Skip to lesson

Math · Consumer Math

Chapter 7: Insurance and Risk

How Insurance Works

Trading a small certain loss for a large uncertain one.

Lesson
1
Time
About 21 minutes
0 of 12 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Insurance pools risk. Many people pay small premiums so that the few who suffer a large loss are covered.

The premium

The premium is what you pay regularly, whether or not you ever claim.

The deductible

The deductible is what you pay yourself before coverage begins. A $500 deductible on a $3000 claim means you pay $500.

The trade-off

A higher deductible lowers the premium. That is a good trade only if you could actually pay the deductible tomorrow.

Expected value is negative

Insurers must collect more than they pay out. Buying insurance is expected to lose money, and that is not the point.

When to buy it

Insure against losses you could not absorb: a house fire, a serious illness. Do not insure a cheap phone.

A small certain loss against a large uncertain one

A premium is a definite cost paid to avoid the risk of a much larger one. The expected value of a policy is negative for the buyer — that is how insurers operate — and it can still be entirely rational.

Risk pooling

Many people each pay a small amount so that the few who suffer losses are covered. Insurance works because losses are rare and unpredictable individually while being predictable across a large group.

Deductibles and premiums trade off

A higher deductible means paying more of any claim yourself and a lower premium. Choosing between them depends on how much of a loss could be absorbed without borrowing.

Insure what you cannot absorb

The general principle is to insure against losses that would be financially catastrophic and to self-insure small ones. Extended warranties on inexpensive goods usually fail that test.

Step 2: Try It Yourself

Tap and try it out.

A claim split between the deductible you pay and the amount covered.
You pay500
Insurer pays2500

Insurer pays has the most. It has 2000 more than You pay.

Step 3: Watch an Example

One step at a time.

Watch Tomas Compare Two Policies

Policy A costs $1200 a year with a $500 deductible. Policy B costs $900 with a $1500 deductible.

  1. Step 1

    With no claim, Policy B saves $300 a year.

Step 4: Your Turn

Practice makes it stick.

The Claim

Problem 1 of 2

A $3000 claim with a $500 deductible. How much do you pay, in dollars?

dollars

The Year

Problem 2 of 2

Premium $1200 plus a $500 deductible paid once. Total for the year, in dollars?

dollars

Who Pays What

1 of 8

A $4000 claim with a $1000 deductible. Insurer pays how much, in dollars?

2 of 8

Premium $900 plus a $1500 deductible. Total in dollars?

3 of 8

A $300 claim with a $500 deductible. Insurer pays how much, in dollars?

4 of 8

A higher deductible means a higher or lower premium? 1 higher, 2 lower.

5 of 8

Premium $100 a month. Annual premium in dollars?

6 of 8

Is the expected value of buying insurance positive for the buyer? 1 yes, 0 no.

7 of 8

Sort each risk by whether insuring it makes sense.

Tap something to move it.

  • Empty
  • Empty

8 of 8

A $10000 claim with a $2000 deductible. Insurer pays how much, in dollars?

Step 5: Quick Check

Show what you know.

Question 1 of 2

A $5000 claim with a $750 deductible. Insurer pays how much, in dollars?

Question 2 of 2

Why buy insurance when its expected value is negative?

What You Learned

  • Insurance pools risk: many small premiums cover a few large losses.
  • The deductible is what you pay before coverage begins.
  • Insure what you could not absorb yourself, and skip the rest.