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Sagot :
## Part A: Calculate how much Portfolio 1 earns.
To determine the earnings from Portfolio 1, we need to consider each investment type and its respective Rate of Return (ROR). We'll calculate the earnings for each type of investment and sum them up.
### Savings Account
- Investment Amount: \[tex]$1,425 - Rate of Return: 2.80% The earnings from the savings account can be calculated as follows: \[ \text{Earnings from Savings Account} = \$[/tex]1,425 \times \left( \frac{2.80}{100} \right) = \[tex]$1,425 \times 0.028 = \$[/tex]39.90 \]
### Government Bond
- Investment Amount: \[tex]$1,380 - Rate of Return: -1.55% The earnings from the government bond can be calculated as follows: \[ \text{Earnings from Government Bond} = \$[/tex]1,380 \times \left( \frac{-1.55}{100} \right) = \[tex]$1,380 \times -0.0155 = -\$[/tex]21.39 \]
### Preferred Stock
- Investment Amount: \[tex]$3,400 - Rate of Return: 11.70% The earnings from the preferred stock can be calculated as follows: \[ \text{Earnings from Preferred Stock} = \$[/tex]3,400 \times \left( \frac{11.70}{100} \right) = \[tex]$3,400 \times 0.117 = \$[/tex]397.80 \]
### Common Stock
- Investment Amount: \[tex]$3,100 - Rate of Return: 8.49% The earnings from the common stock can be calculated as follows: \[ \text{Earnings from Common Stock} = \$[/tex]3,100 \times \left( \frac{8.49}{100} \right) = \[tex]$3,100 \times 0.0849 = \$[/tex]263.19 \]
### Total Earnings for Portfolio 1
Now, we sum up the earnings from each type of investment to get the total earnings for Portfolio 1:
[tex]\[ \text{Total Earnings for Portfolio 1} = \$39.90 + (-\$21.39) + \$397.80 + \$263.19 = \$679.50 \][/tex]
So, Portfolio 1 earns \[tex]$679.50. ## Part B: Identify the portfolio that earns the most. What information from the table could be used to justify why that portfolio has higher earnings? ### Comparing Earnings From Part A, we know that: - Portfolio 1 earns \$[/tex]679.50.
- Portfolio 2 earns \[tex]$489.85. ### Determining the Higher-Earning Portfolio We can see that Portfolio 1 earns \$[/tex]679.50, while Portfolio 2 earns \$489.85. Therefore, Portfolio 1 earns more than Portfolio 2.
### Justification Using Information from the Table
To understand why Portfolio 1 has higher earnings, consider the following information from the table:
- Investment Amounts: Portfolio 1 has higher investment amounts in savings accounts and common stocks, which generally have the specified rates of return.
- Rates of Return (ROR):
- The savings account in both portfolios has a moderate ROR of 2.80%.
- The government bond has a negative ROR (-1.55%); thus, it pulls down earnings slightly.
- The preferred stock has a high ROR of 11.70%, generating significant earnings.
- The common stock has a relatively strong ROR of 8.49%.
The higher investment amounts in the preferred stock and common stock with their respective high RORs contribute to the overall higher earnings in Portfolio 1. This combined effect of higher amounts and generally favorable rates of return leads to the conclusion that Portfolio 1 is the higher-earning portfolio.
To determine the earnings from Portfolio 1, we need to consider each investment type and its respective Rate of Return (ROR). We'll calculate the earnings for each type of investment and sum them up.
### Savings Account
- Investment Amount: \[tex]$1,425 - Rate of Return: 2.80% The earnings from the savings account can be calculated as follows: \[ \text{Earnings from Savings Account} = \$[/tex]1,425 \times \left( \frac{2.80}{100} \right) = \[tex]$1,425 \times 0.028 = \$[/tex]39.90 \]
### Government Bond
- Investment Amount: \[tex]$1,380 - Rate of Return: -1.55% The earnings from the government bond can be calculated as follows: \[ \text{Earnings from Government Bond} = \$[/tex]1,380 \times \left( \frac{-1.55}{100} \right) = \[tex]$1,380 \times -0.0155 = -\$[/tex]21.39 \]
### Preferred Stock
- Investment Amount: \[tex]$3,400 - Rate of Return: 11.70% The earnings from the preferred stock can be calculated as follows: \[ \text{Earnings from Preferred Stock} = \$[/tex]3,400 \times \left( \frac{11.70}{100} \right) = \[tex]$3,400 \times 0.117 = \$[/tex]397.80 \]
### Common Stock
- Investment Amount: \[tex]$3,100 - Rate of Return: 8.49% The earnings from the common stock can be calculated as follows: \[ \text{Earnings from Common Stock} = \$[/tex]3,100 \times \left( \frac{8.49}{100} \right) = \[tex]$3,100 \times 0.0849 = \$[/tex]263.19 \]
### Total Earnings for Portfolio 1
Now, we sum up the earnings from each type of investment to get the total earnings for Portfolio 1:
[tex]\[ \text{Total Earnings for Portfolio 1} = \$39.90 + (-\$21.39) + \$397.80 + \$263.19 = \$679.50 \][/tex]
So, Portfolio 1 earns \[tex]$679.50. ## Part B: Identify the portfolio that earns the most. What information from the table could be used to justify why that portfolio has higher earnings? ### Comparing Earnings From Part A, we know that: - Portfolio 1 earns \$[/tex]679.50.
- Portfolio 2 earns \[tex]$489.85. ### Determining the Higher-Earning Portfolio We can see that Portfolio 1 earns \$[/tex]679.50, while Portfolio 2 earns \$489.85. Therefore, Portfolio 1 earns more than Portfolio 2.
### Justification Using Information from the Table
To understand why Portfolio 1 has higher earnings, consider the following information from the table:
- Investment Amounts: Portfolio 1 has higher investment amounts in savings accounts and common stocks, which generally have the specified rates of return.
- Rates of Return (ROR):
- The savings account in both portfolios has a moderate ROR of 2.80%.
- The government bond has a negative ROR (-1.55%); thus, it pulls down earnings slightly.
- The preferred stock has a high ROR of 11.70%, generating significant earnings.
- The common stock has a relatively strong ROR of 8.49%.
The higher investment amounts in the preferred stock and common stock with their respective high RORs contribute to the overall higher earnings in Portfolio 1. This combined effect of higher amounts and generally favorable rates of return leads to the conclusion that Portfolio 1 is the higher-earning portfolio.
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