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For a whole life insurance of 1 on (x), you are given

i) The force of mortality µx(t) (not constant)
ii) δ = 0.06
iii) The benefits are payable at the moment of death
iv) A¯ x (A bar x) = 0.60
Calculate the revised actuarial present value of this insurance assuming µx(t) is increased by 0.03 for all t and δ decreased by 0.03

User Manda
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Final answer:

To calculate the revised actuarial present value of a life insurance policy with changes to the force of mortality and discount rate, one must integrate the increased mortality with the present value of the death benefit, discounting it at the new rate. Exact calculations require additional actuarial data and computations.

Step-by-step explanation:

The student is asking for the calculation of the actuarial present value of a whole life insurance policy assuming changes to the force of mortality and discount rate. Since we know that the original present value was given as 0.60 when the force of mortality is μ_x(t) and the discount rate is δ = 0.06, we need to adjust this value based on the given changes: increasing the force of mortality by 0.03 and decreasing δ by 0.03.

The revised actuarial present value is calculated by integrating the product of the increased force of mortality and the present value of a benefit of 1, payable at the moment of death, over the entire lifetime, and then discounting it at the new discount rate. In practice, this entails a more complex actuarial computation that typically requires the use of life tables and the application of actuarial mathematics. The exact calculation would depend on the actual form of μ_x(t) over time.

To provide a more concrete answer, further details on the force of mortality's mathematical form as well as additional actuarial assumptions would be needed. However, it's clear that the present value will increase due to a higher force of mortality (implying higher likelihood of death and hence higher insurance payouts earlier) and it will further be influenced by the lower discount rate, which increases the present value of future payments.

User Shorpy
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