Question

Sara is a 60-year-old Anglo female in reasonably good health. She wants to take out a $50,000 term (i.e., straight death benefit) life insurance policy until she is 65. The policy will expire on her 65th birthday. The probability of death in a given year is provided. 63 64 X = age 60 61 62 P(death at this age) 1 0.00607 0.00803 0.00875 0.01062 0.01165 Sara is applying to Big Rock Insurance Company for her term insurance policy. (a) What is the probability that Sara will die in her 60th year? (Use 5 decimal places.) Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance? (b) Repeat part (a) for ages 61, 62, 63, and 64. Age Expected Cost A 61 62 A 63 A 64 A What would be the total expected cost to Big Rock Insurance over the years 60 through 64? (C) If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Sara's death, how much should it charge for the policy? ta (d) If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make?

Answer 1

Given the table - age 60 161 162 163 164 PC death at this age ..oob07 10.00803/ 0.00875 oolot2 | 0.01165 a) probability (death as age) to) = 0.00607 from the above table Death beneft = $50,000 Expected cost to company = cost & probability E(GO) - 50,000 X 0.00607 = $ 303.5 b) probability (death at age 61) = 0.00803 Expected cost to company = cont & probability E(6) - 50,000 X 0.00803 = $ 401.5

probability (death at age 62) = 0.00875 Expected Cost to company = cost & probability - 50,000 X 0.00875 - $ 437.5 Probability (death at age 63) = 0.01062 Expected cost probability to company = cost EL 63) 50,000 x 0.01062 US $ 531 Probability ( death at age 64) = 0.01165 Expected cost to (64) company - Copt x probabity = 50000 x 0.01165 = $ 582.5 toral Expected cott - E(60) +E(61) +E(62) +E (63) +E(tu) -$30 3.5 + $401.5 + $ 437.5+$ 631 +$ 522.5 - $ 2256

profit of $700 above expected total cost So, charges a Total expected cont + projet COME + - $2256 + $700 = $ 2956 a) Total Total charges charges = $ 55,000 Total expected cost = $2256 Profit = $5000 $2256 = $ 2744