Q60. - Algebra 2

Question

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

Step-by-Step Solution

Answer

The average annual rate of depreciation is $800.

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:      

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_4=a_1+(4-1)d\\ 600=3000+3d\\ 3d=600-3000\\ 3d=-2400\\ d=-800\end{array}$

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.