Question

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

$9240.16
$9240.16

$49,278.25

Answer 1

To calculate the value of the car after five years given that it loses 15% of its value each year, we can use the formula for exponential decay:

\[
V = P(1 - r)^t
\]

where:
- \( V \) is the future value of the car,
- \( P \) is the initial value of the car ($24,500),
- \( r \) is the rate of depreciation (15% or 0.15),
- \( t \) is the number of years (5).

Plugging in the values:

\[
V = 24500(1 - 0.15)^5
\]
\[
V = 24500(0.85)^5
\]
Calculating \( (0.85)^5 \):

\[
(0.85)^5 \approx 0.4437
\]

Now multiply by the initial value:

\[
V \approx 24500 \times 0.4437 \approx 10870.78
\]

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

The correct response is:

**$10,870.78**