QuestionJune 5, 2025

XYZ Corporation invests 11,000 into 91-day treasury bills with an interest rate of 2.3% . If the broker charges a 20 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 11,000 into 91-day treasury bills with an interest rate of 2.3% . If the broker charges a 20 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 11,000 into
91-day treasury bills with an interest
rate of 2.3%  . If the broker charges a
 20 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
4.7(247 votes)

Answer

The yield is approximately ( 2.28\% ). Explanation 1. Calculate Interest Earned Use the formula for interest: \( \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{360} \). Here, Principal = 11,000, Rate = 2.3\% = 0.023, Time = 91 \text{ days}. So, \( \text{Interest} = 11000 \times 0.023 \times \frac{91}{360} \). 2. Calculate Total Amount After Interest Add the interest to the principal: \( \text{Total Amount} = 11000 + \text{Interest} \). 3. Calculate Yield Use the yield formula: \[ \text{Yield} = \frac{\text{Interest}}{\text{Principal} + \text{Commission}} \times 100 \] Substitute the values: \( \text{Yield} = \frac{\text{Interest}}{11000 + 20} \times 100 \).

Explanation

1. Calculate Interest Earned<br /> Use the formula for interest: \( \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{360} \). Here, Principal = $11,000, Rate = 2.3\% = 0.023, Time = 91 \text{ days}. So, \( \text{Interest} = 11000 \times 0.023 \times \frac{91}{360} \).<br /><br />2. Calculate Total Amount After Interest<br /> Add the interest to the principal: \( \text{Total Amount} = 11000 + \text{Interest} \).<br /><br />3. Calculate Yield<br /> Use the yield formula: <br />\[ \text{Yield} = \frac{\text{Interest}}{\text{Principal} + \text{Commission}} \times 100 \]<br /> Substitute the values: \( \text{Yield} = \frac{\text{Interest}}{11000 + 20} \times 100 \).
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