A vehicle is purchased for $45000. If the vehicle depreciates (loses value) at a rate of 20 percent per year, determine the value of the vehicle after 6 years. Round answer to the nearest cent. $
A vehicle is purchased for $45000. If the vehicle depreciates (loses value) at a rate of 20 percent per year, determine the value of the vehicle after 6 years. Round answer to the nearest cent. $
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem Statement:**
A vehicle is purchased for $45,000. If the vehicle depreciates (loses value) at a rate of 20 percent per year, determine the value of the vehicle after 6 years. Round your answer to the nearest cent.
**Solution:**
To solve this problem, you will use the formula for depreciation:
\[ \text{Future Value} = \text{Present Value} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}} \]
Given:
- Present Value = $45,000
- Depreciation Rate = 20% = 0.20
- Number of Years = 6
**Step-by-Step Calculation:**
1. Substitute the values into the equation:
\[ \text{Future Value} = 45000 \times (1 - 0.20)^6 \]
2. Calculate \(1 - 0.20 = 0.80\).
3. Raise 0.80 to the power of 6:
\[ 0.80^6 = 0.262144 \]
4. Multiply by the present value:
\[ 45000 \times 0.262144 = 11796.48 \]
The value of the vehicle after 6 years is approximately **$11,796.48**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ba0c8e6-85b4-498d-be15-eb5646d0aebd%2F0b3d4fd5-f145-4b05-a643-44df03378929%2F767kgaz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A vehicle is purchased for $45,000. If the vehicle depreciates (loses value) at a rate of 20 percent per year, determine the value of the vehicle after 6 years. Round your answer to the nearest cent.
**Solution:**
To solve this problem, you will use the formula for depreciation:
\[ \text{Future Value} = \text{Present Value} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}} \]
Given:
- Present Value = $45,000
- Depreciation Rate = 20% = 0.20
- Number of Years = 6
**Step-by-Step Calculation:**
1. Substitute the values into the equation:
\[ \text{Future Value} = 45000 \times (1 - 0.20)^6 \]
2. Calculate \(1 - 0.20 = 0.80\).
3. Raise 0.80 to the power of 6:
\[ 0.80^6 = 0.262144 \]
4. Multiply by the present value:
\[ 45000 \times 0.262144 = 11796.48 \]
The value of the vehicle after 6 years is approximately **$11,796.48**.
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