Archive for category Insurance Math

Premium and Deductible — health insurance math

distribution of annual health costs

This premium and that deductible — which to choose?  If you ever had to purchase health insurance it’s not all that clear — and you wonder, what are they hiding?

We all face the risk of serious illness and the associated high costs.  The above graph is about the risk for a couple age 60 to 64.   The horizontal axis is the possible health bill from zero to something very large.  The vertical axis  is the number of people who accumulated the health costs enumerated on the horizontal axis. Although the most likely bill is about $10,000 there is a possibility of any amount.  Unless a person has an extra million dollars lying around we purchase insurance to cover the unexpected health bill (or go bankrupt).

An insurance company keeps detailed records of health care bills for people of of various ages.  Point C on the graph is the mean (average).     Insurance companies have thousands if not millions of customers.  So, they don’t need to know what might happen to any one person, all they need to know is the mean cost for the age group.  100,000 people times the mean of $18,000 is $1.8 billion — that’s how much they will pay out in a year (plus or minus a small percent).

The insurance company knows that point C on the graph for the benefits they offer.  Then they devise an insurance plan to collect  that amount so they can pay customer health bills.  You might think that amount of money is a secret but not really.  Below is a graph of the offerings on the internet of a real insurance company in May of 2013 for 2 people age 60-64.  The yearly premium is on the vertical and the deductible is on the horizontal.  The blue dots are the plans offered.

Analysis of premium and dedcutible

Interestingly, the blue dots are on a straight line! The line B to C is that straight line through the offered products.  Point A (numerically the same as point C) is that amount you would pay in premiums if there was no deductible — in other words “first dollar coverage”.  Point C is the deductible you would pay to have no premiums (true, no insurance offers such a plan).  Thus, point C is that mean cost per customer as in the top graph (it also includes the operational costs and profit for the company — usually about 20%).

What is Point B?  — it lines up with the blue dots of the actual plan.  It looks like the amount you would pay if the deductible was zero.  Not so fast, the difference between Point A and Point B is the amount the customer is likely to pay in co-pays and co-insurance.

The gap between the red line and the blue line is paid by the customer if they use health services.   The part the customer pays is usually limited by the “out of pocket maximum”.  If the customer does things to stay healthy it gives them a chance to actually pay less.

Comparison shopping is very difficult.  The plans and benefits from insurance companies are different.  The best advice is to purchase from a top rated company with good customer satisfaction.  If you don’t  have much savings a low deductible plan has advantages. If you can stand occasional high bills a high deductible plan may work.  Check out insurance company ratings by Consumer Reports and JD Power.

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