Having received a bonus of $\$ 30,000$ for accepting early retirement in July, 2000, a company's project manager invested $\$ 9,000$ in a municipal bond paying $3.69 \%, \$ 14,000$ in a money market fund paying $4.01 \%$, and $\$ 7000$ in a certificate of deposit paying $3.29 \%$. Using the respective amounts invested as weights, find the weighted mean of the three percentages.
A) $\bar{x}_{w}=3.75 \%$
B) $\bar{x}_{w}=3.66 \%$
C) $\bar{x}_{w}=3.74 \%$
D) $\bar{x}_{w}=3.67 \%$

Question

Quizplus · Accepted Answer

The weighted mean $\bar{x}_{w}$ is calculated by multiplying each percentage by its respective weight (amount invested), summing these products, and then dividing by the total amount invested. Thus, $\bar{x}_{w} = \frac{(9000 \times 3.69) + (14000 \times 4.01) + (7000 \times 3.29)}{9000 + 14000 + 7000} = \frac{33210 + 56140 + 23030}{30000} = \frac{112380}{30000} = 3.746\%$, which rounds to $3.75\%$.

Having Received a Bonus Of $30,000\$ 30,000$30,000 For Accepting Early Retirement in July, 2000, a Company's Project

Having Received a Bonus Of $\$ 30,000$ For Accepting Early Retirement in July, 2000, a Company's Project