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Questions and Answers
What is the formula for the present value (PV) of benefits payable immediately on death in a continuous term assurance contract?
What is the formula for the present value (PV) of benefits payable immediately on death in a continuous term assurance contract?
How is the expected present value (EPV) calculated for deferred whole life assurance contracts when benefits are payable at the end of the year?
How is the expected present value (EPV) calculated for deferred whole life assurance contracts when benefits are payable at the end of the year?
What does the variance formula for benefits payable immediately on death in a continuous whole life assurance contract illustrate?
What does the variance formula for benefits payable immediately on death in a continuous whole life assurance contract illustrate?
In a discrete term assurance contract, how is the variance for benefits payable at the end of the death year represented mathematically?
In a discrete term assurance contract, how is the variance for benefits payable at the end of the death year represented mathematically?
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What is indicated by the PV formula for deferred whole life assurance when benefits are payable at the end of the death year?
What is indicated by the PV formula for deferred whole life assurance when benefits are payable at the end of the death year?
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Which statement best describes the expected present value for 'deferred' benefits payable immediately in a continuous term assurance contract?
Which statement best describes the expected present value for 'deferred' benefits payable immediately in a continuous term assurance contract?
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Which benefit structure is represented by the sum $ ext{sum}(k=0)^n V_{k+1}k_{12}^*x$ in the context of term assurance contracts?
Which benefit structure is represented by the sum $ ext{sum}(k=0)^n V_{k+1}k_{12}^*x$ in the context of term assurance contracts?
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In an endowment life assurance contract, what does the formula $A_{x:n} = ar{A}x + rac{1}{eta} A{x:n}$ signify?
In an endowment life assurance contract, what does the formula $A_{x:n} = ar{A}x + rac{1}{eta} A{x:n}$ signify?
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Study Notes
Whole Life Assurance Contracts
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Product Benefits Payable at End of Death Year (Discrete): The present value (PV) of benefits payable at the end of the death year is calculated as V * Kxt for all K. Variance is 2Ax - (Ax)2.
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Product Benefits Payable Immediately on Death (Continuous): The present value (PV) is V * Vx for all tx. Variance is 2Ax - (Ax)2.
Term Assurance Contract
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Product Benefits Payable at End of Death Year (Discrete): Present value (PV) is calculated as Σ Vk * kt * kx where k starts at 0. Variance is 2Ax - (Ax)2
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Product Benefits Payable Immediately on Death (Continuous): Present value (PV) = ∫ Vt * tx * ax * ∫Vt * tx * ax dt if tx < n. Variance = Ax∫0tVtPxt * µx+tdt - (Ax)2.
Endowment Life Assurance Contracts
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Product Benefits Payable at End of Death Year (Discrete): PV is Vn if k ≤ n = Σ Vk * k/2x, OR Vmin(k,n) = (Ax+x + Ax - V). Variance = 2Ax:m - (Ax:m)2.
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Product Benefits Payable Immediately on Death (Continuous): PV = Vmin(Tx,n), OR = Vtx ∫ Vtpxµx+t dt , OR Ax:m + Ax -V. Variance = 2Ax:m - (Ax:m)2
Pure Endowment Assurance Contract
- Benefits Payable at End of Death Year (Discrete): Benefits are payable at a fixed time, independent of survival. Ax = Σ (Vk nPx) if k ≥ n, Variance = Ax - (Ax)2. Important Note: Benefits are payable only at the end of the contracted term.
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Description
This quiz focuses on Whole Life Assurance and Term Assurance Contracts, detailing the present value calculations and variance for benefits payable at different intervals. Test your knowledge on the mathematical principles behind these insurance products.
