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For a 25-year fully continuous endowment insurance of $1,000 issued to (40), you are given: Mortality follows the AM92 Ultimate table, assuming uniform distribution of

  1. For a 25-year fully continuous endowment insurance of $1,000 issued to (40), you
  2. are given:
  • Mortality follows the AM92 Ultimate table, assuming uniform distribution of deaths over fractional years.
  • The interest rate is assumed to be 4% effective.
  1. (a)Write down Lt, the (net) loss random variable for this policy at time t.
  2. (b)Calculate the net premium policy value at the end of year 10.
  3. (c)Calculate Var(L10|T40 > 10), where T40 is the future lifetime random variable for (40).
  4. (d)Calculate P(L10 > 500|T40 > 10).

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