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?

ACV=$4,500

Step-by-step explanation:

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

Where:

actual cash value

replacement cost or purchase price of the item

expected life of the item

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:

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

Then the ACV is $4,500

x/3-10=8

x/3=18

x=48

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: