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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

Pfin (with Mindtap, 1 Term Printed Access Card) (mindtap Course List)
Pfin (with Mindtap, 1 Term Printed Access Card) (mindtap Course List)
7th Edition
ISBN:9780357033609
Author:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk
Publisher:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk
Chapter2: Using Financial Statements And Budgets
Section: Chapter Questions
Problem 7FPE: Funding a retirement goal. Austin Miller wishes to have 800,000 in a retirement fund 20 years from...
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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?

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**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.
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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