Question

treasury bills and commercial paper
xyz corporation invests $6,000 into 91-day treasury bills with an interest rate of 1.6%. if the broker charges a $30 commission, what is the yield?
yield = ?%
yield = \frac{\text{amount invested}(\text{interest rate})\left(\frac{\text{days invested}}{360\text{ days}}\
ight)}{\text{amount invested}\left(\frac{\text{days invested}}{360\text{ days}}\
ight) + \text{commission}}
give your answer as a percent rounded to the nearest hundredth.

Explanation:

Step1: Calculate numerator

First, find the numerator: \( \text{amount invested} \times \text{interest rate} \times \frac{\text{days invested}}{360} \)
Substitute values: \( 6000 \times 0.016 \times \frac{91}{360} \)
Calculate \( 6000 \times 0.016 = 96 \), then \( 96 \times \frac{91}{360} = \frac{96\times91}{360} = \frac{8736}{360} = 24.266\cdots \)

Step2: Calculate denominator

Next, find the denominator: \( \text{amount invested} \times \frac{\text{days invested}}{360} + \text{commission} \)
Substitute values: \( 6000 \times \frac{91}{360} + 30 \)
Calculate \( 6000 \times \frac{91}{360} = \frac{6000\times91}{360} = \frac{546000}{360} = 1516.666\cdots \), then add 30: \( 1516.666\cdots + 30 = 1546.666\cdots \)

Step3: Calculate yield

Now, yield is numerator divided by denominator, then multiply by 100 to get percentage: \( \frac{24.266\cdots}{1546.666\cdots} \times 100 \)
Calculate \( \frac{24.266\cdots}{1546.666\cdots} \approx 0.01569 \), then \( 0.01569 \times 100 \approx 1.57 \) (rounded to nearest hundredth)

Answer:

\( 1.57\% \)