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To determine how much the insurer will pay for the fire damage, it's necessary to apply the principle of underinsurance, which considers the proportion of the insured amount to the actual value of the property.

In this scenario, the building is valued at $200,000, but it was insured for only $140,000. The loss incurred from the fire is $50,000. However, because the insurance coverage is less than the full value of the building (which represents 70% of the total value), the insurer calculates the payment based on the ratio of the actual coverage to the total value.

The calculation involves first determining the proportion of the value covered: $140,000 (insurance limit) ÷ $200,000 (actual value) = 0.7 or 70%. This means the insurance covers only 70% of losses. Thus, in the event of a claim, the insurer will only pay 70% of the $50,000 loss from the fire damage.

So, applying this percentage to the loss: $50,000 (the loss) × 0.7 = $35,000. Therefore, the insurer would only pay $35,000 due to the underinsurance, reflecting the fact