# A Crazy Little Thing Called Insurance Math

What if I told you that you could get \$250,000 of life insurance cheaper than \$200,000? Or double your auto liability limit for less?

First off, whoever decided to spend the time reading an article with the words “insurance” and “math” in the same title, I applaud you. Most people are discouraged when they think of insurance math, because they think of these crazy-smart actuaries with 130 IQs crunching numbers all day. Though that may be somewhat accurate, there is something pretty interesting about insurance math. But before we begin, we have a couple concepts to go over:

The first concept is called the “Law of Large Numbers”. The law of large numbers simply states that the more examples we have, the more accurate our numbers can be. For example, let’s say you’re flipping a coin. If you only flip it one time and land on ‘heads’, then your conclusion would state that there is a 100% chance that your coin lands on ‘heads’. But if you flip it 10,000 times, odds are, your conclusion will be pretty close to the chance that your coin lands on ‘heads’ is 50%. After flipping the coin 10,000 times, you could probably take this a step further and say that there is a 25% chance of getting 2 ‘heads’ back-to-back (50% of 50%). Insurance companies create their rates off of what actuaries tell them with data similar to this. But instead of the probability of landing on ‘heads’, they are looking at the probability of having a claim.

The next concept is called “weighted probability”. Let’s say you decided to gamble with your coin-flipping obsession. You find someone who said that you must pay them \$3 per flip to play, but if the coin lands on ‘heads’, you get \$5. That would not be a good deal for you. We know that the average probability of landing on heads is 50%, so if you played 100 times, you would’ve paid \$300 to play, but only receive \$250 back as winnings. Insurance companies must do the same thing to stay afloat. They must calculate how much they will pay in future claims, and collect just above that to account for catastrophes, administrative expenses, and a bit of profit.

The last concept we will go over is called “price banding”. This is most-common in life insurance pricing. For a young, healthy female, the price bands for a 10 year term life insurance may be the following: \$100,000 is \$10/month, \$250,000 is \$20/month, and \$500,000 is \$30/month. Any additional \$1,000 after the main price band is \$0.15/month. In this example, if this person wants \$200,000 of life insurance, they would pay \$25/month (\$10 for the \$100k band, then add \$15 for the additional coverage [100,000 x \$0.15] ). This example appears too good to be true, but in many cases, it is. The sad thing is that there are many agents out there that aren’t aware of this. So if someone sells you life insurance that is outside of these banded rates, you should probably get that looked at.

Now, by using the law of large numbers, insurance companies are able to determine the probability of someone with a certain car, occupation, education level, and liability limits having a claim. So if an insurance company determines that those with state minimum liability have a 10% chance of having a claim, but those with twice the liability coverage only has a 5% chance of having a claim, those with the higher coverage may have a lower cost of insurance. And sometimes, that cost may be even lower than the liability tier under them.

My best advice is to find a trusted insurance advisor to review your policies. Check around every year, and ask questions like, “how we can use insurance math to my advantage?”.