A new car is purchased for 17600 dollars. The value of the car depreciates at 11.75% per year. What will the value of the car be, to the nearest cent, after 11 years?
Question
A new car is purchased for 17600 dollars. The value of the car depreciates at 11.75% per year. What will the value of the car be, to the nearest cent, after 11 years?
Solution
To calculate the value of the car after 11 years, we need to apply the annual depreciation rate for each year.
Step 1: Convert the depreciation rate from a percentage to a decimal. 11.75% = 0.1175
Step 2: Subtract the depreciation rate from 1. 1 - 0.1175 = 0.8825
This means that each year, the car retains 88.25% of its value from the previous year.
Step 3: Apply the depreciation for 11 years. To do this, we raise the yearly depreciation rate to the power of the number of years. 0.8825^11 = 0.3133 (rounded to four decimal places)
Step 4: Multiply the original value of the car by the depreciated value. 5514.08
So, the value of the car after 11 years, to the nearest cent, will be approximately $5514.08.
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