ABC Inc., a manufacturer of batteries, has asked you to insure it against a fail

Question

ABC Inc., a manufacturer of batteries, has asked you to insure it against a failure of its products. You are told the following: The force of failure is constant, mu = 0.04. The value of a battery is $100. A battery's value depreciates uniformly over 5 years. The insurance will pay the depreciated value of the battery. No insurance payments will be made after five years. ABC will self-insure failures during the first year after manufacture of a battery (i.e., you will not have to pay for failures in the first year after manufacture). Assuming a constant force of interest, b = 0.06, calculate the actuarial present value of the insurance for one battery.

Explanation / Answer

Solution :

   100*e^(-.1) * (4 Year term insurance of 1 minus 4 year increasing insurance of (0.25t))

When I do it this way, I get the following using the formulas in table 13.1:

100 * e^(-1(.04+.06)) * ( (2/5)*(1-e^(-.4)) - (1/4)(.04)( [1-(1.4)e^(-.4)]/[.01] ) ) = $6.36

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