Joe purchased his home five years ago for $100,000. To protect his investment, he also purchased homeowners insurance at that time with a limit equal to the full value of his home ($100,000). The homeowners policy covers the dwelling on a replacement cost basis, subject to an 80% coinsurance clause. Because of rising construction costs over the past 5 years, the replacement cost of the dwelling has increased to $150,000. However, Joe never increased the limit of his policy. A severe windstorm has damaged Joe's roof, and the damage is estimated at $12,000.
How much of the $12,000 loss will be paid by Joe's homeowner?s policy? (Ignore deductibles).