Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12% on his contributions, how much will he have at the end of the twentieth year? a) $192,292 O b) $75,938 c) $40,000 d) $144,104
Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12% on his contributions, how much will he have at the end of the twentieth year? a) $192,292 O b) $75,938 c) $40,000 d) $144,104
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12% on his contributions, how much will he have at the end of the twentieth year?
(Please show work)
![**IRA Growth Calculation Problem**
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**Problem Statement:**
Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12% on his contributions, how much will he have at the end of the twentieth year?
**Options:**
a) $192,292
b) $75,938
c) $40,000
d) $144,104
**Explanation:**
To determine how much Bill will have at the end of the twentieth year, one must use the future value formula for an annuity, which accounts for regular contributions and compound interest. The formula is:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
- \( P \) is the annual contribution ($2,000).
- \( r \) is the annual interest rate (12% or 0.12).
- \( n \) is the number of years (20).
The correct option for the future value (FV) is calculated and represented among the choices given. Please solve this calculation to select the right answer.
**Further Reading:**
Understanding the growth of investments over time with compound interest can significantly impact retirement planning and financial literacy. It is recommended to familiarize yourself with annuity calculations and the principles of compound interest.
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Always consider leveraging financial calculators or spreadsheet software to compute future values and verify your understanding of annuity formulas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6ce828-7421-4579-a347-7b809a44673d%2F0972a74f-b9b9-4152-8b20-f70a59606cd1%2Fxdtbtto_processed.png&w=3840&q=75)
Transcribed Image Text:**IRA Growth Calculation Problem**
---
**Problem Statement:**
Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12% on his contributions, how much will he have at the end of the twentieth year?
**Options:**
a) $192,292
b) $75,938
c) $40,000
d) $144,104
**Explanation:**
To determine how much Bill will have at the end of the twentieth year, one must use the future value formula for an annuity, which accounts for regular contributions and compound interest. The formula is:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
- \( P \) is the annual contribution ($2,000).
- \( r \) is the annual interest rate (12% or 0.12).
- \( n \) is the number of years (20).
The correct option for the future value (FV) is calculated and represented among the choices given. Please solve this calculation to select the right answer.
**Further Reading:**
Understanding the growth of investments over time with compound interest can significantly impact retirement planning and financial literacy. It is recommended to familiarize yourself with annuity calculations and the principles of compound interest.
---
Always consider leveraging financial calculators or spreadsheet software to compute future values and verify your understanding of annuity formulas.
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