A life insurance company sells annuities to men aged exactly 60. Each policyholder pays a single net premium, P, and then receives an annuity of $30,000 a year in arrear (so that the first annuity payment is on the 61st birthday). Assume that mortality follows the Standard Select Life Table, and that the interest rate is 5% per year. (a) Calculate P. (b) Calculate the probability that the present value of profit on a single policy is positive.

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