To find the scrap value of the machine, we use the given formula:

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

Where:

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

Given:

• Original cost $C = 52,000$ dollars
• Life $n = 6$ years
• Annual rate of value lost $r = 11\% = 0.11$

Now, we can calculate the scrap value $S(6)$:

$S(6) = 52,000 \times (1 - 0.11)^6$

Let's calculate this.The scrap value of the machine after 6 years is approximately $25,843.03 (rounded to the nearest cent).

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the scrap value change if the annual rate of value loss increased to 15%?
2. What would be the scrap value if the machine's life were 10 years instead of 6?
3. How is the formula derived for the scrap value of a machine?
4. How does compound depreciation compare to straight-line depreciation?
5. How would you calculate the original cost if you only knew the scrap value and depreciation rate?

Tip: When dealing with percentages in formulas, always convert the percentage to a decimal by dividing by 100.