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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}{|c|l|l|l|}
\hline
\multicolumn{1}{|c|}{Investment} & Portfolio 1 & Portfolio 2 & ROR \\
\hline
Tech Company Stock & [tex]$\$[/tex] 2,300[tex]$ & $[/tex]\[tex]$ 1,575$[/tex] & [tex]$2.35 \%$[/tex] \\
\hline
Government Bond & [tex]$\$[/tex] 3,100[tex]$ & $[/tex]\[tex]$ 2,100$[/tex] & [tex]$1.96 \%$[/tex] \\
\hline
Junk Bond & [tex]$\$[/tex] 650[tex]$ & $[/tex]\[tex]$ 795$[/tex] & [tex]$10.45 \%$[/tex] \\
\hline
Common Stock & [tex]$\$[/tex] 1,800[tex]$ & $[/tex]\[tex]$ 1,900$[/tex] & [tex]$-2.59 \%$[/tex] \\
\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]$\$[/tex] 24.08[tex]$.
B. Portfolio 2 has the higher total weighted mean amount of money by $[/tex]\[tex]$ 24.08$[/tex].
C. Portfolio 1 has the higher total weighted mean amount of money by [tex]$\$[/tex] 18.90[tex]$.
D. Portfolio 2 has the higher total weighted mean amount of money by $[/tex]\[tex]$ 18.90$[/tex].



Answer :

GinnyAnswer
Let's solve this step-by-step and determine which portfolio has the higher total weighted mean amount of money and by how much.

Firstly, for each portfolio, we need to calculate the weighted mean amount based on the given ROR (Rate of Return) percentages.

### Portfolio 1 Calculations:

#### Step 1: Convert ROR to decimal form.
- Tech Company Stock ROR: [tex]\(2.35\%\)[/tex] = [tex]\(0.0235\)[/tex]
- Government Bond ROR: [tex]\(1.96\%\)[/tex] = [tex]\(0.0196\)[/tex]
- Junk Bond ROR: [tex]\(10.45\%\)[/tex] = [tex]\(0.1045\)[/tex]
- Common Stock ROR: [tex]\(-2.59\%\)[/tex] = [tex]\(-0.0259\)[/tex]

#### Step 2: Calculate the weighted amounts for Portfolio 1.
- Tech Company Stock: [tex]\(2300 \times 0.0235 = 54.05\)[/tex]
- Government Bond: [tex]\(3100 \times 0.0196 = 60.76\)[/tex]
- Junk Bond: [tex]\(650 \times 0.1045 = 67.92\)[/tex]
- Common Stock: [tex]\(1800 \times -0.0259 = -46.62\)[/tex]

#### Step 3: Sum the weighted amounts to get the total weighted mean for Portfolio 1.
[tex]\[54.05 + 60.76 + 67.92 - 46.62 = 136.115\][/tex]

### Portfolio 2 Calculations:

#### Step 1: Convert ROR to decimal form.
- The ROR values are the same as for Portfolio 1.

#### Step 2: Calculate the weighted amounts for Portfolio 2.
- Tech Company Stock: [tex]\(1575 \times 0.0235 = 37.0125\)[/tex]
- Government Bond: [tex]\(2100 \times 0.0196 = 41.16\)[/tex]
- Junk Bond: [tex]\(795 \times 0.1045 = 83.0475\)[/tex]
- Common Stock: [tex]\(1900 \times -0.0259 = -49.18\)[/tex]

#### Step 3: Sum the weighted amounts to get the total weighted mean for Portfolio 2.
[tex]\[37.0125 + 41.16 + 83.0475 - 49.18 = 112.04\][/tex]

### Comparison and Conclusion:

Now, we compare the total weighted mean amounts:

[tex]\[ \text{Portfolio 1: } 136.115 \\ \text{Portfolio 2: } 112.04 \\ \][/tex]

Portfolio 1 has the higher total weighted mean amount.

The difference between the two portfolios is:

[tex]\[ 136.115 - 112.04 = 24.075 \][/tex]

Rounding to two decimal places:

[tex]\[ 24.075 \approx 24.08 \][/tex]

Thus, the conclusion is:

Portfolio 1 has the higher total weighted mean amount of money by [tex]\(\$24.08\)[/tex].

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