A new car is purchased for 17900 dollars. The value of the car depreciates at 13% per year. What will the value of the car be, to the nearest cent, after 7 years?

To determine the value of the car after 7 years, given that it depreciates at 13% per year, we can use the formula for exponential depreciation:

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

Where:
- $ V $ is the value of the car after $ t $ years,
- $ P $ is the initial value of the car,
- $ r $ is the annual depreciation rate (expressed as a decimal),
- $ t $ is the number of years.

Given:
- $ P = 17900 $ dollars,
- $ r = 13\% = 0.13 $,
- $ t = 7 $ years.

Substitute the values into the formula:

\[
V = 17900 \times (1 - 0.13)^7
\]

\[
V = 17900 \times (0.87)^7
\]

Let's calculate the value.The value of the car after 7 years will be approximately $6,752.86.

Would you like more details or have any further questions?

Here are some related questions you might find interesting:
1. What is the formula for compound interest and how does it compare to depreciation?
2. How would the value change if the depreciation rate was 10% instead of 13%?
3. How long would it take for the car's value to drop below $5,000 at the same depreciation rate?
4. What is the future value of an investment that grows at a rate of 13% per year?
5. How does exponential depreciation differ from linear depreciation?
6. What would the car's value be after 10 years instead of 7 years?
7. How can inflation affect the real depreciation rate of the car?
8. How do depreciation rates typically vary across different types of vehicles?

**Tip:** Always double-check the decimal conversion of percentages when working with financial formulas to avoid errors in calculations.

Discover how to calculate the value of a car after 7 years with a depreciation rate of 13% per year. Use the exponential depreciation formula V = P * (1 - r)^t. Start with an initial value of $17,900. Suitable for financial math students in Grades 9-12.

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