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

$49,278.25
$49,278.25

$12,789.15
$12,789.15

$10,870.78
$10,870.78

$9240.16

Answer 1

To find the value of the car after five years, we can use the formula for exponential decay. The value of the car after each year can be calculated using:

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

In this case, the initial value of the car is $24,500, the depreciation rate is 15% (which as a decimal is 0.15), and \( n = 5 \).

Now, let's calculate it:

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

Calculating \( (1 - 0.15) \):

\[ 1 - 0.15 = 0.85 \]

Now, raise 0.85 to the power of 5:

\[ 0.85^5 \approx 0.4437 \]

Now multiply this by the initial value:

\[ \text{Value after 5 years} = 24,500 \times 0.4437 \approx 10,871.15 \]

Rounding this to two decimal points, we find:

\[ \text{Value after 5 years} \approx 10,870.78 \]

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

Therefore, the correct response is:

$10,870.78