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

The owner of a

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 11:14pm
The 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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