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A 65 year old man intends to use his retirement funds to purchase an annuity from a life insurance company.?

given the amount of money the man has available to invest, the insurance company is able to offer two alternatives. the first option is to receive $2785 each month for as long as he lives; the second option is to receieve $3500 each month, but for only 20 years (payments will be made to his estate if he should die before that time) the relevant interest rate is 6 percent per year. how long must the man live so that the first option is a better deal? can someone plz help me answer this question for my finance assignment?

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1. Let: p be the amount of each payment, r be the fractional interest rate per year, n be the number of years, k be the number of payments and compounding periods per year, s be the sum invested. The present value of payments is the sum of a geometric series with first term p and common ratio (1 + r / k)^(-1): s = p sum(i = 0 to nk - 1) (1 + r / k)^(-ki) s= p(1 - (1 + r / k)^(-nk)) / (r / k) s = (pk / r)(1 - (1 + r / k)^(-nk)) ...(1) Solving for n: sr / kp = 1 - (1 + r / k)^(-nk) 1 - sr / kp = (1 + r / k)^(-nk) log(1 - sr / kp) = - nk log(1 + r / k) n = - log(1 - sr / kp) / k log(1 + r / k) ...(2) For the 20 year option, (1) gives: s = (3500*200)(1 - 1.005^(-240)) s = $488,532.70 For the lifetime option, (2) gives: n = - log(1 - 488,532.70 * 0.06 / (12 * 2785)) / 12 log(1.005) n = 35.02yr.