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

\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{1}{|c|}{Investment} & Portfolio 1 & Portfolio 2 & ROR \\
\hline Tech Company Stock & \[tex]$2,300 & \$[/tex]1,575 & 2.35\% \\
\hline Government Bond & \[tex]$3,100 & \$[/tex]2,100 & 1.96\% \\
\hline Junk Bond & \[tex]$650 & \$[/tex]795 & 10.45\% \\
\hline Common Stock & \[tex]$1,800 & \$[/tex]1,900 & -2.59\% \\
\hline
\end{tabular}

Which portfolio has a higher total weighted mean amount of money, and by how much?

A. Portfolio 1 has the higher total weighted mean amount of money by \[tex]$24.08.
B. Portfolio 2 has the higher total weighted mean amount of money by \$[/tex]24.08.
C. Portfolio 1 has the higher total weighted mean amount of money by \[tex]$18.90.
D. Portfolio 2 has the higher total weighted mean amount of money by \$[/tex]18.90.



Answer :

GinnyAnswer
To determine which portfolio has the higher total weighted mean amount of money, let's go through the given investments and their respective Rate of Return (ROR) step by step.

1. Calculate Weighted Returns for Portfolio 1:

For each investment in Portfolio 1:
- Tech Company Stock: \[tex]$2300 2.35% = \$[/tex]2300 0.0235 = \[tex]$54.05 - Government Bond: \$[/tex]3100 1.96% = \[tex]$3100 0.0196 = \$[/tex]60.76
- Junk Bond: \[tex]$650 10.45% = \$[/tex]650 0.1045 = \[tex]$67.925 - Common Stock: \$[/tex]1800 -2.59% = \[tex]$1800 -0.0259 = -\$[/tex]46.62

Summing these results gives the total weighted return for Portfolio 1:
[tex]\[ 54.05 + 60.76 + 67.925 - 46.62 = \$136.115 \][/tex]

2. Calculate Weighted Returns for Portfolio 2:

For each investment in Portfolio 2:
- Tech Company Stock: \[tex]$1575 2.35% = \$[/tex]1575 0.0235 = \[tex]$37.0125 - Government Bond: \$[/tex]2100 1.96% = \[tex]$2100 0.0196 = \$[/tex]41.16
- Junk Bond: \[tex]$795 10.45% = \$[/tex]795 0.1045 = \[tex]$83.0775 - Common Stock: \$[/tex]1900 -2.59% = \[tex]$1900 -0.0259 = -\$[/tex]49.21

Summing these results gives the total weighted return for Portfolio 2:
[tex]\[ 37.0125 + 41.16 + 83.0775 - 49.21 = \$112.04 \][/tex]

3. Comparison:

- Total weighted return for Portfolio 1: \[tex]$136.115 - Total weighted return for Portfolio 2: \$[/tex]112.04

Portfolio 1 has a higher total weighted mean amount of money than Portfolio 2.

4. Difference Between the Portfolios:
[tex]\[ 136.115 - 112.04 = \$24.075 \][/tex]

Therefore, Portfolio 1 has the higher total weighted mean amount of money by \[tex]$24.08 (rounded to two decimal places). The correct statement is: Portfolio 1 has the higher total weighted mean amount of money by $[/tex]\[tex]$24.08$[/tex].

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