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Q60.

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Algebra 2

Found in: Page 582

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Suppose a computer that costs $3000 new is only worth $600 after 3 years. What is the average annual rate of depreciation?

The average annual rate of depreciation is $800.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given a computer that costs $3000 new is only worth $600 after 3 years.

Step 2. Calculation.

The statement as an arithmetic sequence can be written as: $3000, ? , ? , $600.

The n^th term of an arithmetic sequence is given by $a_{n} = a_{1} + (n - 1) d$ .

Since there are two arithmetic means between $3000 and $600,

The first term is $a_{1} = 3000$ $a_{1} = 3000$

And the fifth term is $a_{4} = 600$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{4} = a_{1} + (4 - 1) d \\ 600 = 3000 + 3 d \\ 3 d = 600 - 3000 \\ 3 d = - 2400 \\ d = - 800 \end{array}$

Hence the common difference is -800.

i.e. every year the value is reduced by $800

Step 3. Conclusion.

Hence, the average annual rate of depreciation is $800.

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