A new car is purchased for 16200 dollars. The value of the car depreciates at \( 14.25 \% \) per year. What will the value of the car be, to the nearest cent, after 6 years?

To find the value of the car after 6 years, you can use the formula for depreciation: \[ V = P \times (1 - r)^t \] Where: - \( V \) is the future value of the car, - \( P \) is the initial price (16200 dollars), - \( r \) is the depreciation rate (14.25%, or 0.1425 as a decimal), - \( t \) is the number of years (6). Plugging in the numbers: \[ V = 16200 \times (1 - 0.1425)^6 \] Calculating it step by step: 1. Calculate \( 1 - 0.1425 = 0.8575 \). 2. Raise \( 0.8575 \) to the power of 6, which is approximately \( 0.517949 \). 3. Multiply \( 16200 \) by \( 0.517949 \): \[ V \approx 16200 \times 0.517949 \approx 8396.75 \] So, the value of the car after 6 years will be approximately **$8396.75**.