To determine which portfolio earns the most and by how much, we first need to calculate the earnings for both portfolios based on the given investments and their respective rates of return (ROR). Here's a step-by-step solution:
Step 1: Calculate earnings for Portfolio 1
1. Tech Company Stock:
Investment: [tex]$2,800
ROR: \(-3.75\%\)
Earnings: \(2800 \times \left(\frac{-3.75}{100}\right) = 2800 \times -0.0375 = -105\)
2. Government Bond:
Investment: $[/tex]3,200
ROR: [tex]\(2.95\%\)[/tex]
Earnings: [tex]\(3200 \times \left(\frac{2.95}{100}\right) = 3200 \times 0.0295 = 94.4\)[/tex]
3. Junk Bond:
Investment: [tex]$950
ROR: \(4.56\%\)
Earnings: \(950 \times \left(\frac{4.56}{100}\right) = 950 \times 0.0456 = 43.32\)
4. Common Stock:
Investment: $[/tex]1,500
ROR: [tex]\(7.18\%\)[/tex]
Earnings: [tex]\(1500 \times \left(\frac{7.18}{100}\right) = 1500 \times 0.0718 = 107.7\)[/tex]
Adding up all the earnings for Portfolio 1:
Earnings for Portfolio 1 = [tex]\(-105 + 94.4 + 43.32 + 107.7 = 140.42\)[/tex]
Step 2: Calculate earnings for Portfolio 2
1. Tech Company Stock:
Investment: [tex]$1,275
ROR: \(-3.75\%\)
Earnings: \(1275 \times \left(\frac{-3.75}{100}\right) = 1275 \times -0.0375 = -47.8125\)
2. Government Bond:
Investment: $[/tex]2,200
ROR: [tex]\(2.95\%\)[/tex]
Earnings: [tex]\(2200 \times \left(\frac{2.95}{100}\right) = 2200 \times 0.0295 = 64.9\)[/tex]
3. Junk Bond:
Investment: [tex]$865
ROR: \(4.56\%\)
Earnings: \(865 \times \left(\frac{4.56}{100}\right) = 865 \times 0.0456 = 39.42\)
4. Common Stock:
Investment: $[/tex]1,700
ROR: [tex]\(7.18\%\)[/tex]
Earnings: [tex]\(1700 \times \left(\frac{7.18}{100}\right) = 1700 \times 0.0718 = 122.06\)[/tex]
Adding up all the earnings for Portfolio 2:
Earnings for Portfolio 2 = [tex]\(-47.8125 + 64.9 + 39.42 + 122.06 = 178.5915\)[/tex]
Step 3: Determine the difference and which portfolio earns more
Earnings for Portfolio 1 = [tex]$140.42
Earnings for Portfolio 2 = $[/tex]178.59
Difference in earnings:
[tex]\[ 178.59 - 140.42 = 38.17 \][/tex]
Since Portfolio 2 has higher earnings:
Portfolio 2 earns \[tex]$38.17 more.
Thus, the correct answer is:
Portfolio 2 earns \$[/tex]38.17 more.
