To find the scrap value of the machine after 6 years, we can use the given formula:

$S(n) = C(1 - r)^n$

Where:

• $C$ is the original cost of the machine.
• $r$ is the annual rate of value lost (expressed as a decimal).
• $n$ is the useful life of the machine in years.

Given:

• $C = 46,000$ dollars
• $n = 6$ years
• $r = 13\%$ or 0.13 (as a decimal)

Now, plug these values into the formula:

$S(6) = 46,000 \times (1 - 0.13)^6$

First, calculate $1 - 0.13$:

$1 - 0.13 = 0.87$

Next, calculate $0.87^6$:

$0.87^6 \approx 0.522$

Finally, multiply by the original cost $C$:

$S(6) = 46,000 \times 0.522 \approx 24,012$

So, the scrap value of the machine after 6 years is approximately $24,012.

Would you like more details or have any questions?

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Here are 5 related questions to explore further:

1. How would the scrap value change if the annual rate of value lost was 10% instead of 13%?
2. What is the impact on the scrap value if the useful life is extended to 8 years?
3. Can you calculate the scrap value if the original cost was $50,000 and the annual rate of value lost was 15%?
4. How would the formula change if the value loss was not constant but increased each year?
5. What is the difference in scrap value between a 5-year and a 6-year useful life with the same rate of value loss?

Tip: Remember to always convert percentages to decimals when using them in formulas. For example, 13% becomes 0.13.