There was water damage to personal property in a home. The items damaged were originally priced at $4000. The items lose value by 11% per year. The items were four years old when they were damaged. The owner had actual cash value coverage with a deductible of $250.
How much will the insurance company pay the policy holder?
$3600
$250
$1990
$4000
Is it $1990? 11% of 4000 is 440... 440* 4 years is $1760.... 4000-1760=2240 So the items were worth $2240 after 4 years, but then the policy holder has to pay the $250 deductible, so the insurance company will pay him $1990 right?
Yes, your calculation is correct. The items were originally priced at $4000 and lost 11% of their value each year. After 4 years, the value of the items would be $4000 - (0.11 * $4000 * 4) = $2240.
Since the policy holder has a deductible of $250, the insurance company will pay the difference between the value of the items and the deductible. Therefore, the insurance company will pay $2240 - $250 = $1990 to the policy holder. So your answer of $1990 is correct.
I don't get any of those answers.
What you did is to take simple interest, instead of the standard compound interest.
Value at end of 4 years = 4000(.89)^4 = 2509.69
with a deductible of $250, payout would be 2509.69 - 250 = appr $2260
long way:
value at end of 1 year = 4000(.89) = 3560
value at end of 2 years = 3560(.89) = 3168.4
value at end of 3 years = 3168.4(.89) = 2819.88
value at end of 4 years = 2509.69 <---- same as the single step calculation above
less the 250 deductible .... same answer