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January 25, 2015

January 25, 2015

Posted by **chandice** on Wednesday, July 8, 2009 at 10:09pm.

rental house can depreciate its value over a period of 27 1/2

years, meaning that the value of the house declines

at an even rate over that period of time until the value is $0

a. By what fraction does the value of the house depreciate

the first year?

b. If the house is judged to be worth $85,000, what is

the value of the first year’s depreciation?

- math word problem -
**Reiny**, Wednesday, July 8, 2009 at 11:14pmThe wording of the question is somewhat confusing.

You state that the value declines at an "even" rate.

Are you saying that the rate is the same for each year? I am sure that is what you meant.

Mathematically, the value can never be zero, but since we are dealing with money, I picked .004 cents arbitrarily.

So let the rate of depreciation be r

then

85000(1-r)^27.5 = .004

(1-r)^27.5 = .004/85000

[(1-r)^27.5]^(1/27.5) = (.004/85000)^(1/27.5)

1-r = .54144

r = .45856

so it depreciates at a rate of 45.856% per year

for a) change the % to a fraction

for b) take 45.856% of 85000

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