To calculate the value of a machine that depreciates by one fourth of its value each year, we can use the following method:
- Initial value: $570,000
- 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.