Question 4.153

4.153 Life insurance.

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 0.00039 0.00044 0.00051 0.00057 0.00060
  1. What is the probability that the man does not die in the next five years?
  2. An online insurance site offers a term insurance policy that will pay $100,000 if a 25-year-old man dies within the next five years. The cost is $175 per year. So the insurance company will take in $875 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 the man paid, as follows:
    Age at
    death    		 25 26 27 28 29
    Loss $99,825 $99,650 $99,475 $99,300 $99,125

    What is the insurance company's mean cash intake (income) from such polices?

4.153

(a) 0.99749. (b) $623.22.