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
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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.
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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