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Sagot :
Let's go through the solution step-by-step.
### Part A: Calculate the Earnings for Portfolio 2
1. Identify the values and the rates of return (ROR) for each investment in Portfolio 2:
- Savings Account: \[tex]$1,450 with a ROR of 2.80% - Government Bond: \$[/tex]2,200 with a ROR of -1.55%
- Preferred Stock: \[tex]$3,700 with a ROR of 11.70% - Common Stock: \$[/tex]1,500 with a ROR of 8.496%
2. Convert the rates of return from percentages to decimal form:
- Savings Account: [tex]\( \text{ROR} = 2.80\% = 0.028 \)[/tex]
- Government Bond: [tex]\( \text{ROR} = -1.55\% = -0.0155 \)[/tex]
- Preferred Stock: [tex]\( \text{ROR} = 11.70\% = 0.117 \)[/tex]
- Common Stock: [tex]\( \text{ROR} = 8.496\% = 0.08496 \)[/tex]
3. Calculate the earnings for each investment:
- Savings Account:
[tex]\[ \text{Earnings} = \$1,450 \times 0.028 = \$40.60 \][/tex]
- Government Bond:
[tex]\[ \text{Earnings} = \$2,200 \times -0.0155 = -\$34.10 \][/tex]
- Preferred Stock:
[tex]\[ \text{Earnings} = \$3,700 \times 0.117 = \$432.90 \][/tex]
- Common Stock:
[tex]\[ \text{Earnings} = \$1,500 \times 0.08496 = \$127.44 \][/tex]
4. Calculate the total earnings for Portfolio 2:
[tex]\[ \text{Total Earnings} = \$40.60 + (-\$34.10) + \$432.90 + \$127.44 = \$566.84 \][/tex]
### Summary for Part A
Earnings for each investment in Portfolio 2:
- Savings Account: \[tex]$40.60 - Government Bond: -\$[/tex]34.10
- Preferred Stock: \[tex]$432.90 - Common Stock: \$[/tex]127.44
Total earnings for Portfolio 2: \[tex]$566.84 ### Part B: Identify the Portfolio That Earns the Most Given the total earnings of: - Portfolio 1: \$[/tex]465.93
- Portfolio 2: \[tex]$566.84 Portfolio 2 earns the most. #### Justification: 1. Savings Account: - Portfolio 2 has a savings account that earns \$[/tex]40.60.
2. Government Bond:
- Portfolio 2 has a loss of \[tex]$34.10 from the government bond. 3. Preferred Stock: - Portfolio 2 earns a significant amount \$[/tex]432.90 from preferred stock.
4. Common Stock:
- Portfolio 2 earns \[tex]$127.44 from common stock. When comparing to Portfolio 1, which has a total earning of \$[/tex]465.93, Portfolio 2's higher earnings are mainly attributed to better returns from the Preferred Stock and decent returns from the Common Stock, despite the loss incurred in the Government Bond.
Thus, Portfolio 2 is the portfolio that earns the most, considering the individual contributions of each investment type reflected in the calculated earnings.
### Part A: Calculate the Earnings for Portfolio 2
1. Identify the values and the rates of return (ROR) for each investment in Portfolio 2:
- Savings Account: \[tex]$1,450 with a ROR of 2.80% - Government Bond: \$[/tex]2,200 with a ROR of -1.55%
- Preferred Stock: \[tex]$3,700 with a ROR of 11.70% - Common Stock: \$[/tex]1,500 with a ROR of 8.496%
2. Convert the rates of return from percentages to decimal form:
- Savings Account: [tex]\( \text{ROR} = 2.80\% = 0.028 \)[/tex]
- Government Bond: [tex]\( \text{ROR} = -1.55\% = -0.0155 \)[/tex]
- Preferred Stock: [tex]\( \text{ROR} = 11.70\% = 0.117 \)[/tex]
- Common Stock: [tex]\( \text{ROR} = 8.496\% = 0.08496 \)[/tex]
3. Calculate the earnings for each investment:
- Savings Account:
[tex]\[ \text{Earnings} = \$1,450 \times 0.028 = \$40.60 \][/tex]
- Government Bond:
[tex]\[ \text{Earnings} = \$2,200 \times -0.0155 = -\$34.10 \][/tex]
- Preferred Stock:
[tex]\[ \text{Earnings} = \$3,700 \times 0.117 = \$432.90 \][/tex]
- Common Stock:
[tex]\[ \text{Earnings} = \$1,500 \times 0.08496 = \$127.44 \][/tex]
4. Calculate the total earnings for Portfolio 2:
[tex]\[ \text{Total Earnings} = \$40.60 + (-\$34.10) + \$432.90 + \$127.44 = \$566.84 \][/tex]
### Summary for Part A
Earnings for each investment in Portfolio 2:
- Savings Account: \[tex]$40.60 - Government Bond: -\$[/tex]34.10
- Preferred Stock: \[tex]$432.90 - Common Stock: \$[/tex]127.44
Total earnings for Portfolio 2: \[tex]$566.84 ### Part B: Identify the Portfolio That Earns the Most Given the total earnings of: - Portfolio 1: \$[/tex]465.93
- Portfolio 2: \[tex]$566.84 Portfolio 2 earns the most. #### Justification: 1. Savings Account: - Portfolio 2 has a savings account that earns \$[/tex]40.60.
2. Government Bond:
- Portfolio 2 has a loss of \[tex]$34.10 from the government bond. 3. Preferred Stock: - Portfolio 2 earns a significant amount \$[/tex]432.90 from preferred stock.
4. Common Stock:
- Portfolio 2 earns \[tex]$127.44 from common stock. When comparing to Portfolio 1, which has a total earning of \$[/tex]465.93, Portfolio 2's higher earnings are mainly attributed to better returns from the Preferred Stock and decent returns from the Common Stock, despite the loss incurred in the Government Bond.
Thus, Portfolio 2 is the portfolio that earns the most, considering the individual contributions of each investment type reflected in the calculated earnings.
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