When calculating premiums on life insurance products, insurance companies often use life tables that enable the probability of a person dying in any age interval to be calculated. The following data obtained from the ‘New Zealand Abridged Period Life Table: 2014-16’ gives the number out of 100,000 New Zealand-born males and females who are still alive during each five-year period of life between age 20 and 60 (inclusive).

Suppose a New Zealand-born female on her 35th birthday purchases a one million dollar, five-year term life policy from an insurance company. That is, the insurance company must pay her estate $1 million if she dies within the next five years.

a. Determine the insurance company’s expected payout on this policy.

b. What would be the minimum you would expect the insurance company to charge her for this policy?

c. What would the expected payout be if the same policy were taken out by a New Zealand-born female on her 40th birthday?

d. Repeat parts (a) to (c) for a New Zealand-born male