Consider two independent lives, Michael and his wife, Lily, aged 65 and 63 respectively. Michael is...

 

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Consider two independent lives, Michael and his wife, Lily, aged 65 and 63 respectively. Michael is entitled to a continuous annuity of $10,000 upon retirement payable every year, and the normal retirement age is 65. Michael and Lily are subjected to a force of mortality of x = 100x where 0<x<100 and a constant force of mortality of 0.04, respectively. Given the force of interest is 5% per annum, (i) Calculate the actuarial present value of the annuity at Michael's retirement date. (3 marks) If Michael considers a continuous reversionary annuity where $5,000 per year is payable to Lily after his death, calculate the actuarial present value of this annuity. Consider two independent lives, Michael and his wife, Lily, aged 65 and 63 respectively. Michael is entitled to a continuous annuity of $10,000 upon retirement payable every year, and the normal retirement age is 65. Michael and Lily are subjected to a force of mortality of x = 100x where 0<x<100 and a constant force of mortality of 0.04, respectively. Given the force of interest is 5% per annum, (i) Calculate the actuarial present value of the annuity at Michael's retirement date. (3 marks) If Michael considers a continuous reversionary annuity where $5,000 per year is payable to Lily after his death, calculate the actuarial present value of this annuity.

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