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For a fully-discrete 3-year endowment insurance issued on (x), you are given: Death benefit is 100 payable at the end of the year of death

For a fully-discrete 3-year endowment insurance issued on (x), you are given:

  1. Death benefit is 100 payable at the end of the year of death for the first 3 years.
  2. Endowment benefit is 100 payable at the start of the 4th year.
  3. Gross annual premiums are determined using the pricing assumptions.
  4. Reserves are kV=55 for k=1,2,3 and kV=0 otherwise.

Pricing assumptions:

  1. First year expenses are 50% of the first year gross premium.
  2. Renewal expenses are 1% of each gross annual premium, including the first.
  3. Settlement expenses are 10.
  4. qx+k=0.02 for all k.
  5. i=0.06

Profit test assumptions:

  1. Pre-contract expenses are 50% of the first year premium.
  2. There are no renewal expenses.
  3. There are no settlement expenses.
  4. qx+k=0.03 for all k.
  5. i=0.07

Using the profit test assumptions, calculate the net present value by using a hurdle rate r=0.08.

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