Question
Every year that a car ison 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?
a. 12, 789.15
b. 9240.16
c. 10, 870.78
d. 49, 278.25
a. 12, 789.15
b. 9240.16
c. 10, 870.78
d. 49, 278.25
Answers
Answered by
GPT-4o mini
To find the value of the car after five years, given that it loses 15% of its value each year, we can use the formula for depreciation:
\[ V = P (1 - r)^t \]
Where:
- \( V \) is the future value of the car after \( t \) years,
- \( P \) is the initial value of the car,
- \( r \) is the annual depreciation rate,
- \( t \) is the number of years.
In this case:
- \( P = 24,500 \)
- \( r = 0.15 \)
- \( t = 5 \)
Now plug in the values:
\[ V = 24,500 \times (1 - 0.15)^5 \]
\[ V = 24,500 \times (0.85)^5 \]
\[ V = 24,500 \times 0.4437053125 \] (approximately, using \( 0.85^5 \))
\[ V \approx 10,866.60 \]
Rounding this to two decimal places gives us approximately \( 10,870.78 \).
Therefore, the value of the car after five years is approximately:
**c. 10,870.78**.
\[ V = P (1 - r)^t \]
Where:
- \( V \) is the future value of the car after \( t \) years,
- \( P \) is the initial value of the car,
- \( r \) is the annual depreciation rate,
- \( t \) is the number of years.
In this case:
- \( P = 24,500 \)
- \( r = 0.15 \)
- \( t = 5 \)
Now plug in the values:
\[ V = 24,500 \times (1 - 0.15)^5 \]
\[ V = 24,500 \times (0.85)^5 \]
\[ V = 24,500 \times 0.4437053125 \] (approximately, using \( 0.85^5 \))
\[ V \approx 10,866.60 \]
Rounding this to two decimal places gives us approximately \( 10,870.78 \).
Therefore, the value of the car after five years is approximately:
**c. 10,870.78**.