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 $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 $350: that is what the plan pays after a theft, far more than the $30 premium for it
   • About $30: a fair premium equals the average payout, so the two must match for the plan to be sold
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: its $26 premium is lower than Plan 1's $30, and the lower premium settles the choice
   • Plan 2 is better on average: it saves $4 in premium and adds only $2.50 of expected cost
   • 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

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?

   • 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
   • 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
7. 5.

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

   • With many homes the share that burns stays near 1 percent, but with 10 homes one fire is 10 percent
   • 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 1,000 homes the insurer can be sure that exactly 10 will burn, so its claims are fixed in advance

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
   • $40, since the low-risk people are the ones the insurer most wants and they set the price
   • $100: the average of $40 and $160 across the 1,000 people, since both kinds pay the same premium
10. 7.

    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 $110, since the new premium sets what the plan costs the insurer on each member
    • 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. 8.

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

    • It lets the insurer tell who is high-risk, so each person can be charged a premium that matches their own claims
    • 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 lowers the claims of high-risk people, since a penalty makes them healthier and less costly to cover

12. 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.

13. 9.

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

    • 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
    • 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
14. 10.

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

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