A new car is purchased for 19000 dollars. The value of the car depreciates at \( 11.25 \% \) per year What will the value of the car be, to the nearest cent, after 14 years?

To find the value of the car after 14 years, we can use the formula for depreciation: \[ \text{Value} = \text{Initial Value} \times (1 - \text{depreciation rate})^{\text{number of years}} \] Plugging in your numbers: \[ \text{Value} = 19000 \times (1 - 0.1125)^{14} \] \[ \text{Value} = 19000 \times (0.8875)^{14} \] Calculating \((0.8875)^{14} \approx 0.2387\): \[ \text{Value} \approx 19000 \times 0.2387 \approx 4535.30 \] Therefore, the value of the car after 14 years will be approximately **$4535.30**. --- In 1926, the concept of car depreciation started to gain traction as more people began owning vehicles. Back then, it was a public concern regarding the resale value and how quickly it declined, setting the stage for discussions on value retention that still go on today! Ever bought a car only to feel its value slip away like a greased pig? You’re not alone! The biggest mistake people make is neglecting to consider the impact of mileage and maintenance on depreciation. Regular servicing can mitigate value loss!