A 65-year-old intends to use their retirement funds to buy an annuity from a life insurance company.?
given the amount of money that man has available to invest, the insurance company is able to offer two alternatives. The first option is to receive $ 2,785 each month for as long as he lives, the second option is to receieve $ 3,500 each month, but only 20 years (payments made to his property if he died before that date) the rate benchmark interest is 6 percent per year. How long should a man live so that the first option is a better deal? can someone help me plz reply this question for my job as finance?
Sea: p the amount of each payment, interest rate r the fractional year, n the number of years, the number k of payments and compounding periods per year, s the sum invested. The present value of payments is the sum of a geometric series with first term p and the common ratio (1 + R / k) ^ (-1): s = sum p (i = 0 to nk – 1) (1 + r / k) ^ (-ki) s = p (1 – (1 + r / k) ^ (-nk)) / (r / k) s = (pk / r) (1 – (R + 1 / k) ^ (-nk)) … (1) Solving for n: sr / kp = 1 – (+ r 1 / k) ^ (-nk) 1 – sr / kp = (1 + r / k) ^ (-nk) log (1 – sr / kp) = – log nk (1 + r / k) = n – log (1 – sr / kp) / log k (1 + r / k) … (2) For the option of 20 years, (1) gives: s = (3500 * 200) (1-1005 ^ (-240)) s = $ 488,532.70 for the choice of life, (2) yields: n = – log (1 – 488,532.70 * 0.06 / (12 * 2785)) / 12 log (1,005) n = 35.02yr.
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