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)

Question

Responses

$12,789.15
$12,789.15

$49,278.25
$49,278.25

$10,870.78
$10,870.78

$9240.16

Answer 1

To determine the value of the car after five years when it loses 15% of its value each year, we can use the formula for depreciation based on percentage loss:

\[ \text{Value after } n \text{ years} = \text{Initial value} \times (1 - \text{depreciation rate})^n \]

In this case:

• The initial value of the car = $24,500
• The depreciation rate = 15% = 0.15
• Number of years (n) = 5

Plugging in the values:

\[ \text{Value after 5 years} = 24500 \times (1 - 0.15)^5 \]

Calculating \(1 - 0.15 = 0.85\):

\[ \text{Value after 5 years} = 24500 \times (0.85)^5 \]

Now calculating \( (0.85)^5 \):

\[ (0.85)^5 \approx 0.4437 \quad \text{(approximately)} \]

Now multiply this by the initial value:

\[ \text{Value after 5 years} \approx 24500 \times 0.4437 \approx 10870.78 \]

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

The correct response is: $10,870.78