Today is 1 January 2020. Jay is 40 years old. Jay is considering paying single premium to purchase a two-year term life insurance with disability cover. This product pays $100,000 at the end of the year of death and pays $20,000 at the end of a year if the policy holder is permanently disabled in that year (with a maximum of two payments). Policyholder can only be regarded as healthy, disabled or dead for each year. Currently, Jay is healthy. His probability of surviving (being healthy) during each year is 0.995 given that he is healthy. Probability of becoming disabled during each year is 0.004 given that Jay is healthy. Probability of dying during each year is 0.001 given that Jay is healthy. Probability of dying during each year is 0.15 given that Jay is disabled. Probability of remaining in the disabled state during each year is 1-0.15 = 0.85 given that Jay is disabled (i.e., disability is assumed to be irreversible). The life insurance company incurs initial expenses of $200 per policy at the beginning of the term of the insurance. The life insurance company incurs claim costs of $120 when a death or disability payment is made (at the end of the year in which death or disability occurs). The interest rate is j1 = 3.5% p.a. The insurance company wants the policy to earn a profit of 15% of premium at the beginning of 20 . a) Calculate Jay's probabilities of being in the disabled state at the beginning of 2022 b) Calculate Jay's probabilities of being in the dead state at the beginning of 2022 given that Jay is alive at the beginning of 2021. C) Calculate the expected benefit paid (including death and disability benefits and excluding the claim cost) at the beginning of 2022. Round your answer to two decimal places.
Today is 1 January 2020. Jay is 40 years old. Jay is considering paying single premium to purchase a two-year term life insurance with disability cover. This product pays $100,000 at the end of the year of death and pays $20,000 at the end of a year if the policy holder is permanently disabled in that year (with a maximum of two payments). Policyholder can only be regarded as healthy, disabled or dead for each year. Currently, Jay is healthy. His probability of surviving (being healthy) during each year is 0.995 given that he is healthy. Probability of becoming disabled during each year is 0.004 given that Jay is healthy.
Probability of dying during each year is 0.001 given that Jay is healthy. Probability of dying during each year is 0.15 given that Jay is disabled. Probability of remaining in the disabled state during each year is 1-0.15 = 0.85 given that Jay is disabled (i.e., disability is assumed to be irreversible). The life insurance company incurs initial expenses of $200 per policy at the beginning of the term of the insurance. The life insurance company incurs claim costs of $120 when a death or disability payment is made (at the end of the year in which death or disability occurs). The interest rate is j1 = 3.5% p.a. The insurance company wants the policy to earn a profit of 15% of premium at the beginning of 20
.
a) Calculate Jay's probabilities of being in the disabled state at the beginning of 2022
b) Calculate Jay's probabilities of being in the dead state at the beginning of 2022 given that Jay is alive at the beginning of 2021.
C) Calculate the expected benefit paid (including death and disability benefits and excluding the claim cost) at the beginning of 2022. Round your answer to two decimal places.
d) Calculate Jay's fair single premium value which is paid on the issue date of this policy. Round your answer to two decimal places.
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