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1. A whole-life insurance contract provides for 1 unit payable at the moment of death. Level premiums are payable continuously for life at the annual rate of 0.08. The force of mortality is a constant 0.05, and the force of interest is a constant 0.10. How many contracts must be sold in order that there is at least a 95% chance that the total premiums on all these contracts will cover the total benefits? Use a normal approximation.
2. An insurer sells 100 whole-life insurance policies each providing for 1 unit payable at the moment of death. Level premiums are payable continuously for life. The force of interest is a constant 0.06, and the force of mortality is a constant 0.04. What should the rate of premium payment be on each policy, in order that there is a 95% chance that total premiums on all 100 policies will cover the total benefits on all policies? Use a normal approximation.
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A manufacturer of batteries offers a two-year limited warranty. If the battery fails for any reason during the first two years, it is replaced. What percentage of the batteries is expected to fail within the warranty period?
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