Can this insurance decision be assisted using probability?

[Markg2]

USAA offers an auto insurance vehicle replacement option as follows: If the vehicle is totaled, they will increase their payout 20% above the vehicle's depreciated value.

My 2018 Honda Ridgeline's December 2020 ~depreciated value = $38k.

Does the decision to buy/not buy the option lend itself to probability or not?

Thanks,

Mark

 

[fed2]

Indeed it does! There is probably some actuary(=stats booky) making odds on this as we speak! Its a very lucrative profession, and you are paying for it.

I would think 'even money' on average is going to look like:
(probability of totaling the ridgeline)*premium of option == .2 * 38k

you might also have to factor in interest/time value of money to get more sophisticated about it. The premium probably gets paid on a monthly basis or something. Well this probably isn't exactly the answer, but hopefully you see what its getting at. Basically the idea is if the above equation holds then the expected earnings of the company is 0. That's not a company you would invest in.

 

[fed2]

sorry i got that backwards i think should be:

.2*38k * (probability of totaling the ridgeline) == cost of premium option

 

[Markg2]

Thanks for taking the time with this question. Once you wrote out 'probability of totaling...', I realized the excess premium option was not of value. Forget for the moment the relationship between vehicle cost/depreciated value/premium... my age/driving history/location vs. industry published odds of *anyone having an accident makes the (IMO) option purchase dumb.

Thanks again--

Mark