Additional Math Pages & Resources

Thursday, December 8, 2011

Everybody loves a discount, but this is ridiculous!

I got my auto insurance renewal this week. Like mobile phone contracts, or buying a cable entertainment package, understanding the details demands that we use mathematics. Will the simple operations we learned in elementary school be adequate ... or not?

At least I know how to construct a 3-column, 10-row table. That's useful:

 Insurance Category Car 1 Car 2
 Liability 112 157
 Medical 5 8
 Uninsured Motorist 24 26
 Comprehensive Damage 14 31
 Collision Damage $500 ded. 63 94
 Towing & Rental Car 4 4
 Collision Ded. Waiver 11 11
 Miles Driven Annually750012000

Despite my boring blue cars (Honda, Volvo) I still have a total premium of 564 dollars and no cents.

After looking at the total price, I dove into the 3 pages of fine print regarding discounts on my policy premium. Here are the possible discounts off the "list price" for my policy:
  • 20% for a Good Driver discount (no more than one moving violation "point", no more than one accident) Applied
  • 25% for being At-Fault Accident Free for five years (5% for each year, up to 25%) Applied
  • 22.5% for Cross Sold Credit (this does not mean I am angry, but I have Homeowner's insurance with this same company) Applied
  • 12% for Continual Renewal for six years without lapsing (2% for each year, up to 12%) Applied
  • 30% for Physical Damage Deductible of $500 rather than $100 Applied
  • 15% for Multi-car Discount when two or more cars owned by the same person are insured Applied
  • 5% off Medical premium for Passive Restraints (airbags) Applied
  • 15% off Comprehensive for Passive Anti-theft Devices (factory car alarm/security system) Applied
  • 10% off for Educator Discount (my wife is employed by a school district) Applied
  • 5% off for Mature Driver Improvement Certificate (I'm insulted by the very thought of this!) Not applicable
  • 1.5% discount for Good Student Grade Point Average (B or above) Not applicable
  • Discount for Distant Student living more than 100 miles from home (without a car) Not applicable
  • Discount for low annual mileage driven Applied
Now I suspect you are beginning to think the same way that I was thinking. Are all these discounts additive?


If you add them all up, you get:   20 + 25 + 22.5 + 12 + 30 + 15 + 5 + 15 + 10 = 154.5%

Take 154.5% times $564 and that means they owe me $871. Right?

Alas, no. That's not how it works. Each of the discounts can apply to only one type of coverage, and the discounts have already been applied to the prices shown above. Elementary math is really no use at all in deciphering exactly how the discounts decreased my price.


As Bob in our office is fond of saying, "It is difficult to say at this time."  Comparison shopping with other companies is your best bet, or you might ask your insurance agent (if you have one) to go through the details with you.


I was thinking about getting a more interesting car for driving in my spare time. What do you think of the engine in this red Pantera? Do you suppose my insurance company will give me a discount, or no discount?