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Chapter 7

Insurance

Deductibles, premiums, car insurance, and when to buy any of it

Insurance is the one product you buy hoping never to use, described in three words that people routinely mix up. They apply in a fixed order, and the order is most of the answer.

Chapter 7 · The idea

Three words, in order

How a bill is split
  1. The deductible
    What you pay in full before the insurer pays anything at all. Until this is met, the bill is entirely yours.
  2. Co-insurance
    Once the deductible is met, the rest is shared at a fixed split — 80/20 means the insurer pays 80% and you pay 20% of everything above the deductible.
  3. The out-of-pocket maximum
    A ceiling on your share for the year. Once your deductible and co-insurance together reach it, the insurer pays everything after that.
PassesSo your share of a bill is the deductible, plus your percentage of what is left, capped at the out-of-pocket maximum.
Figure 5Drag the bill. The first band is the deductible, all yours; above it the split takes over; and the dashed line is the out-of-pocket maximum, past which your share stops growing.
Chapter 7 · Worked problem

Elias breaks his arm

The problem
Elias has a $1,000 deductible and an 80/20 co-insurance split. He breaks his arm and receives a $5,000 hospital bill. How much does he pay out of pocket?
Working1 / 4
  1. The deductible comes first, and in fulldeductible=1000\text{deductible} = 1000

Elias pays $1,800 and the insurer pays $3,200 — so on a bill of this size his effective share is 36%, not the 20% the split appears to promise. The deductible is what makes those two numbers different, and it is why a plan with a low premium and a high deductible is not automatically the cheaper one.

Chapter 7 · The fourth word

The premium is the price of the plan

The three words above are what a plan costs when something goes wrong. The premium is what it costs every month regardless. A plan with a low premium and a high deductible is cheap in a healthy year and expensive in a bad one; a high premium buys a lower deductible, and costs more in every year that nothing happens. The comparison is a year at a time.

What a plan costs you in a yearcost=12×premium+your share of the bills\text{cost} = 12 \times \text{premium} + \text{your share of the bills}
The problem
Plan A: $150 a month, a $1,000 deductible, 80/20, and a $6,000 out-of-pocket maximum. Plan B: $400 a month, a $250 deductible, 80/20, and a $3,000 maximum. Compare a year with no bills, a year with Elias's $5,000 bill, and a year with a $40,000 one.
Plan A1 / 3
  1. A quiet year: premiums only12×150=180012 \times 150 = 1800
Plan B1 / 3
  1. A quiet year12×400=480012 \times 400 = 4800

In the worst year the two plans cost exactly the same. In every other year Plan A is cheaper — by $3,000 with nothing wrong, and by $2,400 with a broken arm. The higher premium bought a lower deductible that never paid for itself. It does not always come out that way, but it comes out that way often enough that the premium has to be in the sum.

Chapter 7 · The car

What the numbers on the insurance card mean

The parts of a car policy
  1. Liability — 100/300/50
    What the insurer pays other people if you are at fault: up to $100,000 per injured person, $300,000 per accident, and $50,000 for their property. Required by law, and the part that protects everything you own.
  2. Collision
    Your own car, when you hit something. It carries its own deductible, which you choose — and the choice sets the premium.
  3. Comprehensive
    Your own car, when something else happens to it: theft, hail, a tree. Same deductible logic.
The problem
Nadia's collision deductible is $500. Raising it to $1,000 would cut her premium by $12 a month. She has $1,000 in savings. Should she?
Working1 / 4
  1. What the higher deductible saves each year12×12=14412 \times 12 = 144
Chapter 7 · Whether to

When to buy insurance at all

Every policy costs more than it pays out on average — that is how insurers stay in business — so on expected value alone you should never buy any. The reason to buy it anyway is that averages do not pay bills: a loss you cannot absorb is worth paying above the odds to remove. The rule that follows is short. Insure what you cannot afford to lose. Self-insure the rest.

What a risk costs on averageexpected loss=probability×loss\text{expected loss} = \text{probability} \times \text{loss}
The problem
Phone insurance costs $8 a month on an $800 phone. About one phone in ten is broken or lost in a year. Is it worth it?
Working1 / 4
  1. The expected loss in a year0.10×800=800.10 \times 800 = 80
Three questions before any policy
  1. Could you pay the loss from savings?
    If yes, you are the insurer, and you keep the premium.
  2. Would the loss change your life?
    A house, a car needed for work, a hospital bill: yes. Insure these whatever the premium.
  3. Does the deductible match the savings?
    The highest deductible you could pay tomorrow is the cheapest policy you can safely hold.
PassesHealth, car liability, and the home: always. The phone, the extended warranty, the flight: almost never.