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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

$49,278.25
$49,278.25

$9240.16
$9240.16

$12,789.15
$12,789.15

$10,870.78
$10,870.78
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Answer 1

To calculate the value of the car after five years, we can use the formula for the value of a car that depreciates by a certain percentage each year. Here, the formula is:

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

where:

• \( V \) is the value of the car after time \( t \),
• \( P \) is the initial value of the car,
• \( r \) is the rate of depreciation (as a decimal),
• \( t \) is the number of years.

In this case:

• \( P = 24,500 \),
• \( r = 0.15 \) (15% as a decimal),
• \( t = 5 \).

Now, substituting the values into the formula:

\[ V = 24,500(1 - 0.15)^5 \] \[ V = 24,500(0.85)^5 \]

Calculating \( (0.85)^5 \):

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

Now, substituting this back into the earlier equation:

\[ V \approx 24,500 \times 0.4437 \] \[ V \approx 10,870.78 \]

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

The correct response is: $10,870.78.