Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) Profit Analysis Practice Questions
Profit analysis on SOA Exam ALTAM tests profit measures (NPV of profits, profit margin, IRR), embedded value, asset share calculations, and the impact of experience deviations on product profitability.
111 questions45 easy55 medium11 hard2026 syllabus
Sample Questions
Question 1
Easy
In profit testing, the term px+t−1⋅tV appears in the profit recursion. What does this term represent?
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Correct Answer: A
Solution
A is correct.
The profit recursion tallies all cash outflows at year-end. For each policy that survives to year-end — a fraction px+t−1 of those in force at year-start — the insurer must hold the reserve tV. The expected total reserve held for survivors is px+t−1⋅tV, which is a cash outflow (from the profit perspective) representing the liability being carried forward.
Question 2
Medium
Year-4 gains: q(b)=0.018, q(a)=0.012, NAR=35,000; i(b)=8%, i(a)=6%, fund =20,000; e(b)=160, e(a)=130. Compute total gain.
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Correct Answer: B
Solution
B is correct.
Mortality gain (actual 0.012 lighter than basis 0.018 — favorable): Gμ=(0.018−0.012)×35,000=0.006×35,000=210
Interest gain (actual 6% below basis 8% — unfavorable): Gi=(0.06−0.08)×20,000=−0.02×20,000=−400
Expense gain (actual 130 below basis 160 — favorable): Ge=(160−130)(1.08)=30×1.08=32.40
Gtotal=210+(−400)+32.40=−157.60
Question 3
Hard
A 5-year profit signature: Π0∗=−2,000, Πt∗=600−20(t−1) for t=1,…,5. Compute NPV at r=16% and estimate the IRR. (Python:numpy.irr([−2000,600,580,560,540,520])≈0.178)
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Correct Answer: E
Solution
E is correct.
Compute NPV at r=16%: NPV=−2,000+517.24+430.98+358.76+298.25+247.58=−147.19<0 Since NPV(16%)<0, IRR<16%, not 17.8%. The Python result of 17.8% would require a positive NPV at 16%. Testing at r=5%: NPV=+433.43>0 Interpolating between 5% and 16%: IRR≈5+11×433.43/(433.43+147.19)=5+8.21=13.2%.
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