To determine the value of compensation expected from the insurer after a fire accident, we need to analyze the situation step by step. Step-by-Step Explanation

1. Understanding the Insurance Coverage:
2. The sole proprietor insured his goods worth N200,000 but only for half the value. This means the insured amount is: [ \text{Insured Amount} = \frac{N200,000}{2} = N100,000 ]
3. Assessing the Loss:
4. During the fire accident, goods valued at N80,000 were destroyed. This is the actual loss incurred by the sole proprietor.
5. Calculating the Compensation:
6. The compensation from the insurer is typically based on the insured amount and the actual loss. However, since the goods were underinsured (insured for less than their full value), we need to apply the principle of average in insurance.
7. The formula for calculating the compensation in the case of underinsurance is: [ \text{Compensation} = \left( \frac{\text{Insured Amount}}{\text{Actual Value}} \right) \times \text{Loss} ]
8. Plugging in the values: [ \text{Compensation} = \left( \frac{N100,000}{N200,000} \right) \times N80,000 ] [ \text{Compensation} = 0.5 \times N80,000 = N40,000 ]
9. Final Compensation Amount:
10. Therefore, the value of compensation expected from the insurer is N40,000.

Why the Other Options are Incorrect

• Option A: N40,000 (Correct)
• This is the correct answer based on the calculations above.
• Option B: N80,000
• This option suggests that the sole proprietor would receive the full value of the loss. However, since the goods were underinsured, the compensation cannot exceed the insured amount, which is N100,000. Thus, this option is incorrect.
• Option C: N100,000
• This option implies that the sole proprietor would receive the full insured amount. However, since the actual loss is N80,000 and the insured amount is only half of the total value, the compensation must be calculated based on the principle of average, leading to a lower compensation amount of N40,000. Therefore, this option is incorrect.
• Option D: N200,000
• This option suggests that the sole proprietor would receive the full value of the goods. This is not possible because the goods were only insured for N100,000, and the principle of indemnity in insurance prevents the insured from profiting from a loss. Thus, this option is also incorrect.

Summary of Key Points

• The sole proprietor insured goods worth N200,000 for half the value, which is N100,000.
• The actual loss from the fire was N80,000.
• Due to underinsurance, the compensation is calculated using the formula for average, resulting in N40,000.
• The correct answer is A: N40,000.

This thorough breakdown should help you understand how to approach similar insurance-related questions in the future.