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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross premiums and reserves

An insurer values a portfolio of non-profit endowment policies using a net premium valuation, and then strengthens the valuation basis by lowering the valuation interest rate, keeping mortality unchanged. Which is the most likely effect on the reserves?

Reserves increase. A lower valuation interest rate raises the present values of both benefits and premiums, but benefits lie further in the future on average, so their value rises more, leaving higher reserves where premiums are held at the original level.

  1. AReserves increase, since the present value of benefits rises by more than the present value of net premiumsCorrect
  2. BReserves decrease, since discounting is stronger
  3. CReserves are unchanged because the net premium is recalculated
  4. DReserves fall because future benefits are lower
  5. Reserves become negative for all policies

Explanation

A lower valuation rate raises present values of both benefits and premiums. Benefits are paid later on average than premiums, so they are affected more, giving higher reserves when premiums are held at the original level. Option B misreads the direction of the discount effect.

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