Suggested languages for you:

Americas

Europe

Q60.

Expert-verifiedFound in: Page 582

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**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.**

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

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

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

94% of StudySmarter users get better grades.

Sign up for free