A new car is purchased for 20700 dollars. The value of the car depreciates at 11% per year. What will the value of the car be, to the nearest cent, after 11 years?
Question
A new car is purchased for 20700 dollars. The value of the car depreciates at 11% per year. What will the value of the car be, to the nearest cent, after 11 years?
Solution
To solve this problem, we will use the formula for exponential decay, which is:
V = P * (1 - r)^t
where:
- V is the final value of the car
- P is the initial value of the car
- r is the rate of depreciation
- t is the time in years
Given in the problem: P = $20,700 r = 11% or 0.11 t = 11 years
Substituting these values into the formula, we get:
V = 20700 * (1 - 0.11)^11
Now, calculate the value inside the parentheses:
1 - 0.11 = 0.89
So, the formula becomes:
V = 20700 * (0.89)^11
Now, calculate the value of (0.89)^11, which is approximately 0.31381059609.
So, the formula becomes:
V = 20700 * 0.31381059609
Finally, calculate the value of 20700 * 0.31381059609, which is approximately $6496.88.
So, the value of the car after 11 years, to the nearest cent, will be $6496.88.
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