You have just made your first $4,400 contribution to your retirement account. Assume you earn a return of 13 percent per year and make no additional contributions. What will your account be worth when you retire in 29 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What if you wait 10 years before contributing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
You have just made your first $4,400 contribution to your retirement account. Assume you earn a return of 13 percent per year and make no additional contributions. What will your account be worth when you retire in 29 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What if you wait 10 years before contributing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
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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![### Future Value of Retirement Contributions
In this exercise, we'll explore the future value of a retirement account given a specific contribution and interest rate. Let's assume an initial contribution of $4,400 with an annual return of 13 percent. No additional contributions will be made.
#### Scenarios
1. **Scenario A - Immediate Contribution**:
- **Question**: What will your account be worth when you retire in 29 years if you make the contribution now?
- **Instruction**: Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).
2. **Scenario B - Delayed Contribution**:
- **Question**: What will your account be worth if you wait 10 years before contributing?
- **Instruction**: Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).
To aid in your calculations, here is a table where you can enter the future values for each scenario:
| Scenario | Future Value Calculation |
|----------|---------------------------------------------------|
| a. | Future value for starting now |
| b. | Future value if waiting 10 years |
By inputting the figures correctly into the formula for compound interest, you can determine the future value of your retirement account under both scenarios.
### Key Formula
The formula to calculate the future value (FV) is:
\[ \text{FV} = PV \times (1 + r)^n \]
where:
- \( PV \) = Present Value (initial contribution, $4,400)
- \( r \) = annual interest rate (13% or 0.13)
- \( n \) = number of years
Use this formula to solve for each scenario, ensuring intermediate calculations are accurate up to several decimal points before rounding the final result to 2 decimal places.
Do your calculations and fill in the table with your results!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4075dd7b-7cf0-4080-a9ab-c20ff4793850%2F3fa70e29-0e90-48b7-847f-7891cfd00311%2Fbi8bkw_processed.png&w=3840&q=75)
Transcribed Image Text:### Future Value of Retirement Contributions
In this exercise, we'll explore the future value of a retirement account given a specific contribution and interest rate. Let's assume an initial contribution of $4,400 with an annual return of 13 percent. No additional contributions will be made.
#### Scenarios
1. **Scenario A - Immediate Contribution**:
- **Question**: What will your account be worth when you retire in 29 years if you make the contribution now?
- **Instruction**: Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).
2. **Scenario B - Delayed Contribution**:
- **Question**: What will your account be worth if you wait 10 years before contributing?
- **Instruction**: Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).
To aid in your calculations, here is a table where you can enter the future values for each scenario:
| Scenario | Future Value Calculation |
|----------|---------------------------------------------------|
| a. | Future value for starting now |
| b. | Future value if waiting 10 years |
By inputting the figures correctly into the formula for compound interest, you can determine the future value of your retirement account under both scenarios.
### Key Formula
The formula to calculate the future value (FV) is:
\[ \text{FV} = PV \times (1 + r)^n \]
where:
- \( PV \) = Present Value (initial contribution, $4,400)
- \( r \) = annual interest rate (13% or 0.13)
- \( n \) = number of years
Use this formula to solve for each scenario, ensuring intermediate calculations are accurate up to several decimal points before rounding the final result to 2 decimal places.
Do your calculations and fill in the table with your results!
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