1200K×0.65=780K= 1200K \times 0.65 = 780K.

BF =500K+0.333×780K=500K+260K=760K= 500K + 0.333 \times 780K = 500K + 260K = 760K. CL =750K= 750K. ELR =780K= 780K.

(A) too low. (B) CL estimate. (D) ELR estimate. (C) too high.

The answer is $760,000\$760{,}000.
Question 3 Hard
Complete loss cost indication per exposure: undeveloped L&LAE \$500, dev factor 1.20, trend factor 1.10, fixed expenses \$60, V = 20%, Q = 5%, current premium \$950.

Calculate the indicated rate change.
Solution
Developed: 500×1.20=600500 \times 1.20 = 600. Trended: 600×1.10=660600 \times 1.10 = 660. Total: 660+60=720660 + 60 = 720. PLR =1−0.20−0.05=0.75= 1 - 0.20 - 0.05 = 0.75. Indicated: 720/0.75=960720/0.75 = 960. Change: 960/950−1=+1.05%≈+1.1%960/950 - 1 = +1.05\% \approx +1.1\%.

(A) large decrease, not supported. (B) moderate decrease, not supported. (D) overstates the change. (C) too high.

The answer is +1.1%+1.1\%.
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More Exam FAM Topics

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

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