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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?

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?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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.
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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