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The problem asks to determine the approximate value of a vehicle purchased for $32,500 that depreciates at a constant rate of 7% per year, 11 years after the purchase. 

This situation can be modeled using the formula for exponential depreciation:

\[
V = P(1 - r)^t
\]

Where:
- $ V $ is the value of the vehicle after $ t $ years.
- $ P $ is the initial value of the vehicle ($32,500).
- $ r $ is the depreciation rate (7% or 0.07).
- $ t $ is the time in years (11 years in this case).

Substituting the values into the formula:

\[
V = 32,500 \times (1 - 0.07)^{11}
\]

\[
V = 32,500 \times (0.93)^{11}
\]

Now, calculating this:

\[
V \approx 32,500 \times 0.422744
\]
\[
V \approx 13,748.18
\]

Rounding to the nearest whole dollar:

\[
V \approx 13,748
\]

So, the approximate value of the vehicle after 11 years is **$13,748**.

Would you like more details on any specific part of the solution?

Here are 5 questions to deepen your understanding:
1. How would the value change if the depreciation rate were 5% instead of 7%?
2. What would the value be if the depreciation continued for 15 years?
3. How does compounding depreciation differ from simple depreciation?
4. Could this formula be applied to items other than vehicles, and how would that affect the assumptions?
5. What would happen to the car's value after 20 years of depreciation?

**Tip:** Depreciation calculations can be critical when deciding on large purchases, as they help estimate long-term value!

A vehicle purchased for $32,500 depreciates at a constant rate of 7%. Determine the approximate value of the vehicle 11 years after purchase. Round to the nearest whole dollar.

Calculate the value of a vehicle purchased for $32,500 after 11 years of depreciation at a constant rate of 7%. Learn how to apply the exponential depreciation formula to find that the car is worth approximately $13,748.

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