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
100% Free

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\%.
Create a Free Account to Access All 117 Questions →

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

About FreeFellow

FreeFellow is a free exam prep platform for actuarial (SOA & CAS), CFA, CFP, CPA, CAIA, and securities licensing candidates. Every question includes a detailed solution. Full lessons, flashcards with spaced repetition, timed mock exams, performance analytics, and a personalized study plan are all included — no paywalls, no ads.