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The value of a certain office machine de- preciates in such a way tha

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The value of a certain office machine de- preciates in such a way tha  [#permalink]

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New post 15 Feb 2018, 23:46
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The value of a certain office machine depreciates in such a way that its value at the end of each year is 4/5 of its value at the beginning of the same year. If the initial value of the machine is $5,000, what is its value at the end of 3 years?

(A) $4,750.25

(B) $4,000.00

(C) $2,560.00

(D) $2,000.00

(E) $640.00

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Re: The value of a certain office machine de- preciates in such a way tha  [#permalink]

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New post 16 Feb 2018, 00:21
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Initial Value= $5000
At the end of 1st year: \(\frac{4}{5}\)*5000= $4000

At the end of 2nd year: 4000*\(\frac{4}{5}\)= $3200

At the end of 3rd year: 3200*\(\frac{4}{5}\)= $2560

OR

5000*\(\frac{4}{5}\)*\(\frac{4}{5}\)*\(\frac{4}{5}\)= $2560

Answer: C.
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Re: The value of a certain office machine de- preciates in such a way tha  [#permalink]

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New post 16 Feb 2018, 00:25
Bunuel wrote:
The value of a certain office machine depreciates in such a way that its value at the end of each year is 4/5 of its value at the beginning of the same year. If the initial value of the machine is $5,000, what is its value at the end of 3 years?

(A) $4,750.25

(B) $4,000.00

(C) $2,560.00

(D) $2,000.00

(E) $640.00


end of 1 year = 4/5 of value

end of 3 years = 4/5 ^ 3 of original


5000 x 4/5 x 4/5 x 4/5

40 x 64

2560

(C) imo
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Re: The value of a certain office machine de- preciates in such a way tha  [#permalink]

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New post 19 Feb 2018, 10:10
5000*64/125 = 40*64 = 2560 (c)
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Re: The value of a certain office machine de- preciates in such a way tha  [#permalink]

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New post 21 Feb 2018, 14:09
Bunuel wrote:
The value of a certain office machine depreciates in such a way that its value at the end of each year is 4/5 of its value at the beginning of the same year. If the initial value of the machine is $5,000, what is its value at the end of 3 years?

(A) $4,750.25

(B) $4,000.00

(C) $2,560.00

(D) $2,000.00

(E) $640.00


After 3 years the value of the machine is:

5,000 x 4/5 x 4/5 x 4/5 = 5 x 10 x 10 x 10 x 4/5 x 4/5 x 4/5 = 40 x 4 x 4 x 4 = 2,560

Answer: C
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Re: The value of a certain office machine de- preciates in such a way tha   [#permalink] 21 Feb 2018, 14:09
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