A new car is purchased for 16500 dollars. The value of the car depreciates at 5.75% per year. What will the value of the car be, to the nearest cent, after 5 years?

To calculate the depreciated value of the car after 5 years, 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 ($16,500),
- $r$ is the depreciation rate per year (5.75%, or 0.0575),
- $t$ is the number of years (5 years).

Now, let's plug in the values and calculate the car's value after 5 years.

\[
V = 16500 \times (1 - 0.0575)^5
\]

\[
V = 16500 \times (0.9425)^5
\] 

Let me calculate that for you.The value of the car after 5 years, depreciating at a rate of 5.75% per year, will be approximately **$12,271.30**.

Would you like further details or have any questions?

Here are five related questions you might find interesting:
1. What will the car's value be after 10 years with the same depreciation rate?
2. How does changing the depreciation rate affect the car's value over time?
3. How much value does the car lose after 3 years?
4. How long would it take for the car's value to be halved at this depreciation rate?
5. What would the value be after 5 years if the depreciation rate were 6.5%?

**Tip:** Depreciation affects different assets at varying rates, so understanding exponential depreciation helps in evaluating investments!

Calculate the depreciated value of a car originally worth $16,500, after 5 years at a depreciation rate of 5.75% per year. This problem involves exponential decay and is suitable for students in Grades 9-12.

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