XYZ Corporation invests \( \$ 8,000 \) into 91-day treasury bills with an interest rate of \( 2.1 \% \). If the broker charges a \( \$ 30 \) commission, what is the yield? \[ \begin{array}{c} \text { yield }=[?] \% \\ \text { yield }=\frac{\text { amount invested (interest rate) }\left(\frac{\text { days invested }}{360 \text { days }}\right)}{\text { amount invested }\left(\frac{\text { days invested }}{360 \text { days }}\right)+\text { commission }} \end{array} \] Give your answer as a percent rounded to the nearest hundredth

To find the yield, we first need to calculate the interest earned from the investment in treasury bills over 91 days. 1. **Calculate Interest Earned:** \[ \text{Interest} = 8000 \times 0.021 \times \left(\frac{91}{360}\right) = 8000 \times 0.021 \times 0.2528 \approx 42.44 \] 2. **After deducting the commission, the total amount is:** \[ \text{Total Amount} = 8000 + 42.44 - 30 = 8012.44 \] 3. **The denominator for yield calculation:** \[ \text{Amount Invested + Commission} = 8000 + 30 = 8030 \] 4. **Finally, substitute into the yield formula:** \[ \text{Yield} = \frac{42.44}{8030} \approx 0.005286 = 0.5286\% \] Now, rounding to the nearest hundredth, the yield is approximately: \[ \text{yield} \approx 0.53\% \]