FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans
An insurer issues a one-year term policy with a death benefit of 500,000 to a person whose probability of dying within the year is 0.4%. Benefits are paid at year end and premium is paid at the start of the year. The risk-free rate is 5% and the insurer ignores expenses and profit. What is the net single premium?
The net single premium is 1,904.76. The expected death benefit is 0.4% times 500,000, or 2,000, paid at year end. Discounting that for one year at 5% gives 2,000 divided by 1.05. Not discounting gives 2,000, and compounding upward gives 2,100, both wrong.
- A2,000.00
- B2,100.00
- C1,904.76Correct
- D1,950.00
Explanation
Expected benefit = 0.004 x 500,000 = 2,000 paid at year end. Discounting one year at 5%: 2,000/1.05 = 1,904.76. Omitting discounting gives 2,000, and multiplying by 1.05 gives 2,100, which compounds in the wrong direction.
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