To calculate the value of the car after 11 years with an annual depreciation rate of 11%, we can use the formula for exponential decay:
\[ V = P \times (1 - r)^t \]
where:
- \( V \) is the future value of the car,
- \( P \) is the original purchase price,
- \( r \) is the rate of depreciation (as a decimal),
- \( t \) is the time in years.
In this case:
- \( P = 20700 \) dollars,
- \( r = 0.11 \),
- \( t = 11 \).
Now, we can substitute these values into the formula:
\[ V = 20700 \times (1 - 0.11)^{11} \] \[ V = 20700 \times (0.89)^{11} \]
Next, we need to calculate \( (0.89)^{11} \):
\[ (0.89)^{11} \approx 0.305 \]
Now, we can find the future value:
\[ V \approx 20700 \times 0.305 \] \[ V \approx 6313.50 \]
Thus, the value of the car after 11 years is approximately 6313.50 dollars.
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