Poppy has purchased a $45000 motor vehicle for her business. It depreciates at a rate of 18 % per annum. Find the value of the motor vehicle after 10 years using the declining balance depreciation.

To find the value of the motor vehicle after 10 years using the declining balance depreciation method, we can use the following formula:

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

Where:
- $ V $ is the value of the motor vehicle after $ t $ years.
- $ P $ is the initial purchase price of the motor vehicle.
- $ r $ is the annual depreciation rate (as a decimal).
- $ t $ is the number of years.

Given:
- $ P = 45000 $ dollars
- $ r = 18\% = 0.18 $
- $ t = 10 $ years

Substitute the given values into the formula:

\[
V = 45000 \times (1 - 0.18)^{10}
\]

\[
V = 45000 \times (0.82)^{10}
\]

Now, calculate $ (0.82)^{10} $:

\[
V = 45000 \times 0.16737 \approx 7531.65
\]

So, the value of the motor vehicle after 10 years is approximately **$7,531.65**.

Would you like further details or have any questions? Here are 5 related questions you might find useful:

1. What would be the value of the motor vehicle after 5 years?
2. How does the declining balance depreciation differ from straight-line depreciation?
3. What would be the depreciation rate needed to reduce the vehicle's value to $5,000 in 10 years?
4. How would the value change if the depreciation rate were 20% per annum?
5. Can you calculate the total depreciation amount over 10 years?

**Tip:** In declining balance depreciation, the asset depreciates by a fixed percentage of its current value, which means the depreciation amount decreases each year.

Discover how to calculate the value of a $45,000 motor vehicle after 10 years using declining balance depreciation. This problem involves applying the declining balance depreciation formula with a depreciation rate of 18% per annum.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation