Risk and Insurance Coverage

3.1 Risk and Insurance Coverage
MATHEMATICS • Form 5 • Chapter 3: Consumer Mathematics: Insurance

3.1 Risk and Insurance Coverage

Every person is constantly exposed to risks and unforeseen events such as accidents, property damage due to fire, and critical illnesses. While such occurrences cannot be fully avoided or predicted, insurance provides financial protection to transfer these risks and alleviate the financial burden borne by individuals and families.

Learning Objectives

  • Explain the meaning of risk and the importance of insurance coverage.
  • Determine and differentiate the types of life insurance and general insurance that protect against various risks.
  • Investigate, interpret, and perform calculations involving insurance rates and premiums for life insurance and motor insurance.
  • Solve problems involving insurance, including the application of deductible and co-insurance provisions.

Classification of Insurance Policies and Problem-Solving Provisions

Categorise Life vs General Insurance and distinguish between Deductible and Co-insurance.

Life Insurance

  • Death
  • Total and permanent disability
  • Critical illness

General Insurance

  • Motor
  • Fire
  • Medical & Health
  • Personal Accident
  • Travel

Deductible

A fixed amount deducted upfront before the insurer pays the remaining eligible claim.

Co-insurance

Proportional cost sharing between the insurance company and the policyholder.

Brief Explanation

What is Risk?

Risk is the possibility of an unavoidable disaster. Important elements of risk: risk is unpredictable, and risk involves loss.

What is Insurance?

Insurance is a contract signed between the insurance company and the policyholder to transfer risks from individuals to insurance organisations.

Premium and Compensation

Premium is an amount of money payable by the policyholder to the insurance company. Compensation is payment made by the insurance company to the policyholder for covered losses.

Principle of Indemnity

The Principle of Indemnity ensures the insurance company pays compensation to restore the financial position of the policyholder to the pre-loss condition, for an amount not exceeding the actual loss incurred, subject to the sum insured. It does not allow the policyholder to gain profit from insurance.

Type of Insurance Coverage Key Notes
Life Insurance Death, total and permanent disability, critical illness Protects dependents financially
Motor Insurance Loss or damage related to motor vehicle use Compulsory under Road Transport Act 1987
Fire Insurance Damage caused by fire, lightning, explosion Additional perils can be added for extra premium
Medical & Health Insurance Hospitalisation, surgery, critical illness, disability income Covers medical expenses
Personal Accident Insurance Bodily injury, disability, death from accidents Direct result of accidents
Travel Insurance Death, permanent disability, luggage/money/passport loss, medical expenses Protects against losses during travel
Group Insurance Groups such as employees or students Example: Takaful Pelajar Sekolah Malaysia (TPSM)
1
Life Insurance Premium
\[ \text{Premium} = \frac{\text{Face value of policy}}{\text{RM}x} \times (\text{Premium rate per RM}x) \]
2
Motor Comprehensive Basic Premium
\[ \text{Peninsular Malaysia: Rate for first RM1 000} + \text{RM26 for each RM1 000 or part thereof exceeding RM1 000} \]
3
Gross Premium
\[ \text{Gross Premium} = \text{Basic Premium} - \text{NCD amount} \]
4
Deductible
If loss \(\le\) deductible, compensation = RM0. If loss \(>\) deductible, compensation = loss − deductible.
5
Co-insurance in Property Insurance
\[ \text{Amount of required insurance} = \text{Percentage of co-insurance} \times \text{Insurable value of property} \]

Try Answering First

Read the question, answer it in your mind, then press “Check Answer”.

1

Mr Tan buys a life insurance policy with a face value of RM150 000. The annual premium rate is RM2.26 per RM1 000 face value. Calculate his annual premium.

Answer: \[ \text{Annual Premium} = \frac{\text{RM}150\,000}{\text{RM}1\,000} \times \text{RM}2.26 = 150 \times \text{RM}2.26 = \text{RM}339.00 \]
2

Encik Rizal has a motor insurance policy with a deductible provision of RM400. In an accident, his car suffered damage worth RM1 850. Calculate the compensation amount paid by the insurance company.

Answer: Since the loss of RM1 850 exceeds the deductible of RM400: \[ \text{Compensation} = \text{RM}1\,850 - \text{RM}400 = \text{RM}1\,450 \]
3

Puan Aminah owns a house with an insurable value of RM300 000. Her fire insurance policy requires an 80% co-insurance and has a RM2 000 deductible. She insures her house for RM240 000. If her house suffers a partial fire loss of RM30 000, what is the compensation amount she will receive?

Answer: \[ \text{Amount of required insurance} = 80\% \times \text{RM}300\,000 = \text{RM}240\,000 \] Since the insured value equals the required insurance: \[ \text{Compensation} = \text{Loss} - \text{Deductible} = \text{RM}30\,000 - \text{RM}2\,000 = \text{RM}28\,000 \]

Common Mistakes

  • ! Forgetting to subtract the deductible after calculating the proportional loss in co-insurance formulas.
  • ! Applying co-insurance penalty calculations when a total loss occurs; for total loss, compensation is simply the amount of insurance purchased minus deductible.
  • ! Assuming that third-party motor insurance covers the policyholder's own car damage or medical expenses.
  • ! Forgetting to deduct the No Claim Discount (NCD) when computing gross motor insurance premium.

Misconceptions

Misconception

Believing insurance can be bought to make a financial profit.

Correct Fact

Under the principle of indemnity, compensation only restores the policyholder to the pre-loss financial condition and does not exceed the actual loss.

Misconception

Believing that motor comprehensive insurance covers medical costs of the driver and their passenger.

Correct Fact

Standard motor comprehensive policies protect third parties and own vehicle damage/theft/fire, but exclude bodily injury and death claims for the driver and passengers.

Misconception

Thinking that co-insurance penalty applies to medical and health insurance.

Correct Fact

Co-insurance penalty applies to property insurance when the property is under-insured; health insurance co-insurance is a predetermined cost-sharing participation ratio.

Summary

  • Risk: Unpredictable possibility of loss.
  • Principle of Indemnity: Restoring pre-loss financial standing without profit.
  • Life Insurance: Protection against death, disability, or critical illness based on age, gender, face value, and smoking status.
  • General Insurance: Includes Motor, Fire, Medical & Health, Personal Accident, and Travel insurance.
  • Deductible: A pre-agreed amount borne by the policyholder before insurance payout is made.
  • Co-insurance (Property): Condition requiring insurance up to a certain percentage of the insurable value; under-insuring results in a co-insurance penalty.

Short Activity

Complete all parts first, then press the check answer button.

A. Objective Quiz

1 Which type of motor insurance policy provides coverage against liability to third parties, loss of property suffered by third parties, loss to own vehicle due to accidental fire or theft, AND loss and damage to own vehicle due to an accident?

2 Under the principle of indemnity, what is the maximum financial compensation an insurance company will pay to a policyholder?

B. Fill in the Blanks

3 The amount of money that must be borne by the policyholder before they can make a claim from the insurance company is known as the .

4 In property insurance, the penalty borne by the policyholder for failing to meet the required insurance sum under the co-insurance clause is known as the penalty.

C. Drag and Drop: Match Each Insurance Term to Its Definition

Drag each term to the correct description. On a phone, tap the answer choice first, then tap the description box.

Insurance Term
Premium
Principle of Indemnity
Deductible
Co-insurance
Description
The amount payable by the policyholder to the insurance company for coverageCorrectTry againEmpty
Key principle that restores the policyholder's financial position to the pre-loss condition without profitCorrectTry againEmpty
Initial fixed loss amount borne entirely by the policyholder before a claim is paidCorrectTry againEmpty
Cost sharing of the loss between the insurance company and the policyholderCorrectTry againEmpty
 

Key Terms

Risk Policyholder Premium Principle of Indemnity Deductible Co-insurance Co-insurance Penalty No Claim Discount (NCD)

Risk and Insurance Coverage

3.1 Risk and Insurance Coverage
MATHEMATICS • Form 5 • Chapter 3: Consumer Mathematics: Insurance

3.1 Risk and Insurance Coverage

Every person is constantly exposed to risks and unforeseen events such as accidents, property damage due to fire, and critical illnesses. While such occurrences cannot be fully avoided or predicted, insurance provides financial protection to transfer these risks and alleviate the financial burden borne by individuals and families.

Learning Objectives

  • Explain the meaning of risk and the importance of insurance coverage.
  • Determine and differentiate the types of life insurance and general insurance that protect against various risks.
  • Investigate, interpret, and perform calculations involving insurance rates and premiums for life insurance and motor insurance.
  • Solve problems involving insurance, including the application of deductible and co-insurance provisions.

Classification of Insurance Policies and Problem-Solving Provisions

Categorise Life vs General Insurance and distinguish between Deductible and Co-insurance.

Life Insurance

  • Death
  • Total and permanent disability
  • Critical illness

General Insurance

  • Motor
  • Fire
  • Medical & Health
  • Personal Accident
  • Travel

Deductible

A fixed amount deducted upfront before the insurer pays the remaining eligible claim.

Co-insurance

Proportional cost sharing between the insurance company and the policyholder.

Brief Explanation

What is Risk?

Risk is the possibility of an unavoidable disaster. Important elements of risk: risk is unpredictable, and risk involves loss.

What is Insurance?

Insurance is a contract signed between the insurance company and the policyholder to transfer risks from individuals to insurance organisations.

Premium and Compensation

Premium is an amount of money payable by the policyholder to the insurance company. Compensation is payment made by the insurance company to the policyholder for covered losses.

Principle of Indemnity

The Principle of Indemnity ensures the insurance company pays compensation to restore the financial position of the policyholder to the pre-loss condition, for an amount not exceeding the actual loss incurred, subject to the sum insured. It does not allow the policyholder to gain profit from insurance.

Type of Insurance Coverage Key Notes
Life Insurance Death, total and permanent disability, critical illness Protects dependents financially
Motor Insurance Loss or damage related to motor vehicle use Compulsory under Road Transport Act 1987
Fire Insurance Damage caused by fire, lightning, explosion Additional perils can be added for extra premium
Medical & Health Insurance Hospitalisation, surgery, critical illness, disability income Covers medical expenses
Personal Accident Insurance Bodily injury, disability, death from accidents Direct result of accidents
Travel Insurance Death, permanent disability, luggage/money/passport loss, medical expenses Protects against losses during travel
Group Insurance Groups such as employees or students Example: Takaful Pelajar Sekolah Malaysia (TPSM)
1
Life Insurance Premium
\[ \text{Premium} = \frac{\text{Face value of policy}}{\text{RM}x} \times (\text{Premium rate per RM}x) \]
2
Motor Comprehensive Basic Premium
\[ \text{Peninsular Malaysia: Rate for first RM1 000} + \text{RM26 for each RM1 000 or part thereof exceeding RM1 000} \]
3
Gross Premium
\[ \text{Gross Premium} = \text{Basic Premium} - \text{NCD amount} \]
4
Deductible
If loss \(\le\) deductible, compensation = RM0. If loss \(>\) deductible, compensation = loss − deductible.
5
Co-insurance in Property Insurance
\[ \text{Amount of required insurance} = \text{Percentage of co-insurance} \times \text{Insurable value of property} \]

Try Answering First

Read the question, answer it in your mind, then press “Check Answer”.

1

Mr Tan buys a life insurance policy with a face value of RM150 000. The annual premium rate is RM2.26 per RM1 000 face value. Calculate his annual premium.

Answer: \[ \text{Annual Premium} = \frac{\text{RM}150\,000}{\text{RM}1\,000} \times \text{RM}2.26 = 150 \times \text{RM}2.26 = \text{RM}339.00 \]
2

Encik Rizal has a motor insurance policy with a deductible provision of RM400. In an accident, his car suffered damage worth RM1 850. Calculate the compensation amount paid by the insurance company.

Answer: Since the loss of RM1 850 exceeds the deductible of RM400: \[ \text{Compensation} = \text{RM}1\,850 - \text{RM}400 = \text{RM}1\,450 \]
3

Puan Aminah owns a house with an insurable value of RM300 000. Her fire insurance policy requires an 80% co-insurance and has a RM2 000 deductible. She insures her house for RM240 000. If her house suffers a partial fire loss of RM30 000, what is the compensation amount she will receive?

Answer: \[ \text{Amount of required insurance} = 80\% \times \text{RM}300\,000 = \text{RM}240\,000 \] Since the insured value equals the required insurance: \[ \text{Compensation} = \text{Loss} - \text{Deductible} = \text{RM}30\,000 - \text{RM}2\,000 = \text{RM}28\,000 \]

Common Mistakes

  • ! Forgetting to subtract the deductible after calculating the proportional loss in co-insurance formulas.
  • ! Applying co-insurance penalty calculations when a total loss occurs; for total loss, compensation is simply the amount of insurance purchased minus deductible.
  • ! Assuming that third-party motor insurance covers the policyholder's own car damage or medical expenses.
  • ! Forgetting to deduct the No Claim Discount (NCD) when computing gross motor insurance premium.

Misconceptions

Misconception

Believing insurance can be bought to make a financial profit.

Correct Fact

Under the principle of indemnity, compensation only restores the policyholder to the pre-loss financial condition and does not exceed the actual loss.

Misconception

Believing that motor comprehensive insurance covers medical costs of the driver and their passenger.

Correct Fact

Standard motor comprehensive policies protect third parties and own vehicle damage/theft/fire, but exclude bodily injury and death claims for the driver and passengers.

Misconception

Thinking that co-insurance penalty applies to medical and health insurance.

Correct Fact

Co-insurance penalty applies to property insurance when the property is under-insured; health insurance co-insurance is a predetermined cost-sharing participation ratio.

Summary

  • Risk: Unpredictable possibility of loss.
  • Principle of Indemnity: Restoring pre-loss financial standing without profit.
  • Life Insurance: Protection against death, disability, or critical illness based on age, gender, face value, and smoking status.
  • General Insurance: Includes Motor, Fire, Medical & Health, Personal Accident, and Travel insurance.
  • Deductible: A pre-agreed amount borne by the policyholder before insurance payout is made.
  • Co-insurance (Property): Condition requiring insurance up to a certain percentage of the insurable value; under-insuring results in a co-insurance penalty.

Short Activity

Complete all parts first, then press the check answer button.

A. Objective Quiz

1 Which type of motor insurance policy provides coverage against liability to third parties, loss of property suffered by third parties, loss to own vehicle due to accidental fire or theft, AND loss and damage to own vehicle due to an accident?

2 Under the principle of indemnity, what is the maximum financial compensation an insurance company will pay to a policyholder?

B. Fill in the Blanks

3 The amount of money that must be borne by the policyholder before they can make a claim from the insurance company is known as the .

4 In property insurance, the penalty borne by the policyholder for failing to meet the required insurance sum under the co-insurance clause is known as the penalty.

C. Drag and Drop: Match Each Insurance Term to Its Definition

Drag each term to the correct description. On a phone, tap the answer choice first, then tap the description box.

Insurance Term
Premium
Principle of Indemnity
Deductible
Co-insurance
Description
The amount payable by the policyholder to the insurance company for coverageCorrectTry againEmpty
Key principle that restores the policyholder's financial position to the pre-loss condition without profitCorrectTry againEmpty
Initial fixed loss amount borne entirely by the policyholder before a claim is paidCorrectTry againEmpty
Cost sharing of the loss between the insurance company and the policyholderCorrectTry againEmpty
 

Key Terms

Risk Policyholder Premium Principle of Indemnity Deductible Co-insurance Co-insurance Penalty No Claim Discount (NCD)