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

Pricing and reserving for short-term insurance on SOA Exam FAM covers loss development triangles, case reserves, IBNR (incurred but not reported) estimation, and fundamental ratemaking techniques.

135 Questions
58 Easy
46 Medium
31 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
Which is NOT typically a variable expense in ratemaking?
Solution
B is correct.

Variable expenses vary with premium: commissions, taxes, contingent commissions, assessments. Rent is fixed.
Question 2 Medium
Reported $500K; CDF 1.50; EP $1,200K; ELR 65%. Calculate the BF ultimate.
Solution
C is correct.

% 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.
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
B is correct.

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\%. The answer is +1.1%+1.1\%.
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