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An insured's roof cost $4,000 when installed 5 years ago. It has been damaged by hail and must be replaced. The new roof will cost $6,000 at today’s prices. If the roof has been depreciating at $200 per year and the insured’s policy is written on the actual cash value(ACV), how much will the policy pay toward the insured's new roof?

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2134jenny

Answer:

ACV=$4,500

Step-by-step explanation:

We have that the actual cash value (ACV) is defined as:

[tex]ACV=\dfrac{R\times(E-C)}{E}[/tex]

Where:

[tex]ACV =[/tex] actual cash value

[tex]R =[/tex] replacement cost or purchase price of the item

[tex]E =[/tex] expected life of the item

[tex]C =[/tex] current life of the item

Then we have R=$6,000, C=5years, and to find the expected life of the item we can use the depreciating of the roof, then if the roof is depreciating $200 each year we just need to divide $4,000 by $200 to find the expected life of the roof:

[tex]\dfrac{4,000}{200}=20[/tex]

Then the espected life of the roof is 20 years, with this result we have all the data, then:

[tex]ACV=\dfrac{\$6,000\times (20-5)}{20}=\dfrac{\$6,000\times (15)}{20}=\dfrac{\$90,000}{20}=\$4,500[/tex]

Then the ACV is $4,500

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