A new car is purchased for 18000 dollars. The value of the car depreciates at 13.5% per year. What will the value of the car be, to the nearest cent, after 14 years?

To calculate the value of the car after 14 years, we need to apply the annual depreciation rate of 13.5% to the initial value of the car for each year.

Here are the steps:

1. Convert the depreciation rate from a percentage to a decimal by dividing by 100. So, 13.5% becomes 0.135.

2. Subtract the depreciation rate from 1 to find the annual depreciation factor. This gives us 1 - 0.135 = 0.865. This means that each year, the car retains 86.5% of its value from the previous year.

3. Raise the annual depreciation factor to the power of the number of years to find the total depreciation factor. This gives us 0.865^14 = 0.112.

4. Multiply the initial value of the car by the total depreciation factor to find the value of the car after 14 years. This gives us $18,000 * 0.112 =$2,016.

So, the value of the car will be approximately $2,016 after 14 years.