If the contents of a building are insured for $45,000 and valued at $100,000 with a 90% co-insurance clause and a $2,500 deductible, how much will the insurer pay after an $8,000 damage claim?

To determine how much the insurer will pay after an $8,000 damage claim, we first need to calculate the required coverage under the 90% co-insurance clause.

The actual cash value (ACV) of the contents is $100,000. With a 90% co-insurance requirement, the insured amount should be at least 90% of the ACV to avoid penalties. This means the minimum required coverage is calculated as follows:

[ \text{Minimum Required Coverage} = 90% \times 100,000 = 90,000. ]

However, the contents are only insured for $45,000, which is below the required minimum of $90,000. This triggers a penalty on the claim due to insufficient insurance coverage. The penalty is calculated based on the ratio of the insured amount to the required amount:

[ \text{Penalty Ratio} = \frac{\text{Insured Amount}}{\text{Required Amount}} = \frac{45,000}{90,000} = 0.5. ]

This means that the insurer will only pay 50% of any eligible claim amount.

Now, we apply this penalty to the $8,000 damage claim: