A homeowner owns a home that would cost $$80,000$ to replace at present replacement costs. He reasons that any loss sustained would probably be less than this amount, as he is located near a fire department and someone is at home most of the time. In order to save money on his insurance premiums, he purchases a homeowner's policy in the amount of $$40,000.$

Should the property suffer a loss costing $$15,000$ to repair, what would be the amount of recovery? Actual cash value of the loss is $$10,000.$