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Consumer Mathematics: Insurance · Form 5

Consumer Mathematics: Insurance: Worked Examples (Medium)

Two-to-three-step problems: the average (co-insurance) clause when a property is under-insured, adding separate premiums for building and contents, and a medical claim that combines a deductible with a co-insurance percentage. General information only, not financial or insurance advice.

Written by the spmmath.com.my editorial team.

Worked example 1

A shop building is worth RM200,000 but is insured for only RM150,000. A fire causes RM40,000 of damage.

Under the average clause, how much does the insurer pay?

  1. The building is under-insured (RM150,000 < RM200,000), so the average clause applies.
  2. Payout = (sum insured ÷ value) × loss.
  3. = (150,000 ÷ 200,000) × 40,000 = 0.75 × 40,000.
  4. = RM30,000.

Worked example 2

A homeowner insures the building for RM250,000 at RM2.40 per RM1,000, and the contents for RM50,000 at RM1.50 per RM1,000. Find the total annual premium.

  1. Compute each premium separately using Premium = (sum insured ÷ 1,000) × rate.
  2. Building: (250,000 ÷ 1,000) × 2.40 = 250 × 2.40 = RM600.
  3. Contents: (50,000 ÷ 1,000) × 1.50 = 50 × 1.50 = RM75.
  4. Total premium = 600 + 75 = RM675.

Worked example 3

A medical bill comes to RM5,000. The policy has a deductible of RM200 (paid first) and 10% co-insurance on the amount after the deductible.

Find how much the insurer pays.

  1. Deductible is paid first: amount after deductible = 5,000 − 200 = RM4,800.
  2. Co-insurance: insurer pays 90% (100% − 10%) of RM4,800.
  3. Insurer's payout = 0.90 × 4,800 = RM4,320.
  4. Check: policyholder pays 200 + 0.10 × 4,800 = RM680; 680 + 4,320 = RM5,000. ✓

Worked example 4

A house valued at RM300000 is insured for only RM240000. A fire causes RM60000 of damage.

The policy has an average clause. Calculate the insurer's payout.

  1. Property is under-insured (RM240000 < RM300000), so the average clause applies.
  2. Payout = (sum insured ÷ value) × loss
  3. = (240000 ÷ 300000) × 60000 = 0.8 × 60000 = RM48000

Worked example 5

A building is insured for RM180000 at RM2.20 per RM1000 and its contents for RM40000 at RM3.50 per RM1000. Calculate the total annual premium.

  1. Building premium = (180000 ÷ 1000) × 2.20 = 180 × 2.20 = RM396
  2. Contents premium = (40000 ÷ 1000) × 3.50 = 40 × 3.50 = RM140
  3. Total premium = 396 + 140 = RM536

Worked example 6

A medical bill is RM8000. The policy has a deductible of RM300, then a 20% co-insurance on the balance.

How much does the insurer pay?

  1. Amount after deductible = 8000 − 300 = RM7700
  2. Co-insurance: policyholder pays 20%, insurer pays 80%
  3. Insurer payout = 80% × 7700 = 0.8 × 7700 = RM6160

Worked example 7

An office building worth RM350,000 is insured for only RM280,000. A burst pipe causes RM56,000 of water damage.

Under the average clause, calculate the amount the insurer pays.

  1. Fraction insured = sum insured ÷ value of property = RM280,000 ÷ RM350,000 = 0.8
  2. Payout under the average clause = 0.8 × RM56,000 = RM44,800

Worked example 8

A dental treatment bill comes to RM3,600. The policy has a deductible of RM100, paid first by the patient, and then a 15% co-insurance on the amount after the deductible.

Find how much the insurer pays.

  1. Balance after the deductible = RM3,600 − RM100 = RM3,500
  2. Insurer's share = (100% − 15%) × RM3,500 = 85% × RM3,500
  3. = RM2,975

Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)

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Frequently asked questions

What do medium-level insurance questions add beyond basic premium calculation?

Medium questions ask you to compare two or more insurance plans or policies, weighing premium cost against coverage or benefits, and to calculate figures like total premium over several years, or work out compensation received based on policy terms. You need to interpret given conditions, not just plug numbers into one formula.

What's a common pitfall when comparing two insurance policies?

Students sometimes compare only the premium amount and ignore differences in coverage, sum insured, or claim conditions, leading to an incomplete or wrong conclusion about which plan is better. Read every condition given for both policies before deciding, and justify your comparison using the actual figures calculated.

How should students justify their final recommendation in a comparison question?

State the calculated figures for each option clearly, then give a short reasoned conclusion referring back to those numbers, for example, which plan costs less overall or offers better coverage for the same premium. An answer without a clear final statement, even with correct working, may lose marks.

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