FINANCIAL ACCOUNTING
10th Edition
ISBN: 9781259964947
Author: Libby
Publisher: MCG
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Transcribed Image Text:**Sinking Fund Factor Table**
The table below presents the sinking fund factor for $1 per period at different interest rates (%) for various periods (n).
**Sinking Fund Factor of $1 per Period at i% for n Periods**
| Period | 0.5% | 1.0% | 1.5% | 2.0% | 2.5% | 3.0% | 3.5% | 4.0% | 4.5% | 5.0% | 5.5% | 6.0% | 6.5% | 7.0% | 7.5% | 8.0% | 8.5% | 9.0% | 9.5% | 10.0% |
|--------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| 1 | 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000| 1.0000|
| 2 | 0.4988| 0.4975| 0.4963| 0.4951| 0.4939| 0.4928| 0.4916| 0.4904| 0.4892| 0.4878| 0.4866| 0.4853| 0.4842| 0.4829| 0.4817| 0.4805| 0.4793| 0.4781| 0.4769| 0.4756|
| 3 | 0.3317| 0.3290| 0.3264|
![### Financial Planning for Retirement
Recent statistics show that only 54% of workers participate in their company's retirement plan, meaning that 46% do not. This lack of participation presents a significant risk, as reliance on Social Security alone may leave individuals without adequate income during retirement years.
#### Example Calculation:
Let's consider an example to illustrate the importance of early investment for retirement.
**Case Study: Jill Collins**
- **Age:** 20 years old
- **Retirement Goal:** $280,000
- **Retirement Age:** 60 years
- **Annual Interest Rate:** 5% (compounded annually)
**Problem:** How much does Jill need to invest each year to achieve her retirement goal?
**Solution Steps:**
1. **Identify key variables:**
- Future Value (\( FV \)) = $280,000
- Annual interest rate (\( r \)) = 5% or 0.05
- Time period (\( t \)) = 60 - 20 = 40 years
2. **Use the Future Value of an Annuity formula:**
\[
FV = P \frac{(1 + r)^t - 1}{r}
\]
Where \( P \) is the annual investment.
Rearranging to solve for \( P \):
\[
P = \frac{FV \cdot r}{(1 + r)^t - 1}
\]
3. **Plug in the values:**
\[
P = \frac{280,000 \cdot 0.05}{(1 + 0.05)^{40} - 1}
\]
4. **Calculate intermediate steps:**
- \( (1 + 0.05)^{40} = 7.04 \) (approx.)
- \( 7.04 - 1 = 6.04 \)
5. **Compute the yearly investment:**
\[
P = \frac{280,000 \cdot 0.05}{6.04}
\]
6. **Final calculation:**
\[
P = \frac{14,000}{6.04} = 2319.87
\]
Therefore, Jill Collins would need to invest approximately **$2,320** each year (when rounded to the nearest dollar) to meet her retirement goal of $280](https://content.bartleby.com/qna-images/question/84e09e5b-10a3-44ad-9aa5-0e7c6771312d/cbde23ac-6b70-4ef8-9857-4f5e8a03d841/66km3c_processed.png)
Transcribed Image Text:### Financial Planning for Retirement
Recent statistics show that only 54% of workers participate in their company's retirement plan, meaning that 46% do not. This lack of participation presents a significant risk, as reliance on Social Security alone may leave individuals without adequate income during retirement years.
#### Example Calculation:
Let's consider an example to illustrate the importance of early investment for retirement.
**Case Study: Jill Collins**
- **Age:** 20 years old
- **Retirement Goal:** $280,000
- **Retirement Age:** 60 years
- **Annual Interest Rate:** 5% (compounded annually)
**Problem:** How much does Jill need to invest each year to achieve her retirement goal?
**Solution Steps:**
1. **Identify key variables:**
- Future Value (\( FV \)) = $280,000
- Annual interest rate (\( r \)) = 5% or 0.05
- Time period (\( t \)) = 60 - 20 = 40 years
2. **Use the Future Value of an Annuity formula:**
\[
FV = P \frac{(1 + r)^t - 1}{r}
\]
Where \( P \) is the annual investment.
Rearranging to solve for \( P \):
\[
P = \frac{FV \cdot r}{(1 + r)^t - 1}
\]
3. **Plug in the values:**
\[
P = \frac{280,000 \cdot 0.05}{(1 + 0.05)^{40} - 1}
\]
4. **Calculate intermediate steps:**
- \( (1 + 0.05)^{40} = 7.04 \) (approx.)
- \( 7.04 - 1 = 6.04 \)
5. **Compute the yearly investment:**
\[
P = \frac{280,000 \cdot 0.05}{6.04}
\]
6. **Final calculation:**
\[
P = \frac{14,000}{6.04} = 2319.87
\]
Therefore, Jill Collins would need to invest approximately **$2,320** each year (when rounded to the nearest dollar) to meet her retirement goal of $280
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