Faith saves for retirement by depositing $550 each month into an account which earns an APR of 3.5% compounded monthly. How much will Faith have in 20 years?
Faith saves for retirement by depositing $550 each month into an account which earns an APR of 3.5% compounded monthly. How much will Faith have in 20 years?
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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![### Retirement Savings Calculation
**Problem (2.2):**
Faith saves for retirement by depositing $550 each month into an account which earns an APR of 3.5% compounded monthly. How much will Faith have in 20 years?
**Solution Approach:**
1. Review and select the appropriate financial formula to compute the future value of the annuity.
2. Ensure to consider the compounding period and interest rate adjustments accordingly.
**Visualization:**
_Selections To Be Made:_
- **LSS-Comp** (Compounded Monthly)
- **LSS-Cont** (Continuous Compounding)
- **SP** (Single Payment)
- **LP** (Lump Sum Payment)
In this case, LSS-Comp should be selected because the interest is compounded monthly.
**Calculation Recap:**
Let's use the Future Value of an Ordinary Annuity formula to find the total amount accumulated:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
- \( P \) = Monthly deposit ($550)
- \( r \) = Monthly interest rate (APR/12) = 3.5% / 12 ≈ 0.0029167
- \( n \) = Total number of deposits (Years \* 12) = 20 \* 12 = 240
_Future Value Calculation_
By substituting the values:
\[ FV = \$550 \times \left( \frac{(1 + 0.0029167)^{240} - 1}{0.0029167} \right) \]
By solving this, you will get the total amount Faith will have after 20 years.
This problem assists in understanding annuity savings and the impact of interest compounding on long-term savings plans, crucial for retirement planning education.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff24ce67d-5c13-49ab-8f30-49b92ca3e30b%2Face09dc9-cbc4-4ddc-b277-51467102d7a4%2Fbtebsme_processed.png&w=3840&q=75)
Transcribed Image Text:### Retirement Savings Calculation
**Problem (2.2):**
Faith saves for retirement by depositing $550 each month into an account which earns an APR of 3.5% compounded monthly. How much will Faith have in 20 years?
**Solution Approach:**
1. Review and select the appropriate financial formula to compute the future value of the annuity.
2. Ensure to consider the compounding period and interest rate adjustments accordingly.
**Visualization:**
_Selections To Be Made:_
- **LSS-Comp** (Compounded Monthly)
- **LSS-Cont** (Continuous Compounding)
- **SP** (Single Payment)
- **LP** (Lump Sum Payment)
In this case, LSS-Comp should be selected because the interest is compounded monthly.
**Calculation Recap:**
Let's use the Future Value of an Ordinary Annuity formula to find the total amount accumulated:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
- \( P \) = Monthly deposit ($550)
- \( r \) = Monthly interest rate (APR/12) = 3.5% / 12 ≈ 0.0029167
- \( n \) = Total number of deposits (Years \* 12) = 20 \* 12 = 240
_Future Value Calculation_
By substituting the values:
\[ FV = \$550 \times \left( \frac{(1 + 0.0029167)^{240} - 1}{0.0029167} \right) \]
By solving this, you will get the total amount Faith will have after 20 years.
This problem assists in understanding annuity savings and the impact of interest compounding on long-term savings plans, crucial for retirement planning education.
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