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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?
- $S_0$ if $T_x eq 0$
- $S_0$ if $T_x eq n$ \\ $V^t_x$ if $T_x > n$ (correct)
- $S_0$ if $T_x eq n$ \\ $V^t_x$ if $T_x eq m$
- $S_0$ if $T_x eq n$
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?
- $ ext{some fixed value}$ for all k
- $ ext{not defined}$ for all k > n
- $ ext{sum of values starting from n}$ (correct)
- $S_0$ for all k
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?
- Variance is not applicable in the continuous model
- A constant variance irrespective of A_x
- $2A_x - (A_x)^2$ (correct)
- The square of the average of the present value
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?
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?
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?
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?
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?
Flashcards
Present Value (Whole Life, Discrete)
Present Value (Whole Life, Discrete)
The present value of a whole life assurance contract where benefits are payable at the end of the death year. This is calculated as the sum of the discounted benefits over all possible death years.
Present Value (Whole Life, Continuous)
Present Value (Whole Life, Continuous)
The present value of a whole life assurance contract where benefits are payable immediately upon death. It is calculated as the integral of the discounted benefits over all possible times of death.
Present Value (Deferred Whole Life, Discrete)
Present Value (Deferred Whole Life, Discrete)
The present value of a deferred whole life assurance contract where benefits are payable at the end of the death year after a specified deferral period (n). It is calculated as the sum of discounted benefits for death years after the deferral period.
Present Value (Term Assurance, Discrete)
Present Value (Term Assurance, Discrete)
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Present Value (Term Assurance, Continuous)
Present Value (Term Assurance, Continuous)
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Present Value (Deferred Term Assurance, Discrete)
Present Value (Deferred Term Assurance, Discrete)
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Present Value (Endowment Life, Discrete)
Present Value (Endowment Life, Discrete)
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Present Value (Endowment Life, Continuous)
Present Value (Endowment Life, Continuous)
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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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