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:
- Retirement fund: \( w_1 = 0.50 \) and \( r_1 = 0.06 \)
- Stocks: \( w_2 = 0.20 \) and \( r_2 = 0.07 \)
- 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%.