Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) Premium and Policy Valuation for Long-Term Coverages Practice Questions
Premium and policy valuation on SOA Exam ALTAM tests prospective and retrospective reserve calculations, Thiele's differential equation, gross premium valuation, and the effect of mortality and interest assumptions on reserves.
127 questions48 easy56 medium23 hard2026 syllabus
Sample Questions
Question 1
Easy
Under the equivalence principle, the net premium for a life insurance policy is determined by which of the following conditions?
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Correct Answer: A
Solution
A is correct.
The equivalence principle (also called the net premium principle) requires that at the time of policy issue the EPV of the premium stream exactly equals the EPV of the benefit obligations: EPV(premiums)=EPV(benefits). This makes the expected profit at issue equal to zero โ no explicit loading for profit or expenses is built into the net premium.
Question 2
Medium
For the policy in question altam2-079 (whole life, age 40, ฮผ=0.02, ฮด=0.05, benefit 100,000, continuous net premium P=2,000), calculate the policy value 10โV at time t=10.
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Correct Answer: A
Solution
A is correct.
Because the forces ฮผ=0.02 and ฮด=0.05 are constant (age-independent), the prospective quantities Aหx+tโ and aหx+tโ are the same at every age: Aหx+tโ=0.02/0.07 and aหx+tโ=1/0.07. Therefore: 10โV=100,000โ Aห50โโPโ aห50โ=100,000ร0.070.02โโ2,000ร0.071โ=0.072,000โโ0.072,000โ=0 The reserve is identically zero at every policy duration under constant forces.
Question 3
Hard
A 3-year term insurance on (x) with level benefit 1,000 has the following mortality rates: qxโ=0.010, qx+1โ=0.012, qx+2โ=0.015. Interest rate i=0.05. Compute the net premium reserves 1โV, 2โV prospectively.
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Correct Answer: C
Solution
C is correct.
First compute the net single premium (NSP):NSP=1,000[vqxโ+v2pxโqx+1โ+v32โpxโqx+2โ]=1,000[0.01/1.05+0.99ร0.012/1.052+0.99ร0.988ร0.015/1.053]=1,000[0.009524+0.010773+0.013215]=1,000ร0.033512=33.51 The premium annuity aยจ=1+vpxโ+v22โpxโ=1+0.99/1.05+0.99ร0.988/1.052=1+0.942857+0.886984=2.8299. Net premium P=33.51/2.8299=11.843. Prospective reserve at duration 1:1โV=1,000[vqx+1โ+v2px+1โqx+2โ]โP(1+vpx+1โ)=1,000[0.012/1.05+0.988ร0.015/1.052]โ11.843(1+0.988/1.05)=1,000[0.011429+0.013469]โ11.843ร1.94095=24.898โ22.993=1.905
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