A certain car costs `$20,000.` If the car loses 15 percent of its value each year, approximately how much will the car be worth after 5 years ?

Options

A. `$5,000`
B. `$8,900`
C. `$11, 200`
D. `$15, 000`

Answer

To find the worth of the car after 5 years, we will use the formula for depreciation. The car loses 15% of its value each year, so we can calculate its worth after 5 years step by step.

### Step-by-Step Solution:

1. **Identify the Initial Value and Depreciation Rate:**
- The initial cost of the car (C) is $20,000.
- The depreciation rate (D) is 15%.

2. **Convert the Depreciation Rate to Decimal:**
- To use the depreciation rate in calculations, convert it from a percentage to a decimal:
\[ D = \frac{15}{100} = 0.15 \]

3. **Calculate the Remaining Value After One Year:**
- The value of the car after one year can be calculated using the formula:
\[ W = C \times (1 - D) \]
- Substituting the values:
\[ W = 20000 \times (1 - 0.15) = 20000 \times 0.85 = 17000 \]

4. **Repeat for Each Subsequent Year:**
- We can apply the same formula for each subsequent year. However, it is more efficient to use the formula for multiple years:
\[ W = C \times (1 - D)^T \]
- Here, T is the number of years (5 years in this case).

5. **Substitute the Values into the Formula:**
- Now substituting the values into the formula:
\[ W = 20000 \times (1 - 0.15)^5 \]
- This simplifies to:
\[ W = 20000 \times (0.85)^5 \]

6. **Calculate \( (0.85)^5 \):**
- Calculate \( (0.85)^5 \):
\[ (0.85)^5 \approx 0.4437 \]

7. **Final Calculation:**
- Now calculate the worth after 5 years:
\[ W \approx 20000 \times 0.4437 \approx 8874 \]

8. **Conclusion:**
- The approximate worth of the car after 5 years is $8,874.

### Final Answer:
The car will be worth approximately **$8,874** after 5 years.