A vehicle purchased for $22400 depreciates at a rate of 8% per year.

Determine the approximate value of the vehicle 15 years after purchase.

The depreciation of a vehicle can be calculated using the formula for exponential decay:

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

where:
- $ V $ is the value of the vehicle after $ t $ years,
- $ P $ is the initial value (purchase price),
- $ r $ is the annual depreciation rate,
- $ t $ is the number of years.

Given:
- $ P = 22400 $,
- $ r = 0.08 $ (8% depreciation rate),
- $ t = 15 $.

Substitute these values into the formula:

\[
V = 22400 \times (1 - 0.08)^{15}
\]
\[
V = 22400 \times (0.92)^{15}
\]

Now we calculate $ (0.92)^{15} $:

1. $ 0.92^{15} \approx 0.275 $
2. Multiply by the initial value:
   \[
   V \approx 22400 \times 0.275
   \]
   \[
   V \approx 6160
   \]

So, the approximate value of the vehicle 15 years after purchase is **$6,160**.

Would you like further details or have questions?

---

### Related Questions
1. How does the depreciation formula change with a different percentage rate?
2. What would be the vehicle's value after 20 years?
3. How much value is lost in the first 10 years?
4. What if the vehicle appreciated in value at a rate of 8% instead?
5. How would monthly depreciation calculations differ?

### Tip
Depreciation calculations help estimate the future worth of an asset and are often used in financial planning and tax calculations.

A vehicle purchased for $22400 depreciates at a rate of 8% per year. Determine the approximate value of the vehicle 15 years after purchase.

Discover how to calculate vehicle depreciation with an 8% annual rate. Learn to estimate the future value of a $22,400 car, reduced over 15 years, using exponential decay. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation