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

$10,870.78
$10,870.78

$9240.16
$9240.16

$12,789.15
$12,789.15

$49,278.25

Answer 1

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

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

Where:

• \( V \) = future value of the car
• \( P \) = initial value of the car ($24,500)
• \( r \) = rate of depreciation (0.15)
• \( t \) = number of years (5)

Plugging in the values:

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

\[ V = 24500(0.85)^5 \]

Now, calculate \( (0.85)^5 \):

\[ (0.85)^5 \approx 0.443705 \]

Now, calculate \( V \):

\[ V \approx 24500 \times 0.443705 \approx 10870.78 \]

Thus, the value of the car after five years would be approximately $10,870.78. Therefore, the correct response is:

$10,870.78