Question

A copy machine depreciates at the rate of 15% each year. If the original cost of the copy machine was $20,000, what is the approximate value of the machine at the end of 3 years?

Responses

$14,450
$14,450

$14,000
$14,000

$12,283
$12,283

$11,000
$11,000

Answer 1

To calculate the approximate value of the copy machine at the end of 3 years with a depreciation rate of 15% per year, you can use the formula for exponential decay:

\[
\text{Value} = \text{Original Cost} \times (1 - \text{Depreciation Rate})^{\text{Years}}
\]

Given:
- Original Cost = $20,000
- Depreciation Rate = 0.15 (15%)
- Years = 3

Plugging in the values:

\[
\text{Value} = 20000 \times (1 - 0.15)^3
\]
\[
= 20000 \times (0.85)^3
\]
\[
= 20000 \times 0.614125
\]
\[
\approx 12282.50
\]

Thus, the approximate value of the machine at the end of 3 years is about **$12,283**.

The correct answer is **$12,283**.