Every year that a car is on the road it loses value if a car loses 15% of it's value each year and it's beginning value24,500 What will the value of the car be after 5 years

Answer 1

To calculate the value of the car after 5 years with an annual depreciation rate of 15%, we can use the formula for exponential decay:

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

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

Substituting the values into the formula:

\[ \text{Value after 5 years} = 24500 \times (1 - 0.15)^5 \]

Calculating the expression step-by-step:

1. Calculate \( 1 - 0.15 = 0.85 \).
2. Calculate \( 0.85^5 \).

\[ 0.85^5 \approx 0.4437 \]

3. Now calculate the value after 5 years:

\[ \text{Value after 5 years} = 24500 \times 0.4437 \approx 10864.65 \]

Thus, the value of the car after 5 years will be approximately $10,864.65.