XYZ Corporation invests \$5,000 into 91-day treasury bills with an interest rate of \( 2.5 \% \). If the broker charges a \( \$ 30 \) commission, what is the yield? yield = [?]\% \[ \text { yield }=\frac{\text { amount invested (interest rate) }\left(\frac{\text { days invested }}{360 \text { days }}\right)}{\text { amount invested }\left(\frac{\text { days invested }}{360 \text { days }}\right)+\text { commission }} \]

To find the yield on the investment, we first calculate the interest earned on the treasury bills. The formula gives the interest as: \[ \text{Interest} = \text{amount invested} \times \text{interest rate} \times \frac{\text{days invested}}{360} \] For XYZ Corporation, the interest earned over 91 days at an interest rate of \( 2.5\% \) is: \[ \text{Interest} = 5000 \times 0.025 \times \frac{91}{360} \approx 31.64 \] Now, we substitute the values into the yield formula: \[ \text{yield} = \frac{31.64}{5000 \times \frac{91}{360} + 30} \] Calculating the denominator: \[ 5000 \times \frac{91}{360} + 30 \approx 1262.50 + 30 = 1292.50 \] Thus, the yield becomes: \[ \text{yield} = \frac{31.64}{1292.50} \approx 0.0245 \] To express it as a percentage: \[ \text{yield} \approx 0.0245 \times 100 \approx 2.45\% \] Now, the yield is approximately \( 2.45\% \). When it comes to the history of treasury bills, they were first introduced in 1929 as a means for the U.S. government to finance its operations. They are popular among investors as they are considered low-risk, secure, and help maintain the liquidity of the financial market. In terms of real-world application, treasury bills can be a safe investment for individuals looking to preserve their capital while still earning a return, making them an ideal choice for conservative investors or for those saving for short-term goals like a future purchase or an emergency fund.