Question

Assume that a 25-year-old man has these probabilities of dying during the next five years Age at death 25 26 27 28 29 Probability 0.00036 0.00041 0.00054 0.00057 0.00060 (a) What is the probability that the man does not die in the next five years? (Enter your answer to five decimal places.) 99750 (b) An online insurance site offers a term insurance policy that will pay $100,000 if a 25-year-old man dies within the next 5 years. The cost is $170 per year. So the insurance company will take in $850 from this policy if the man does not die within five years. If he does die, the company must pay $100,000. Its loss depends on how many premiums were paid, as follows Age at death 25 26 27 28 29 $99,830 $99,660 $99,490 $99,320 $99,150 Loss What is the insurance company's mean cash intake from such polices? (Round your answer to two decimal places.) 601.25 X

Answer 1

Age	Probability of death	Probability of survive
25	0.00036	0.99964
26	0.00041	0.99959
27	0.00054	0.99946
28	0.00057	0.99943
29	0.00060	0.99940

a)

Probability of die at a certain age is the product of probabilities that he survive up to earlier age and dies in that particular age.

Probability that the man dies in next five years =.00036 + .99964*.00041 + .99964*.99959*.00054 +    .99964*.99959*.99946*.00057 + .99964*.99959*.99946*.99943*.00060

   =0.0024775631

So, probability that the man does not die in next five years = 1-.0024775631 = 0.9975224369 = 0.99752

b)

So, mean cash intake of the company = 170*.99964-99830*.00036+170*.99959-99660*.00041+170*.99946-

99490*.00054+170*.99943-99320*.00057+170*.99940-99150*.00060

= 134+129.0697+116.1836+113.2907+109.408

= 602.952 = 603.95