Chapter 3: Consumer Mathematics: Insurance

3.1 Risk and Insurance Coverage

Risk

Risk is the possibility of facing a loss or misfortune that cannot be predicted.

Insurance

Insurance is a contract signed between an insurance company (insurer) and a policyholder (insured), where the insurer promises to pay compensation for covered financial losses in return for regular payments called premiums.

Principle of Indemnity: The insurer pays compensation to restore the insured to the financial position they were in immediately before the loss occurred, up to the coverage limit (excluding Life and Personal Accident insurance).

Types of Insurance

• Life Insurance: Pays a sum of money upon death, total permanent disability (TPD), or critical illness of the insured.
• General Insurance: Covers financial losses due to property damage, accidents, or medical issues.
  • Motor Insurance: Covers vehicle damages/losses (Third Party; Third Party, Fire & Theft; Comprehensive).
  • Medical and Health Insurance: Covers hospitalization and treatment costs.
  • Fire Insurance: Covers damage caused by fire, lightning, or gas explosion to buildings/contents.
  • Personal Accident Insurance: Compensation in the event of injury, disability, or death caused by accidents.
  • Travel Insurance: Covers travel delays, lost baggage, or medical emergency abroad.

3.2 Calculating Insurance Premiums

General Premium Formula

$$\text{Premium} = \frac{\text{Face Value of Coverage}}{\text{Rate Unit}} \times \text{Premium Rate per Unit}$$

Motor Insurance Premium Calculation

Calculated based on engine capacity (cc), location (Peninsular Malaysia vs. Sabah & Sarawak), vehicle age, market value, and No Claim Discount (NCD).

$$\text{Gross Premium} = (\text{Basic Premium}) \times (100\% - \text{NCD \%})$$

3.3 Deductible and Co-insurance

Deductible

A deductible is a specified amount of loss that must be borne by the policyholder before the insurer pays the remaining claim.

$$\text{Compensation Paid} = \text{Total Loss} - \text{Deductible}$$

Co-insurance in Property Insurance

The policyholder is required to insure the property up to a specified percentage of its total insurable value (usually 80%).

$$\text{Required Coverage} = \text{Co-insurance Percentage} \times \text{Insurable Value}$$

• If Coverage $\ge$ Required Coverage: $$\text{Compensation} = \text{Amount of Loss} - \text{Deductible}$$
• If Coverage $<$ Required Coverage (Under-insured): $$\text{Compensation} = \left(\frac{\text{Amount of Coverage}}{\text{Required Coverage}} \times \text{Amount of Loss}\right) - \text{Deductible}$$
• Co-insurance Penalty (Co-payment): The difference between actual loss and compensation paid.

Co-insurance in Health Insurance

Requires the policyholder to share a percentage of medical expenses after subtracting the deductible (e.g., 80/20 split: 80% paid by insurer, 20% borne by policyholder).