Question

What is the weighted average rate of return for the following investment portfolio? Retirement fund: 50% (6% annual interest) Stocks: 20% (7% annual interest) Bonds: 30% (5% annual interest) (1 point) Responses 6.9% 6.9% 7.0% 7.0% 5.0% 5.0% 5.9%

Answer 1

To calculate the weighted average rate of return for the investment portfolio, we can use the formula for the weighted average, which is:

\[
\text{Weighted Average Return} = (w_1 \cdot r_1) + (w_2 \cdot r_2) + (w_3 \cdot r_3)
\]

where \( w \) is the weight of each investment and \( r \) is the respective rate of return.

Given the data:

1. Retirement fund: \( w_1 = 0.50 \) and \( r_1 = 0.06 \)
2. Stocks: \( w_2 = 0.20 \) and \( r_2 = 0.07 \)
3. Bonds: \( w_3 = 0.30 \) and \( r_3 = 0.05 \)

Now we can substitute the values into the formula:

\[
\text{Weighted Average Return} = (0.50 \cdot 0.06) + (0.20 \cdot 0.07) + (0.30 \cdot 0.05)
\]

Calculating each term:

\[
0.50 \cdot 0.06 = 0.03
\]
\[
0.20 \cdot 0.07 = 0.014
\]
\[
0.30 \cdot 0.05 = 0.015
\]

Now, add these results together:

\[
\text{Weighted Average Return} = 0.03 + 0.014 + 0.015 = 0.059
\]

Convert this to a percentage:

\[
0.059 \times 100 = 5.9\%
\]

Thus, the weighted average rate of return for the investment portfolio is **5.9%**.