Please help with Economic Probability Question?

Question

You recently had an auto accident that was your fault. If you have another accident or receive another moving violation within the next 3 years, you will become part of the "assigned risk" pool, and you will pay an extra $600 per year for insurance. If the probability of an accident or moving violation is 20% per year, what is the probability distribution of your "extra" insurance payments over the next 4 years? Assume that insurance is purchased annually and the violations register at the end of the year - just in time to affect next year's insurance premium.

Answer 1

You require a sunk fund reserve "just in case". Assume that the "extra" $600 has to be paid at the first of the year in a lump sum.

For the first year, your monthly cost is 600*.2/12 or $10. This accumulates to $120 by years end. For the second year, your probability is actually 44% ((1.2*1.2)-1) and not the additive 40% that many would think. So your required reserve by end of year 2 is $264. This requires your new reserve to be $12 per month.

For the third year, your probability is 72.8% ((1.2*1.2*1.2)-1). Your required reserve is $436.80. So your new reserve amount monthly is $14.40. For the last year your probability is over 100% (you are darned likely to have your luck run out by then - ((1.2^4)-1=107%). You are required to make up the difference lacking in a full premium reserve ($600-$436.80 = $163.20), so your monthly reserve is now $13.60.

If this makes no sense to you, write Jeff Skilling in prison. This is how Enron justified some of their reserves, I'm sure.

But I think it is what your prof wants to see.

Answer 2

I don't believe that to be correct

Answer 3

Maybe, but I don't know 100%

Answer 4

thank you for the answers everyone xx