Cogito
Consumer Math · Chapter 7 · Lesson 1
How Insurance Works
Trading a small certain loss for a large uncertain one.
12 problems · about 21 minutes · TEKS M.M.7.A
What this lesson teaches
The student explains premiums, deductibles and coverage, and computes out-of-pocket costs.
- 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.
Warm Up
Straightforward practice. Get the method working first.
5 problemsA $5000 claim with a $750 deductible. Insurer pays how much, in dollars?
Answer 4250
Why $4250.
Why buy insurance when its expected value is negative?
Answer It protects against a loss too large to absorb.
Why It converts a possible catastrophe into a manageable cost.
A $4000 claim with a $1000 deductible. Insurer pays how much, in dollars?
Answer 3000
Why 4000 − 1000.
Premium $900 plus a $1500 deductible. Total in dollars?
Answer 2400
Why Add them.
A $300 claim with a $500 deductible. Insurer pays how much, in dollars?
Answer 0
Why The claim is below the deductible.
Build It Up
The same ideas with more to keep track of.
3 problemsA higher deductible means a higher or lower premium? 1 higher, 2 lower.
Answer 2
Why You take on more risk.
Premium $100 a month. Annual premium in dollars?
Answer 1200
Why 100 × 12.
Is the expected value of buying insurance positive for the buyer? 1 yes, 0 no.
Answer 0
Why Insurers must collect more than they pay.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each risk by whether insuring it makes sense.
Answer Worth insuring: A house fire, A serious illness · Not worth insuring: A cheap phone case, A pair of headphones
Why Insure what you could not absorb yourself.
A $10000 claim with a $2000 deductible. Insurer pays how much, in dollars?
Answer 8000
Why 10000 − 2000.
The Claim: A $3000 claim with a $500 deductible. How much do you pay, in dollars?
Answer 500 dollars
Why $500.
The Year: Premium $1200 plus a $500 deductible paid once. Total for the year, in dollars?
Answer 1700 dollars
Why $1700.