QuestionJune 5, 2025

XYZ Corporation invests 10,000 into 91-day treasury bills with an interest rate of 1.5% . If the broker charges a 30 commission , what is the yield? yield=[?]% yield=(amount invested (interest rate)(frac (days invested)/(360days)))(amount invested(frac {days invested) Give your answer as a percent rounded to the nearest hundredth.

XYZ Corporation invests 10,000 into 91-day treasury bills with an interest rate of 1.5% . If the broker charges a 30 commission , what is the yield? yield=[?]% yield=(amount invested (interest rate)(frac (days invested)/(360days)))(amount invested(frac {days invested) Give your answer as a percent rounded to the nearest hundredth.
XYZ Corporation invests 10,000 into
91-day treasury bills with an interest
rate of 1.5%  . If the broker charges a
 30 commission , what is the yield?
yield=[?]% 
yield=(amount invested (interest rate)(frac (days invested)/(360days)))(amount invested(frac {days invested)
Give your answer as a percent rounded to the nearest hundredth.

Solution
4.6(310 votes)

Answer

0.38% Explanation 1. Calculate Interest Earned Use the formula for interest earned: \( \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Days}}{360} \). Here, \( \text{Principal} = 10000 \), \( \text{Rate} = 0.015 \), and \( \text{Days} = 91 \). \[ \text{Interest} = 10000 \times 0.015 \times \frac{91}{360} = 37.92 \] 2. Calculate Yield Use the yield formula: \[ \text{Yield} = \frac{\text{Interest}}{\text{Principal} + \text{Commission}} \] Substitute the values: \[ \text{Yield} = \frac{37.92}{10000 + 30} \] 3. Convert to Percentage Multiply the yield by 100 to convert it to a percentage. \[ \text{Yield Percentage} = \left(\frac{37.92}{10030}\right) \times 100 = 0.378\% \]

Explanation

1. Calculate Interest Earned<br /> Use the formula for interest earned: \( \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Days}}{360} \). Here, \( \text{Principal} = 10000 \), \( \text{Rate} = 0.015 \), and \( \text{Days} = 91 \).<br /> \[<br />\text{Interest} = 10000 \times 0.015 \times \frac{91}{360} = 37.92<br />\]<br /><br />2. Calculate Yield<br /> Use the yield formula: <br /> \[<br />\text{Yield} = \frac{\text{Interest}}{\text{Principal} + \text{Commission}}<br />\]<br /> Substitute the values:<br /> \[<br />\text{Yield} = \frac{37.92}{10000 + 30}<br />\]<br /><br />3. Convert to Percentage<br /> Multiply the yield by 100 to convert it to a percentage.<br /> \[<br />\text{Yield Percentage} = \left(\frac{37.92}{10030}\right) \times 100 = 0.378\%<br />\]
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