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3,200 2,800 2,400 2,000 Years i= 8% / yr 5th Birthday 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 A = ?

3,200 2,800 2,400 2,000 Years i= 8% / yr 5th Birthday 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 A = ?

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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**Transcription for Educational Website** Title: Calculating Annual Deposits and Withdrawals in a Savings Account **Scenario:** Suppose that the parents of a young child decide to make annual deposits into a savings account, with the first deposit being made on the child's fifth birthday and the last deposit being made on the 15th birthday. Then, starting on the child's 18th birthday, the withdrawals as shown on the diagram below will be made. If the effective annual interest rate is 8% during this period of time, what are the annual deposits in years 5 through 15? Use a uniform gradient amount (G) in your solution. **Analysis:** - **Deposits:** Annual contributions occur from ages 5 to 15. - **Period of Interest:** Explores the effective annual interest of 8%. - **Withdrawals:** Begin on the child’s 18th birthday. **Explanation:** To solve for the annual deposits, consider the balance growth due to compounded interest and the uniform increase in deposits. A uniform gradient amount (G) suggests a consistent incremental value added to each subsequent deposit. Note: A detailed diagram illustrating the withdrawals would provide specific values and timings for clarity.
Transcribed Image Text:**Transcription for Educational Website** Title: Calculating Annual Deposits and Withdrawals in a Savings Account **Scenario:** Suppose that the parents of a young child decide to make annual deposits into a savings account, with the first deposit being made on the child's fifth birthday and the last deposit being made on the 15th birthday. Then, starting on the child's 18th birthday, the withdrawals as shown on the diagram below will be made. If the effective annual interest rate is 8% during this period of time, what are the annual deposits in years 5 through 15? Use a uniform gradient amount (G) in your solution. **Analysis:** - **Deposits:** Annual contributions occur from ages 5 to 15. - **Period of Interest:** Explores the effective annual interest of 8%. - **Withdrawals:** Begin on the child’s 18th birthday. **Explanation:** To solve for the annual deposits, consider the balance growth due to compounded interest and the uniform increase in deposits. A uniform gradient amount (G) suggests a consistent incremental value added to each subsequent deposit. Note: A detailed diagram illustrating the withdrawals would provide specific values and timings for clarity.
The diagram illustrates a timeline of annual financial growth, starting from the 5th birthday to the 21st birthday, with an interest rate of 8% per year. ### Timeline Details: - **Initial Point (5th Birthday):** The timeline begins at the 5th birthday, marked as the starting point. - **Annual Increments (6th to 17th Birthday):** Each year from the 6th to the 17th birthday is marked with a dashed line descending vertically, indicating annual cash flows or investments, labeled as "A = ?". The amount "A" is the unknown value to be determined. - **End Points (18th to 21st Birthday):** - **18th Birthday:** An upward arrow indicates a financial milestone of $2,000. - **19th Birthday:** An upward arrow indicates a financial milestone of $2,400. - **20th Birthday:** An upward arrow indicates a financial milestone of $2,800. - **21st Birthday:** An upward arrow indicates a financial milestone of $3,200. ### Context: The key focus of the diagram is to calculate an unknown annual investment ("A") with an 8% annual interest rate, that results in specific milestones at the ages 18, 19, 20, and 21. Each milestone shows a compounded financial goal likely achieved through regular investments made from ages 5 through 17. ### Purpose: This diagram serves as a visual aid for understanding compound interest and investment growth over time, helping students or learners calculate future values based on consistent yearly investments and interest rates.
Transcribed Image Text:The diagram illustrates a timeline of annual financial growth, starting from the 5th birthday to the 21st birthday, with an interest rate of 8% per year. ### Timeline Details: - **Initial Point (5th Birthday):** The timeline begins at the 5th birthday, marked as the starting point. - **Annual Increments (6th to 17th Birthday):** Each year from the 6th to the 17th birthday is marked with a dashed line descending vertically, indicating annual cash flows or investments, labeled as "A = ?". The amount "A" is the unknown value to be determined. - **End Points (18th to 21st Birthday):** - **18th Birthday:** An upward arrow indicates a financial milestone of $2,000. - **19th Birthday:** An upward arrow indicates a financial milestone of $2,400. - **20th Birthday:** An upward arrow indicates a financial milestone of $2,800. - **21st Birthday:** An upward arrow indicates a financial milestone of $3,200. ### Context: The key focus of the diagram is to calculate an unknown annual investment ("A") with an 8% annual interest rate, that results in specific milestones at the ages 18, 19, 20, and 21. Each milestone shows a compounded financial goal likely achieved through regular investments made from ages 5 through 17. ### Purpose: This diagram serves as a visual aid for understanding compound interest and investment growth over time, helping students or learners calculate future values based on consistent yearly investments and interest rates.
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