Every year that a car is on the road it loses value. If a car loses 15 percent of its value each year and its beginning value is $24,500, what will the value of the car be after five years?(1 point) Responses $12,789.15 $12,789.15 $10,870.78 $10,870.78 $49,278.25 $49,278.25 $9240.16

Answer 1

To calculate the value of the car after five years with a depreciation rate of 15% per year, we can use the formula:

\[ \text{Value after } n \text{ years} = \text{Initial Value} \times (1 - \text{Depreciation Rate})^n \]

Given:

• Initial Value = $24,500
• Depreciation Rate = 15% = 0.15
• n = 5 years

We substitute the values into the formula:

\[ \text{Value after 5 years} = 24,500 \times (1 - 0.15)^5 \]

Calculating \( (1 - 0.15) \):

\[ 1 - 0.15 = 0.85 \]

Now calculate \( 0.85^5 \):

\[ 0.85^5 \approx 0.4437 \]

Now find the value after 5 years:

\[ \text{Value after 5 years} = 24,500 \times 0.4437 \approx 10,870.78 \]

So, the value of the car after five years is approximately $10,870.78.

Thus, the correct response is:

$10,870.78