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.

   Ari works out what the first plan pays out in a year on average. Which statement fits card A?

   • About $350: that is what the plan pays after a theft, far more than the $30 premium for it
   • About $17.50: a 5 percent chance of a $350 payment, which is less than the $30 premium
   • About $20: a 5 percent chance of a $400 loss, which is less than the $30 premium on the plan
   • About $30: a fair premium equals the average payout, so the two must match for the plan to be sold
3. 2.

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

   • Cannot be judged: the 5 percent chance on card A is a guess, so no average payout can be worked out
   • Supported: a plan that pays less than it costs on average is a bad deal, so no one should buy it
   • Refuted: Plan 1 pays $350 after a theft, far more than its $30 premium, so it is plainly a good deal
   • Weakly supported: Plan 1 costs more than it pays on average, but it removes a loss the owner may not afford
4. 3.

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

5. 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.

6. 4.

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

   • Cover for fires larger than $20,000, since the premium is set above the average loss to pay for bigger fires
   • Pure profit of $100 a home, since claims average $200 against the $300 premium paid by each owner
   • 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
7. 5.

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

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

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.

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

   • 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 $110, since the new premium sets what the plan costs the insurer on each member
   • About $100, unchanged, since a change in the premium does not change who is covered by the plan
10. 7.

    Ren reads cards A and C. How could the rule on card C help the insurer?

    • It collects $120 from each person who skips the plan, which adds to the insurer's income from penalties
    • A $100 premium beats a $120 penalty even for low-risk people, so they stay and the average claim stays near $100
    • It lets the insurer tell who is high-risk, so each person can be charged a premium that matches their own claims
    • It lowers the claims of high-risk people, since a penalty makes them healthier and less costly to cover

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

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

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