Sara is a 60-year-old Anglo female in reasonably good health. She wants to take

Question

Sara is a 60-year-old Anglo female in reasonably good health. She wants to take out a $50,000 term (that is, 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 by the Vital Statistics Section of the Statistical Abstract of the United States (116th Edition).

0.01114

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.

$

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?

(d) If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make?

x = age 60 61 62 63 64 P(death at this age) 0.00664 0.00956 0.00938 0.01050

0.01114

Explanation / Answer

a) P(Sara will die in her 60th year) = 0.00664

Expected cost to big rock insurance = 50,000x0.00664 = $332

b)

c) Total expected cost to be paid = 332 + 478 + 469 + 525 + 557

= $2361

So, the should charge 2361 + 700 = $3061

d) Expected profit of the company = 5000 - 2361 = $2639

Age Expected cost 61 0.00956 x 50000 = $478 62 0.00938 x 50,000 = $469 63 0.01050x50,000 = $525 64 0.01114x50,000 = $557

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