Subjects insurance mathematics

Gross Premium 78Ce81

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1. **Stating the problem:** Encik Dhenes wants to buy a third party car insurance policy for a car with 2000 cc engine capacity and a sum insured of 24000. He has a No Claim Discount (NCD) of 55%. We need to calculate the gross premium he needs to pay. 2. **Formula and explanation:** The gross premium is calculated by applying the NCD discount to the base premium. The formula is: $$\text{Gross Premium} = \text{Base Premium} \times (1 - \text{NCD})$$ where NCD is expressed as a decimal (e.g., 55% = 0.55). 3. **Finding the base premium:** Typically, the base premium depends on the sum insured and the car capacity. Since the problem does not provide a direct rate, we assume the base premium is equal to the sum insured for simplicity (or the problem implies this). 4. **Calculating the gross premium:** $$\text{Gross Premium} = 24000 \times (1 - 0.55)$$ $$= 24000 \times 0.45$$ $$= 10800$$ 5. **Conclusion:** Encik Dhenes needs to pay a gross premium of 10800.