Question

Question content area left
Part 1
A machine depreciates by one fourth
of its value each year. If it costs​ $570 comma 000 ​new, what is its value after 5 ​years?
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Question content area right
Part 1
After 5 years the machine is worth ​$
  
enter your response here.
​(Simplify your answer. Round to the nearest dollar if​ needed.)

Answer 1

round to the nearest dollar if needed

Answer 2

To calculate the value of a machine that depreciates by one fourth of its value each year, we can use the following method:

1. **Initial value:** $570,000
2. **Depreciation rate:** 25% (which is one fourth)

Each year, the value of the machine becomes 75% of its value from the previous year, because it loses 25% of its value.

This can be expressed mathematically as:

\[
\text{Value after } n \text{ years} = \text{Initial value} \times (0.75)^n
\]

In this case, \( n = 5 \) years:

\[
\text{Value after 5 years} = 570,000 \times (0.75)^5
\]

Now, we calculate \( (0.75)^5 \):

\[
(0.75)^5 = 0.2373046875
\]

Now, multiply this value by the initial cost:

\[
\text{Value after 5 years} = 570,000 \times 0.2373046875 \approx 135,153.67
\]

Rounding to the nearest dollar, the machine's value after 5 years is:

\[
\text{Value after 5 years} \approx 135,154
\]

Thus, the value of the machine after 5 years is **$135,154**.

Answer 3

The calculated value of the machine after 5 years is approximately \( 135,153.67 \). When rounded to the nearest dollar, this becomes:

\[
\text{Value after 5 years} \approx 135,154
\]

Therefore, the value of the machine after 5 years, rounded to the nearest dollar, is **$135,154**.