To determine which portfolio earns the most, we'll need to calculate the earnings for each portfolio based on their rates of return (ROR) for each type of investment.
### Step-by-Step Solution:
1. Calculate Earnings for Portfolio 1:
- Tech Company Stock:
[tex]\[
\$2800 \times \frac{4.63}{100} = \$2800 \times 0.0463 = \$129.64
\][/tex]
- Government Bond:
[tex]\[
\$3200 \times \frac{-1.87}{100} = \$3200 \times -0.0187 = -\$59.84
\][/tex]
- Junk Bond:
[tex]\[
\$950 \times \frac{2.50}{100} = \$950 \times 0.025 = \$23.75
\][/tex]
- Common Stock:
[tex]\[
\$1500 \times \frac{11.13}{100} = \$1500 \times 0.1113 = \$166.95
\][/tex]
- Total Earnings for Portfolio 1:
[tex]\[
\$129.64 + (-\$59.84) + \$23.75 + \$166.95 = \$260.50
\][/tex]
2. Calculate Earnings for Portfolio 2:
- Tech Company Stock:
[tex]\[
\$1275 \times \frac{4.63}{100} = \$1275 \times 0.0463 = \$59.08
\][/tex]
- Government Bond:
[tex]\[
\$2200 \times \frac{-1.87}{100} = \$2200 \times -0.0187 = -\$41.14
\][/tex]
- Junk Bond:
[tex]\[
\$865 \times \frac{2.50}{100} = \$865 \times 0.025 = \$21.63
\][/tex]
- Common Stock:
[tex]\[
\$1700 \times \frac{11.13}{100} = \$1700 \times 0.1113 = \$189.09
\][/tex]
- Total Earnings for Portfolio 2:
[tex]\[
\$59.08 + (-\$41.14) + \$21.63 + \$189.09 = \$228.73
\][/tex]
3. Determine which portfolio earns the most and by how much:
- Compare Total Earnings:
[tex]\[
\$260.50 \, \text{(Portfolio 1)} > \$228.73 \, \text{(Portfolio 2)}
\][/tex]
- Difference in Earnings:
[tex]\[
\$260.50 - \$228.73 = \$31.77
\][/tex]
### Conclusion:
- Portfolio 1 earns [tex]\(\$260.50\)[/tex].
- Portfolio 2 earns [tex]\(\$228.73\)[/tex].
Portfolio 1 earns [tex]\(\$31.77\)[/tex] more. Therefore, the correct answer is:
Portfolio 1 earns \$31.77 more.
