A is the expected present value of a payment of $1 payable at the end of the year of death (for an insured who is aged exactly x when the policy commences). A:n is the expected present value of a payment of $1 payable at the end of the year of death if death occurs within the next n > 0 years (for an insured who is aged exactly x when the policy commences). (a) Show that: Ax = Am7 + lx+n lx (1 + i)", -"Ax+n (b) Josephine has been quoted a price of $5,000 for a Whole of Life insurance policy with death benefit of $100,000. She was also quoted a price of $1,000 for a term insurance with coverage period of 10 years (and the same death benefit). Josephine's sister (who is 10 years older than Josephine), has been quoted a price of $4,000 for a Whole of Life insurance policy with death benefit of $50,000. The probability that Josephine reaches her sister's current age is 99.75%. Assume that the prices quoted are simply equal to the EPV of insurance benefits. What interest rate has been used to derive those prices?