For a special whole life insurance issued to (40), a benefit of $1,000 is payable at...

 

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For a special whole life insurance issued to (40), a benefit of $1,000 is payable at the moment of death if the insured dies within the first 10 policy years; a benefit of $2,000 is payable at the moment of death if the insured dies in the subsequent 10 policy years; a benefit of $3,000 is payable at the moment of death if the insured dies after 20 years. The annual effective rate of interest is 5%. (a) Write down the present value random variable, Z, of this insurance. (b) Express the expected present value of this insurance, E[Z], in terms of standard actuarial notations. (c) If the mortality follows the LTAM Standard and Ultimate Life Table and deaths are uniformly distributed over each year of age, calculate E[Z]. For a special whole life insurance issued to (40), a benefit of $1,000 is payable at the moment of death if the insured dies within the first 10 policy years; a benefit of $2,000 is payable at the moment of death if the insured dies in the subsequent 10 policy years; a benefit of $3,000 is payable at the moment of death if the insured dies after 20 years. The annual effective rate of interest is 5%. (a) Write down the present value random variable, Z, of this insurance. (b) Express the expected present value of this insurance, E[Z], in terms of standard actuarial notations. (c) If the mortality follows the LTAM Standard and Ultimate Life Table and deaths are uniformly distributed over each year of age, calculate E[Z].

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a The present value random variable is Z 1000e005x if death in years 110 2000e005x if death in year... View the full answer