A new car is purchased for 20000 dollars. The value of the car depreciates at 12.5% per year. What will the value of the car be, to the nearest cent, after 11 years?
Question
A new car is purchased for 20000 dollars. The value of the car depreciates at 12.5% per year. What will the value of the car be, to the nearest cent, after 11 years?
Solution
To solve this problem, we need to understand that the car's value is decreasing by 12.5% each year. This is a compound depreciation problem.
Here are the steps to solve it:
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Convert the depreciation rate from a percentage to a decimal. 12.5% becomes 0.125.
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Subtract the depreciation rate from 1. This gives us the annual depreciation factor. So, 1 - 0.125 = 0.875.
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Raise the annual depreciation factor to the power of the number of years. In this case, it's 11 years. So, 0.875^11 = 0.284.
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Multiply the initial value of the car by the result from step 3. So, 5,680.
So, to the nearest cent, the value of the car after 11 years will be $5,680.
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