ABC Inc., a manufacturer of batteries, has asked you to insure it against a fail
ID: 1720232 • Letter: A
Question
ABC Inc., a manufacturer of batteries, has asked you to insure it against a failure of its products. You are told the following:
(ii) The value of a battery is $100.
(iii) A battery's value depreciates uniformly over 5 years.
(iv) The insurance will pay the depreciated value of the battery.
(v) No insurance payments will be made after 5 years.
(vi) 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)
Explanation / Answer
Your insurance pays 100 at time 1, 75 at time 2, 50 at time 3, 25 at time 4.
The real insurance pays 80 at time 1, 60 at time 2, 40 at time 3, 20 at time 4.
100*e^(-.1) * (4 Year term insurance of 1 minus 4 year increasing insurance of (0.25t))
100 * e^(-1(.04+.06)) * ( (2/5)*(1-e^(-.4)) - (1/4)(.04)( [1-(1.4)e^(-.4)]/[.01] ) ) = $6.36*4/5 = 5.088