A life insurance company issues a joint-life annuity to a male, aged 68, and a female,...

 

Transcribed Image Text:

A life insurance company issues a joint-life annuity to a male, aged 68, and a female, aged 65. The annuity of 10,000 pa is payable annually in arrears and continues until both lives have died. The insurance company values this benefit using PA92C20 mortality (males or females as appropriate) and 4% pa interest. (i) (a) (ii) (b) Calculate the expected present value of this annuity. Derive an expression for the variance of the present value of this annuity in terms of appropriate single and joint-life assurance functions. If the insurance company charges a premium of 150,000 for this policy, calculate the probability that it makes a profit on the contract. Question 8.14 The random variable T, represents the time to failure of the joint-life status (xy). (x) is subject to a constant force of mortality of 0.01, and (y) is subject to a constant force of mortality of 0.02. Calculate the value of E(Ty) assuming that (x) and (y) are independent with respect to mortality. A life insurance company issues a joint-life annuity to a male, aged 68, and a female, aged 65. The annuity of 10,000 pa is payable annually in arrears and continues until both lives have died. The insurance company values this benefit using PA92C20 mortality (males or females as appropriate) and 4% pa interest. (i) (a) (ii) (b) Calculate the expected present value of this annuity. Derive an expression for the variance of the present value of this annuity in terms of appropriate single and joint-life assurance functions. If the insurance company charges a premium of 150,000 for this policy, calculate the probability that it makes a profit on the contract. Question 8.14 The random variable T, represents the time to failure of the joint-life status (xy). (x) is subject to a constant force of mortality of 0.01, and (y) is subject to a constant force of mortality of 0.02. Calculate the value of E(Ty) assuming that (x) and (y) are independent with respect to mortality.