math word problem

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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 -

    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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