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Chapter 11: Q60. (page 582)

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

Short Answer

Expert verified

The average annual rate of depreciation is$800.

Step by step solution

01

Step 1. Given Information.

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

02

Step 2. Calculation.

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

The nth term of an arithmetic sequence is given by an=a1+(n鈭�1)d.

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

The first term is a1=3000a1=3000

And the fifth term is a4=600

Plugging the values in the formula:

an=a1+(n鈭�1)da4=a1+(4鈭�1)d600=3000+3d3d=600鈭�30003d=鈭�2400d=鈭�800

Hence the common difference is -800.

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

03

Step 3. Conclusion.

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

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