XYZ Corporation invests \( \$ 10,000 \) into 91-day treasury bills with an interest rate of \( 2.5 \% \). If the broker charges a \( \$ 20 \) commission, what is the yield? yield = [?]\% \[ \text { yield }=\frac{\text { amount invested (interest rate) }\left(\frac{\text { days invested }}{360 \text { days }}\right)}{\text { amount invested }\left(\frac{\text { days sinvested }}{360 \text { days }}\right)+\text { commission }} \] Give your answer as a percent rounded to the nearest hundredth
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To calculate the yield for XYZ Corporation's investment in treasury bills, we can use the given formula. 1. **Calculate the amount earned from the interest:** \[ \text{Interest} = 10,000 \times 0.025 \times \left(\frac{91}{360}\right) = 10,000 \times 0.025 \times 0.25278 \approx 63.20 \] 2. **Calculate the total amount invested (including commission):** \[ \text{Total invested} = 10,000 + 20 = 10,020 \] 3. **Now substitute into the yield formula:** \[ \text{Yield} = \frac{63.20}{10,020} \times 100 \approx 0.6309 \% \] Rounding it to the nearest hundredth gives us: \[ \text{Yield} \approx 0.63\% \] So the yield is \( \text{yield} = 0.63\% \).
