Consumer Mathematics: Insurance: Mathematics questions

Section A: objective questions

10 marks

Choose the correct answer. Each question carries 1 mark.

Which statement describes risk in insurance?

A loss that is certain to happen
A profit that the policyholder expects
The possibility of a loss that cannot be predicted
The money paid to the insurance company

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Risk is unpredictable and involves loss. The money paid is the premium.

For the teacher: Remembering, low difficulty, standard 3.1.1

Textbook p. 74

According to the principle of indemnity, the compensation paid to a policyholder

can be more than the loss so that the policyholder gains
is only up to the loss suffered, subject to the sum insured
is always equal to the sum insured
is paid even when no loss occurs

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Indemnity restores the policyholder to the position before the loss. It does not allow a profit, and the payment cannot exceed the sum insured.

For the teacher: Understanding, low difficulty, standard 3.1.1

Textbook p. 75

Which risk is covered by life insurance?

Theft of a motorcycle
Fire at a shop
Loss of luggage during a trip
Total and permanent disability

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Life insurance covers death, critical illness and loss of ability (total and permanent disability). The other three are general insurance.

For the teacher: Remembering, low difficulty, standard 3.1.1

Textbook p. 76

Hadi's car was stolen. His policy paid for the loss but would not pay for damage to his car in an accident. Which policy does he have?

Act policy
Third party policy
Comprehensive policy
Third party, fire and theft policy

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Own-vehicle fire or theft is covered by third party, fire and theft and by comprehensive. Accident damage to the own vehicle is only covered by comprehensive, so Hadi must have third party, fire and theft.

For the teacher: Understanding, medium difficulty, standard 3.1.1

Textbook p. 77

Ali drove his car with his friend Budi as a passenger and hit a car driven by Chong. Ali's policy is comprehensive. Which loss is not covered?

Damage to Ali's car
Damage to Chong's car
Budi's medical expenses
Injury claimed by Chong

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Chong is the third party. The driver's and passengers' own injuries are excluded from motor insurance, so Budi's medical costs are not covered.

For the teacher: Applying, medium difficulty, standard 3.1.1

Textbook p. 77

The rate for a 38-year-old male smoker is RM3.05 per RM1 000 of face value. What is the annual premium for RM80 000?

RM24.40
RM244.00
RM2 440.00
RM3.05

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80 000 ÷ 1 000 × 3.05 = 80 × 3.05 = RM244.00.

For the teacher: Applying, low difficulty, standard 3.1.2

Textbook p. 81

The basic premium of a comprehensive policy is RM1 483.10. What is the basic premium of the third party, fire and theft policy for the same car?

RM1 112.33
RM370.78
RM889.86
RM1 186.48

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Third party, fire and theft is 75% of the comprehensive basic premium: 0.75 × 1 483.10 = RM1 112.33. RM370.78 is 25%.

For the teacher: Applying, medium difficulty, standard 3.1.2

Textbook p. 83

A car in Peninsular Malaysia has an engine of 1 500 cc and a sum insured of RM38 000. The comprehensive rate for 1 650 cc is RM305.50 for the first RM1 000. Its NCD is 30%. The gross premium is

RM887.25
RM1 267.50
RM380.25
RM905.45

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Blocks after the first RM1 000 = 37, so basic = 305.50 + 26 × 37 = 1 267.50. NCD = 0.30 × 1 267.50 = 380.25. Gross = 1 267.50 − 380.25 = RM887.25. RM1 267.50 is before the NCD.

For the teacher: Applying, medium difficulty, standard 3.1.2

Textbook p. 83

The insurable value of a house is RM350 000 and the fire policy has a 70% co-insurance clause. The amount of insurance required is

RM105 000
RM245 000
RM350 000
RM280 000

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0.70 × 350 000 = RM245 000. RM105 000 is 30%.

For the teacher: Applying, medium difficulty, standard 3.1.3

Textbook p. 87

A health policy has a deductible of RM400 and an 80/20 co-insurance clause. The covered medical cost is RM15 400. How much does the policyholder pay?

RM3 080
RM3 000
RM3 400
RM12 000

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After deductible: 15 400 − 400 = 15 000. Policyholder pays 20% × 15 000 + 400 = RM3 400. RM3 000 forgets the deductible; RM12 000 is the company's share.

For the teacher: Applying, high difficulty, standard 3.1.3

Textbook p. 89

Section B: structured questions

35 marks

Answer all questions. Show your working.

The annual premium rates per RM1 000 face value are: age 36, male smoker RM2.80; age 38, female non-smoker RM1.63.

[2 marks] (a)Mr Hakim, 36, a smoker, buys a policy of RM100 000. Calculate his annual premium.

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100 000 ÷ 1 000 × 2.80 [1]1
RM280.00 [1]1

Tick each point you got.

[4 marks] (b)Madam Lina, 38, a non-smoker, buys RM150 000 and adds a critical illness cover of 30% of the face value at RM1.69 per RM1 000. Calculate her total annual premium.

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Basic: 150 × 1.63 = RM244.50 [1]1
Critical illness cover: 30% × 150 000 = RM45 000 [1]1
45 × 1.69 = RM76.05 [1]1
Total = RM320.55 [1]1

Tick each point you got.

[1 mark] (c)Why is the premium rate higher for a smoker?

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A smoker has a higher chance of illness [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 3.1.2

Textbook p. 81

Encik Zakri lives in Peninsular Malaysia. His car has an engine of 2 900 cc and a sum insured of RM80 000. The tariff for 3 050 cc is RM372.60 (comprehensive, first RM1 000) and RM167.40 (third party). His NCD is 25%.

[2 marks] (a)Calculate the basic premium for the comprehensive policy.

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372.60 + 26 × 79 [1]1
RM2 426.60 [1]1

Tick each point you got.

[2 marks] (b)Calculate the gross premium for the comprehensive policy.

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NCD = 0.25 × 2 426.60 = RM606.65 [1]1
Gross = RM1 819.95 [1]1

Tick each point you got.

[2 marks] (c)Calculate the gross premium for the third party, fire and theft policy.

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Basic = 0.75 × 2 426.60 = RM1 819.95 [1]1
NCD = 0.25 × 1 819.95 = RM454.99; Gross = 1 819.95 − 454.99 = RM1 364.96 [1]1

Tick each point you got.

[2 marks] (d)Calculate the gross premium for the third party policy.

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NCD = 0.25 × 167.40 = RM41.85 [1]1
Gross = RM125.55 [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 3.1.2

Textbook p. 83

Mr Rajan's motor policy has a deductible of RM400. His medical policy has a deductible of RM3 000 per year.

[3 marks] (a)Mr Rajan has three motor losses: RM350, RM1 200 and RM6 500. State whether he can claim for each and the compensation.

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RM350: no claim, below the deductible [1]1
RM1 200: 1 200 − 400 = RM800 [1]1
RM6 500: 6 500 − 400 = RM6 100 [1]1

Tick each point you got.

[2 marks] (b)In one year his hospital bill is RM45 000. State the amount paid by the insurance company and the amount he bears.

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Company pays 45 000 − 3 000 = RM42 000 [1]1
He bears RM3 000 [1]1

Tick each point you got.

[1 mark] (c)A deductible is paid by the policyholder

before a claim is paidafter a claim is paid

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before a claim is paid

The policyholder bears the deductible first; the company pays the balance.

For the teacher: Applying, medium difficulty, standard 3.1.3

Textbook p. 86

The insurable value of Mr Chan's house is RM400 000. His fire policy has a co-insurance clause of 80% and a deductible of RM1 000.

[1 mark] (a)Calculate the amount of insurance required.

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0.80 × 400 000 = RM320 000 [1]1

Tick each point you got.

[3 marks] (b)A fire causes a loss of RM40 000. Calculate the compensation if he insured the house for RM240 000.

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240 000 < 320 000, so use the co-insurance formula [1]1
240 000 ÷ 320 000 × 40 000 − 1 000 [1]1
RM29 000 [1]1

Tick each point you got.

[2 marks] (c)Calculate the co-insurance penalty.

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Loss before deductible = 30 000 [1]1
Penalty = 40 000 − 30 000 = RM10 000 [1]1

Tick each point you got.

[2 marks] (d)The house is a total loss and was insured for RM250 000. Find the compensation.

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250 000 − 1 000 [1]1
RM249 000 [1]1

Tick each point you got.

For the teacher: Analysing, high difficulty, standard 3.1.3

Textbook p. 88

Madam Tan has a medical policy with a deductible of RM400 and an 80/20 co-insurance clause. Her covered hospital cost is RM10 400.

[1 mark] (a)Calculate the cost after the deductible.

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10 400 − 400 = RM10 000 [1]1

Tick each point you got.

[3 marks] (b)Calculate the amount paid by the insurance company and by Madam Tan.

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Company: 0.80 × 10 000 = RM8 000 [1]1
Madam Tan: 0.20 × 10 000 [1]1
+ 400 = RM2 400 [1]1

Tick each point you got.

[2 marks] (c)Plan X has an annual limit of RM50 000 and a premium of RM506. Plan Y has the same limit and a premium of RM637 but pays a lower room allowance. Which plan is better? Give a reason.

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Plan X [1]1
Same annual limit with a lower premium and a better room allowance [1]1

Tick each point you got.

For the teacher: Evaluating, high difficulty, standard 3.1.3

Textbook p. 89

Section A: objective questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Section B: structured questions

Question 11

Question 12

Question 13

Question 14

Question 15