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

Short-term insurance coverages on SOA Exam FAM cover property and casualty policy forms, deductibles, coinsurance, and reinsurance structures. This topic introduces how insurers transfer and manage underwriting risk.

72 Questions

27 Easy

28 Medium

17 Hard

2026 Syllabus

Sample Questions

Question 1 Easy

Losses follow an exponential distribution with mean 800. Calculate the mean excess loss at

d = 300

Solution

C is correct.

The exponential distribution is memoryless:

e(d) = E[X - d \mid X > d] = \theta

for all

d \ge 0

. With

\theta = 800

e(300) = 800

Question 2 Medium

An excess-of-loss reinsurance treaty has a retention of 50,000. A loss of 80,000 occurs. How much does the reinsurer pay?

Solution

C is correct.

Under excess-of-loss reinsurance with retention

M = 50{,}000

, the reinsurer pays

\max(X - M, 0) = \max(80{,}000 - 50{,}000, 0) = 30{,}000

Question 3 Hard

Losses follow a Pareto distribution with

\alpha = 3

and

\theta = 2{,}000

. Calculate the loss elimination ratio (LER) for an ordinary deductible of

d = 500

Solution

C is correct.

For a Pareto distribution with

\alpha = 3

and

\theta = 2{,}000

:\n\n

E[X] = \theta/(\alpha - 1)

= 2{,}000/2 = 1{,}000.\n\nThe limited expected value at

d = 500

:\n

E[X \wedge d] = \frac{\theta}{\alpha - 1}\left[1 - \left(\frac{\theta}{\theta + d}\right)^{\alpha - 1}\right] = 1{,}000\left[1 - (0.8)^2\right] = 1{,}000 \times 0.36 = 360

\text{LER} = \frac{E[X \wedge d]}{E[X]} = \frac{360}{1{,}000} = 0.3600

Create a Free Account to Access All 72 Questions →

About FreeFellow

FreeFellow is an AI-native exam prep platform for actuarial (SOA & CAS), CFA, CFP, CPA, CAIA, GARP FRM, IRS Enrolled Agent, IMA CMA, and FINRA / NASAA securities licensing candidates — built around modern AI as a core capability rather than as a bolt-on. Every lesson ships with AI-narrated audio. Every constructed-response item has a copy-to-AI prompt builder so candidates can paste their answer into their own ChatGPT or Claude for self-graded feedback. Fellow members get instant AI grading on essays against the official rubric (currently CFA Level III, expanding to other essay-bearing sections).

The 70% you need to pass — question bank, written solutions, lessons, formula sheet, mixed practice, readiness tracking — is free forever, with no trial period and no credit card. Become a Fellow ($59/quarter or $149/year per track) to unlock mock exams, flashcards with spaced repetition, performance analytics, AI essay grading, and a personalized study plan.