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FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans

An insurer writes a 1-year term policy with a 500,000 death benefit. The probability of death within the year is 0.4%, and benefits are paid at year end. The annual risk-free rate is 5%. Ignoring expenses and profit, what is the fair single premium?

The fair premium is about 1,904.76. Expected death cost is 0.4% of 500,000, which is 2,000, and because the benefit is paid at year end it is discounted one year at 5%, giving 2,000 divided by 1.05.

  1. A2,000.00
  2. B1,904.76Correct
  3. C2,100.00
  4. D1,990.04

Explanation

Expected benefit is 0.004 x 500,000 = 2,000. Discounting one year at 5% gives 2,000/1.05 = 1,904.76. Option A omits discounting. Option C compounds instead of discounting, the wrong sign on the adjustment.

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