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
Related questions
Question
20.
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**Question**
**How old will Matthew be?**
Matthew will be [ ] years old. *(Round to the nearest year as needed.)*
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### Explanation
To calculate how old Matthew will be when he retires, we need to determine how many years it takes for his annuity to reach $1,000,000 with the given conditions:
- Monthly deposit: $320
- Annual interest rate: 6%, compounded monthly
To solve this, we use the future value of an annuity formula:
\[ FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right) \]
Where:
- \( FV \) = Future Value of the annuity ($1,000,000)
- \( P \) = Monthly deposit ($320)
- \( r \) = Monthly interest rate (6% annual rate / 12 months = 0.5% per month = 0.005 as a decimal)
- \( n \) = Number of monthly deposits (years \(\times\) 12)
Through the interactive tool, you can input these values to calculate \( n \), the number of months. Then, divide this number by 12 to convert months into years. Finally, add this to Matthew’s starting age (25) to determine his retirement age.
Simply input the values into the interactive tool provided and it will calculate the precise retirement age for Matthew, rounding to the nearest year as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d9df1eb-9cbe-4888-87d6-c14249115dd3%2Fd170689b-000f-4854-9294-ff54539ad5f9%2Fcalqyfe_processed.png&w=3840&q=75)
Transcribed Image Text:### Retirement Annuity Calculation
On his 25th birthday, Matthew started an annuity for his retirement. He deposits $320 each month into an account earning 6% annual interest compounded monthly. He determines that he will be able to retire once he has $1,000,000 in his retirement account. Determine how old Matthew will be when he is able to retire.
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**Interactive Tool**
(Use the interactive figure to answer the following question.)
[Click here to launch the interactive figure.](#)
---
**Question**
**How old will Matthew be?**
Matthew will be [ ] years old. *(Round to the nearest year as needed.)*
---
### Explanation
To calculate how old Matthew will be when he retires, we need to determine how many years it takes for his annuity to reach $1,000,000 with the given conditions:
- Monthly deposit: $320
- Annual interest rate: 6%, compounded monthly
To solve this, we use the future value of an annuity formula:
\[ FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right) \]
Where:
- \( FV \) = Future Value of the annuity ($1,000,000)
- \( P \) = Monthly deposit ($320)
- \( r \) = Monthly interest rate (6% annual rate / 12 months = 0.5% per month = 0.005 as a decimal)
- \( n \) = Number of monthly deposits (years \(\times\) 12)
Through the interactive tool, you can input these values to calculate \( n \), the number of months. Then, divide this number by 12 to convert months into years. Finally, add this to Matthew’s starting age (25) to determine his retirement age.
Simply input the values into the interactive tool provided and it will calculate the precise retirement age for Matthew, rounding to the nearest year as needed.
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