Insurance: premiums, deductibles and why people buy it

Grade 12 Social Studies Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   Cards A and B on a bike plan (all made up for practice). Card A, "A bike plan (made up)". Written for this sheet. Summary in our words, not a quotation: a bike is worth $400. The chance it is stolen in a year is 5 percent, or 1 in 20. Plan 1 costs $30 a year and, after a theft, pays the bike's $400 value minus a $50 deductible. Plan 2 costs $26 a year and pays $400 minus a $100 deductible. Card B, "Reader G (made up)". Written for this sheet. Summary in our words, not a quotation: Reader G says to skip insurance, because the plan's average payout is less than its premium.

2. 1.

   Bo tests reader G's advice on card B. What is the best verdict?

   • Refuted: Plan 1 pays $350 after a theft, far more than its $30 premium, so it is plainly a good deal
   • Supported: a plan that pays less than it costs on average is a bad deal, so no one should buy it
   • Weakly supported: Plan 1 costs more than it pays on average, but it removes a loss the owner may not afford
   • Cannot be judged: the 5 percent chance on card A is a guess, so no average payout can be worked out
3. 2.

   Luz compares Plan 2 with Plan 1 on card A. Which statement about the step from a $50 to a $100 deductible is best?

   • Plan 2 is better on average: it saves $4 in premium and adds only $2.50 of expected cost
   • Neither can be preferred: the bike will be stolen or it will not, so an average cannot guide the choice
   • Plan 1 is better: a theft costs $50 more under Plan 2, which is more than the $4 saved in premium
   • Plan 2 is better: its $26 premium is lower than Plan 1's $30, and the lower premium settles the choice

4. Use this

   Cards A and B on a home insurer (all made up for practice). Card A, "A home insurer (made up)". Written for this sheet. Summary in our words, not a quotation: 1,000 homes each pay $300 a year. Each year 1 percent of the homes, 10 homes, burn, and the insurer pays each $20,000 loss in full. The insurer's running costs are $60 a home a year. Card B, "Pool size (made up)". Written for this sheet. Summary in our words, not a quotation: in a bad year, 20 of the 1,000 homes burn. If the insurer covered only 10 homes, one fire would be 10 percent of its homes. With 1,000 homes, 10 fires are 1 percent.

5. 3.

   Esme compares the premium on card A with the average claim per home. What does the gap pay for?

   • A refund for the 990 homes that did not burn, since the owners of the 10 burned homes should be the ones to pay
   • Running costs of $60 a home, with the other $40 left as profit or a reserve for bad years
   • Pure profit of $100 a home, since claims average $200 against the $300 premium paid by each owner
   • Cover for fires larger than $20,000, since the premium is set above the average loss to pay for bigger fires
6. 4.

   Pia reads card B. Why does the insurer keep a reserve beyond its average claims?

   • Average claims of $200,000 a year already cover a bad year, so a reserve just adds to the insurer's profit
   • In a bad year with 20 fires, claims are $400,000 against $300,000 of premiums, so a reserve covers the gap
   • With 1,000 homes the number of fires is certain to be 10, so the reserve would rarely be needed
   • Running costs of $60,000 a year are larger than the premiums collected, so a reserve pays the bills
7. 5.

   Noah reads card B. Why does insuring 1,000 homes make claims more predictable than insuring 10?

   • With 1,000 homes the insurer can be sure that exactly 10 will burn, so its claims are fixed in advance
   • A bigger pool spreads running costs over more homes, so the premium falls to match the average claim
   • Each added home lowers the chance that any one home burns, so a bigger pool has fewer fires per home
   • With many homes the share that burns stays near 1 percent, but with 10 homes one fire is 10 percent

8. Use this

   Cards A to C on a health plan (all made up for practice). Card A, "A health plan (made up)". Written for this sheet. Summary in our words, not a quotation: 1,000 people could join a plan. Half are low-risk, with expected claims of $40 a year each. Half are high-risk, with expected claims of $160 each. The insurer cannot tell them apart and charges everyone the same premium. Card B, "A premium rise (made up)". Written for this sheet. Summary in our words, not a quotation: the insurer raises the premium from $100 to $110. Then 200 of the 500 low-risk people drop the plan. All 500 high-risk people stay. Card C, "A rule (made up)". Written for this sheet. Summary in our words, not a quotation: the town requires everyone to hold a plan or pay a $120 penalty. The premium is $100.

9. 6.

   Tala reads card A. What premium just covers the plan's claims, and why?

   • $50, since a premium should be half the average claim to leave room for the insurer's profit
   • $160, since the plan must be priced to cover its costliest members and cannot count on the cheaper ones
   • $100: the average of $40 and $160 across the 1,000 people, since both kinds pay the same premium
   • $40, since the low-risk people are the ones the insurer most wants and they set the price
10. 7.

    Zee reads card B. What is the average claim per person after the premium rise?

    • About $110, since the new premium sets what the plan costs the insurer on each member
    • About $160, since the high-risk people are the ones who remain once the low-risk members start to leave
    • About $115, above the new $110 premium, so the rise did not close the shortfall
    • About $100, unchanged, since a change in the premium does not change who is covered by the plan

11. Use this

    Cards A and B on bike locks (all made up for practice). Card A, "A lock study (made up)". Written for this sheet. Summary in our words, not a quotation: 200 bike owners each chose their own plan. 100 chose a plan with no deductible, and 100 chose a plan with a $50 deductible. The number who left a bike unlocked at least once in a week was 12 of the first group and 7 of the second. Thefts that year were 9 per 100 in the first group and 5 per 100 in the second. Card B, "A lock discount (made up)". Written for this sheet. Summary in our words, not a quotation: an insurer offers $5 off the yearly premium to owners who use an approved lock. Each theft costs the insurer $350. Owners with locks have 3 thefts per 100; owners without have 7 per 100.

12. 8.

    Kira reads card A. What does it suggest about full coverage and care?

    • It fits the idea that full cover lowers care: 12 of 100 against 7 of 100 left bikes unlocked
    • It shows insured owners are careless, since 12 of 100 owners left a bike unlocked in a week
    • It shows that deductibles stop theft, since thefts fell from 9 per 100 to 5 per 100 with a deductible
    • It shows full coverage lowers theft, since insured owners worry less and so take more care of their bikes
13. 9.

    Jun lists four claims from card A. Which one goes beyond what the card shows?

    • The group with the deductible had fewer unlocked bikes and fewer thefts than the group without one
    • Choosing a $50 deductible made owners lock their bikes more often than they did before
    • 12 of 100 owners with no deductible left a bike unlocked, against 7 of 100 with a deductible
    • Thefts that year were 9 per 100 owners with no deductible and 5 per 100 with a $50 deductible
14. 10.

    Milo reads card B. Is the $5 lock discount worth offering?

    • No: the discount cuts the premium by $5 on each policy it touches, so the insurer ends up worse off overall
    • No: locks reduce thefts by 4 per 100 owners, which is too few to matter against $350 claims
    • Yes: locks cut expected claims by about $14 a policy (4 in 100 times $350), more than the $5 discount
    • Yes: a $5 discount makes owners feel safe, so they will lock their bikes and thefts will fall