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Two investment portfolios are shown with the amount of money placed in each investment and the ROR.

\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{1}{|c|}{ Investment } & Portfolio 1 & Portfolio 2 & \multicolumn{1}{c|}{ ROR } \\
\hline Tech Company Stock & \[tex]$2,800 & \$[/tex]1,275 & 4.63\% \\
\hline Government Bond & \[tex]$3,200 & \$[/tex]2,200 & -1.87\% \\
\hline Junk Bond & \[tex]$950 & \$[/tex]865 & 2.50\% \\
\hline Common Stock & \[tex]$1,500 & \$[/tex]1,700 & 11.13\% \\
\hline
\end{tabular}

Which portfolio earns the most, and by how much?

A. Portfolio 1 earns \[tex]$31.77 more.
B. Portfolio 2 earns \$[/tex]31.77 more.
C. Portfolio 1 earns \[tex]$69.17 more.
D. Portfolio 2 earns \$[/tex]69.17 more.



Answer :

GinnyAnswer
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.

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