Question

An insurance company offers two policies that cover the cost of repairs from driving accidents. A policy costing ​$600 annually has an ​$800 deductible​ (meaning the driver is responsible for paying the first ​$800 in damages before the insurance kicks​ in), whereas a policy that costs ​$2 comma 500 annually has a ​$350 deductible. Assume that accidents that get reported to the insurance company require more than ​$800 to repair the car. If the number of accidents are modeled as a Poisson random variable with mean mu​, when is the policy with the ​$800 deductible cheaper for the driver on​ average?

Answer 1

Total cost for policy-1 = 600 + 800*mu

Total cost for policy-2 = 2500 + 350*mu

So, at the point of cross-over:

600 + 800*mu = 2500 + 350*mu

or, mu = (2500 - 600) / (800 - 350)

or, mu = 4.22

So, when the average number of accidents is less than or equal to 4.22 (or, simply 4), policy-1 will be cheaper.