ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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You just accepted an offer from XYZ Petrochemical Company in Louisiana. As a sign up bonus, the XYZ will deposit $10,000 in a retirement account for you which generates 12% return annually. In addition, the company deposits $5,000 every year in the same account, if you stays with XYZ. How much money will be accumulated in this account if you decide to retire 40 years from now?
### Investment Opportunity with XYZ Petrochemical Company

**Scenario:**
You have just accepted an offer from XYZ Petrochemical Company in Louisiana. As part of your signing bonus, XYZ will deposit $10,000 into a retirement account for you. This account generates a 12% annual return. 

Additionally, the company commits to depositing an extra $5,000 every year into the same account, contingent on your continuous service with XYZ. 

**Question:**
How much money will accumulate in the retirement account if you decide to retire 40 years from now?

**Solution Approach:**
To determine the total accumulated amount in the retirement account, we need to consider both the initial lump-sum investment and the annual contributions, compounded annually. 

**Key Variables:**
- Initial Deposit (P): $10,000
- Annual Contribution (A): $5,000
- Annual Return (r): 12%
- Number of Years (n): 40

**Steps to Calculate:**
1. **Initial Deposit Growth:**
   - Future Value of Initial Deposit = P(1 + r)^n
   
2. **Annual Contributions Growth:**
   - Future Value of Annual Contributions = \( \sum_{k=1}^{n} A(1 + r)^{n-k} \)

By solving these equations step-by-step or using financial calculator tools, one can determine the total amount accumulated over the 40-year period.

**Educational Insight:**
Understanding compound interest and regular contributions can help in making informed financial decisions that secure your future.
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Transcribed Image Text:### Investment Opportunity with XYZ Petrochemical Company **Scenario:** You have just accepted an offer from XYZ Petrochemical Company in Louisiana. As part of your signing bonus, XYZ will deposit $10,000 into a retirement account for you. This account generates a 12% annual return. Additionally, the company commits to depositing an extra $5,000 every year into the same account, contingent on your continuous service with XYZ. **Question:** How much money will accumulate in the retirement account if you decide to retire 40 years from now? **Solution Approach:** To determine the total accumulated amount in the retirement account, we need to consider both the initial lump-sum investment and the annual contributions, compounded annually. **Key Variables:** - Initial Deposit (P): $10,000 - Annual Contribution (A): $5,000 - Annual Return (r): 12% - Number of Years (n): 40 **Steps to Calculate:** 1. **Initial Deposit Growth:** - Future Value of Initial Deposit = P(1 + r)^n 2. **Annual Contributions Growth:** - Future Value of Annual Contributions = \( \sum_{k=1}^{n} A(1 + r)^{n-k} \) By solving these equations step-by-step or using financial calculator tools, one can determine the total amount accumulated over the 40-year period. **Educational Insight:** Understanding compound interest and regular contributions can help in making informed financial decisions that secure your future.
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