The scrap value of a machine at the end of its useful life is given by ​S(n)equals​C(1minus​r)Superscript n​, where C is the original​ cost, n is the useful life of the machine in​ years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine.
Original​ cost, ​$66 comma 000​; ​life, 9 ​years; annual rate of value​ lost, 15​%

The scrap value formula is given by:

\[
S(n) = C(1 - r)^n
\]

Where:
- $ C $ is the original cost,
- $ r $ is the annual percentage of value lost (in decimal form),
- $ n $ is the useful life of the machine in years.

Let's plug in the values:
- $ C = 66,000 $,
- $ r = 15\% = 0.15 $,
- $ n = 9 $ years.

Now calculate:

\[
S(9) = 66,000 \times (1 - 0.15)^9
\]

Let's compute this.The scrap value of the machine after 9 years is approximately **$15,286.72**.

Do you want more details or have any questions?

Here are 5 related questions:
1. How does the scrap value change if the annual depreciation rate increases?
2. What would the scrap value be after 5 years instead of 9?
3. How does the formula behave if there is no annual depreciation (i.e., $ r = 0 $)?
4. Can you calculate the original cost if you know the scrap value and useful life?
5. How does compound depreciation differ from linear depreciation?

**Tip**: Always express the rate of depreciation as a decimal when using formulas (e.g., 15% as 0.15).

The scrap value of a machine at the end of its useful life is given by ​S(n) = ​C(1 − r)^n​, where C is the original​ cost, n is the useful life of the machine in​ years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine. Original​ cost, ​$66,000​; ​life, 9 ​years; annual rate of value​ lost, 15​%.

Discover how to calculate the scrap value of a machine using the exponential decay formula. In this example, the machine has an original cost of $66,000, a useful life of 9 years, and an annual depreciation rate of 15%. The final scrap value is approximately $15,286.72.

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