An insured has a standard HO-4 policy with a $30,000 limit of coverage for personal property. If a fire destroys clothes and luggage worth $10,000 and jewelry worth $10,000, what amount is the insurer obligated to pay after a 20% depreciation?

The situation involves the calculation of the amount an insurer will pay under a standard HO-4 policy after depreciation is applied to covered personal property that has been damaged.

In this case, the insured has personal property that was destroyed, which includes clothes and luggage valued at $10,000 and jewelry also valued at $10,000.

First, let's determine the total value of the destroyed items:

• Clothes and luggage: $10,000

• Jewelry: $10,000

Total value: $20,000

Next, it’s important to consider the depreciation factor stated in the question. A 20% depreciation means that the value of the items will decrease by that percentage before the payout is calculated.

Calculating the depreciation:

20% of $20,000 is $4,000.

Now, we subtract this depreciation from the total value of the destroyed property:

Total value: $20,000

Less depreciation: -$4,000

Amount after depreciation: $16,000

Since the HO-4 policy has a limit for personal property coverage of $30,000, and the final amount owing after depreciation does not exceed this limit, the insurer is obligated to pay $16,000.