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Ans. For insurance with benefits payable at the end of the year and annual premiums, the net premium reserve at the end of year 9 for a 10-year term insurance of 1000 on (x) is 40.
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12. For insurances with benefits payable at the end of the year and annual premiums: •...
A 3-year endowment insurance policy with the benefits payable at the end of the year of...
A 3-year endowment insurance policy with the benefits payable at the end of the year of death is issued to (46). The benefit formula is given by 1000(1.06) fort 1,2,3 Mortality is based on the following table Age , 45 60 000 46 59 000 47 57 500 48 55 000 49 52 500 50 50 000 51 47 000 52 44 000 53 42 000 Compute the net single premium for this insurance giveni 0.03.
5. Consider a 10-year annual premium endowment insurance with sum insured $200,000 issued to a life...
5. Consider a 10-year annual premium endowment insurance with sum insured $200,000 issued to a life aged 40, Assume initial expenses of 4% of the basic sum insured and 15% of the first premium,and renewal expenses of3% ofthe second and subsequent premiums. Assume that the death benefit is payable at the end of the year of death. (a) Write down an expression for the gross future loss random variable I4 (10 pts.) (b) Calculate the gross annual premium. (8 pts.)
5. Mortality for two independent lives is modeled as a Markov chain wth four states: (1) both ali...
5. Mortality for two independent lives is modeled as a Markov chain wth four states: (1) both alive (2) (x) alive (3) (y) alive (4) neither alive The transition probability matrix is 0.85 0.1 0.04 0.01 0 0.95 0 0.05 0 0 0.9 0.1 A 3-year term insurance has the following provisions withi- 0.05 (i) Premiums are payable at the beginning of the year while both are alive (ii) Benefits are paid at the first death. ii I (y) dies...
3. A 2-year term insurance is issued to (x), with death benefits payable at the end...
3. A 2-year term insurance is issued to (x), with death benefits payable at the end of the year of death. Forj-1,2, the death bene fit for policy year j is bj, bi2 0 Assume bi +b 10, Let Z denote the random variable of the present value of the death bene fit payments Giveni-0,q-0.1 andq-0.3, find the value of b which minimizes Var[Z]
104 Life Insurance-Term and Other The main purpose of life insurance is to provide financial protection...
104 Life Insurance-Term and Other The main purpose of life insurance is to provide financial protection for your dependents in case of your death. You may purchase term life insurance, whole life insurance, limited payment life insurance, of endowment life insurance. ANNUAL PREMIUM - NUMBER OF UNITS PURCHASED X PREMIUM PER $1000 Use the tables below to answer the problems. ANNUAL PREMIUM PER $1000 OF LIFE INSURANCE: 5-YR TERM Age 18 20 25 30 35 45 55 65 Male $...
4. A fully discrete whole life insurance policy paying $50,000 at the end of the year...
4. A fully discrete whole life insurance policy paying $50,000 at the end of the year of death is issued to an individual age 36. The net premium reserve at the end of 10 years is $8,000. The net premium for this policy is $900 and the net premium for an identical policy issued to an individual age 46 is P. The effective annual interest rate of interest is 6%. Determine P.
2. For a special fully discrete 10-payment whole life insurance on (30) with level annual net...
2. For a special fully discrete 10-payment whole life insurance on (30) with level annual net premium P: (i) The death benefit is equal to 1000 plus the refund, without interest, of the net premiums paid. (ii) i = 0.04 (iii) A30 = 0.30 (iv) 30. 10 = 0.014 (v) (14)zo:707 = 0.048 (vi) ä30:101 - 8.5 Calculate P
Page ( 9 > of 1 8. For a 35-year term insurance of 1 on (20),...
Page ( 9 > of 1 8. For a 35-year term insurance of 1 on (20), you are given: Benefits are payable at the moment of death. • Z is the present value random variable at issue of the benefit payment • Mortality follows a uniform distribution with w = 100. • = 0.06 Calculate 1000Var(Z). (13)
Problem 7. (10 pts) The insurance company has a cohort of policyholders, 70% of whom are...
Problem 7. (10 pts) The insurance company has a cohort of policyholders, 70% of whom are non-smokers and 30% of whom are smokers. For the fixed age x, the insurance company's model for mortality has ONS = ONS = 0.15 (non-smoker) and q = = 0.25 (smoker). (a). A policyholder is chosen at random from the cohort. Compute 19 and qx+1 for this poli- cyholder (b). Suppose that both non-smoker and smoker mortality follow UDD in each year of age....
Charlie was hired by Ajax this year as a corporate executive and a member of the...
Charlie was hired by Ajax this year as a corporate executive and a member of the board of directors. During the current year, Charlie received the following payments or benefits paid on his behalf Salary payments Contributions to qualified pension plan Qualified health insurance premiums Year-end bonus Annual director's fee Group-term life insurance premiums (face value $40,000) Whole life insurance premiums (face value $100,000) Disability Insurance premiums (no special elections) $110,500 20, 100 8,800 16,200 11,200 1,050 1,900 4,520 a....
A 3-year endowment insurance policy with the benefits payable at the end of the year of death is issued to (46). The benefit formula is given by 1000(1.06) fort 1,2,3 Mortality is based on the following table Age , 45 60 000 46 59 000 47 57 500 48 55 000 49 52 500 50 50 000 51 47 000 52 44 000 53 42 000 Compute the net single premium for this insurance giveni 0.03.
5. Consider a 10-year annual premium endowment insurance with sum insured $200,000 issued to a life aged 40, Assume initial expenses of 4% of the basic sum insured and 15% of the first premium,and renewal expenses of3% ofthe second and subsequent premiums. Assume that the death benefit is payable at the end of the year of death. (a) Write down an expression for the gross future loss random variable I4 (10 pts.) (b) Calculate the gross annual premium. (8 pts.)
5. Mortality for two independent lives is modeled as a Markov chain wth four states: (1) both alive (2) (x) alive (3) (y) alive (4) neither alive The transition probability matrix is 0.85 0.1 0.04 0.01 0 0.95 0 0.05 0 0 0.9 0.1 A 3-year term insurance has the following provisions withi- 0.05 (i) Premiums are payable at the beginning of the year while both are alive (ii) Benefits are paid at the first death. ii I (y) dies...
3. A 2-year term insurance is issued to (x), with death benefits payable at the end of the year of death. Forj-1,2, the death bene fit for policy year j is bj, bi2 0 Assume bi +b 10, Let Z denote the random variable of the present value of the death bene fit payments Giveni-0,q-0.1 andq-0.3, find the value of b which minimizes Var[Z]
104 Life Insurance-Term and Other The main purpose of life insurance is to provide financial protection for your dependents in case of your death. You may purchase term life insurance, whole life insurance, limited payment life insurance, of endowment life insurance. ANNUAL PREMIUM - NUMBER OF UNITS PURCHASED X PREMIUM PER $1000 Use the tables below to answer the problems. ANNUAL PREMIUM PER $1000 OF LIFE INSURANCE: 5-YR TERM Age 18 20 25 30 35 45 55 65 Male $...
4. A fully discrete whole life insurance policy paying $50,000 at the end of the year of death is issued to an individual age 36. The net premium reserve at the end of 10 years is $8,000. The net premium for this policy is $900 and the net premium for an identical policy issued to an individual age 46 is P. The effective annual interest rate of interest is 6%. Determine P.
2. For a special fully discrete 10-payment whole life insurance on (30) with level annual net premium P: (i) The death benefit is equal to 1000 plus the refund, without interest, of the net premiums paid. (ii) i = 0.04 (iii) A30 = 0.30 (iv) 30. 10 = 0.014 (v) (14)zo:707 = 0.048 (vi) ä30:101 - 8.5 Calculate P
Page ( 9 > of 1 8. For a 35-year term insurance of 1 on (20), you are given: Benefits are payable at the moment of death. • Z is the present value random variable at issue of the benefit payment • Mortality follows a uniform distribution with w = 100. • = 0.06 Calculate 1000Var(Z). (13)
Problem 7. (10 pts) The insurance company has a cohort of policyholders, 70% of whom are non-smokers and 30% of whom are smokers. For the fixed age x, the insurance company's model for mortality has ONS = ONS = 0.15 (non-smoker) and q = = 0.25 (smoker). (a). A policyholder is chosen at random from the cohort. Compute 19 and qx+1 for this poli- cyholder (b). Suppose that both non-smoker and smoker mortality follow UDD in each year of age....
Charlie was hired by Ajax this year as a corporate executive and a member of the board of directors. During the current year, Charlie received the following payments or benefits paid on his behalf Salary payments Contributions to qualified pension plan Qualified health insurance premiums Year-end bonus Annual director's fee Group-term life insurance premiums (face value $40,000) Whole life insurance premiums (face value $100,000) Disability Insurance premiums (no special elections) $110,500 20, 100 8,800 16,200 11,200 1,050 1,900 4,520 a....
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