## Related questions with answers

The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided. Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds.

$\begin{matrix} \text{Days to Maturity} & \text{Dollar Value (\$millions)}\\ \text{20} & \text{20}\\ \text{12} & \text{30}\\ \text{7} & \text{10}\\ \text{5} & \text{15}\\ \text{6} & \text{10}\\ \end{matrix}$

Solutions

VerifiedThe goal of the exercise is to find use the weighted mean to determine the mean number of days. we will use the following formula:

$\bar{x}=\frac{\sum w_{i} x_{i}}{\sum w_{i}}$

The weighted mean is the sum of the products of the values and their weights, divided by the sum of the weights.

The weights are the dollar values and the values are the days to maturity.

$\overline{x}=\dfrac{\sum x\cdot w}{\sum w}=\dfrac{20(20)+30(12)+10(7)+15(7)+10(6)}{20+30+10+15+10}\approx 11.7059$

The weighted mean is the sum of the products of the values and their weights divided by the sum of the weights.

$\begin{gather*} \overline{x} = \frac{\sum x\ \cdot w}{\sum w}\\ \overline{x} = \frac{20\cdot 20 + 30\cdot 12 +... + 10\cdot 6}{85}=11.35294\\ \end{gather*}$

In this five market funds, dollar needs about 11 days to gain maturity.

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