math word problem
posted by chandice .
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?
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
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