My car depreciates 8.4% per year. Its original value was $20,000. Find its value 8 years later. Round to the dollar $
My car depreciates 8.4% per year. Its original value was $20,000. Find its value 8 years later. Round to the dollar $
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Depreciation Calculation Example**
**Problem Statement:**
"My car depreciates 8.4% per year. Its original value was $20,000. Find its value 8 years later. Round to the dollar."
**Solution Approach:**
To calculate the depreciated value of an asset, the formula to use is:
\[ V = P \times (1 - r)^t \]
Where:
- \( V \) is the future value of the car after depreciation.
- \( P \) is the original value of the car ($20,000).
- \( r \) is the annual depreciation rate (8.4% or 0.084).
- \( t \) is the number of years (8 years).
**Calculation Steps:**
1. Convert the percentage depreciation to a decimal:
- 8.4% = 0.084
2. Substitute the values into the formula:
\[ V = 20000 \times (1 - 0.084)^8 \]
3. Calculate the depreciation for 8 years:
\[ V = 20000 \times (0.916)^8 \]
4. Perform the calculations to find the future value:
\[ V \approx 20000 \times 0.543 \]
\[ V \approx 10860 \]
5. Round the result to the nearest dollar.
**Final Answer:**
- The value of the car after 8 years is approximately **$10,860**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa75b3e4-cb9e-42f8-9b91-2e6340659e7d%2F8ed19bea-59d1-4fe1-8310-8451f0c0634f%2Ffbvv1iv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Depreciation Calculation Example**
**Problem Statement:**
"My car depreciates 8.4% per year. Its original value was $20,000. Find its value 8 years later. Round to the dollar."
**Solution Approach:**
To calculate the depreciated value of an asset, the formula to use is:
\[ V = P \times (1 - r)^t \]
Where:
- \( V \) is the future value of the car after depreciation.
- \( P \) is the original value of the car ($20,000).
- \( r \) is the annual depreciation rate (8.4% or 0.084).
- \( t \) is the number of years (8 years).
**Calculation Steps:**
1. Convert the percentage depreciation to a decimal:
- 8.4% = 0.084
2. Substitute the values into the formula:
\[ V = 20000 \times (1 - 0.084)^8 \]
3. Calculate the depreciation for 8 years:
\[ V = 20000 \times (0.916)^8 \]
4. Perform the calculations to find the future value:
\[ V \approx 20000 \times 0.543 \]
\[ V \approx 10860 \]
5. Round the result to the nearest dollar.
**Final Answer:**
- The value of the car after 8 years is approximately **$10,860**.
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