Question

xyz corporation invests $6,000 into 91-day treasury bills with an interest rate of 2.6%. if the broker charges a $25 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 the numerator

The numerator is \( \text{amount invested} \times \text{interest rate} \times \frac{\text{days invested}}{360} \).
Given amount invested = \( \$6000 \), interest rate = \( 2.6\% = 0.026 \), days invested = 91.
So numerator = \( 6000 \times 0.026 \times \frac{91}{360} \)
First, \( 6000 \times 0.026 = 156 \)
Then, \( 156 \times \frac{91}{360} = \frac{156\times91}{360}=\frac{14196}{360}=39.433\overline{3} \)

Step2: Calculate the denominator

The denominator is \( \text{amount invested} \times \frac{\text{days invested}}{360} + \text{commission} \).
\( \text{amount invested} \times \frac{\text{days invested}}{360}=6000\times\frac{91}{360}=\frac{546000}{360}=1516.666\overline{6} \)
Commission = \( \$25 \), so denominator = \( 1516.666\overline{6}+25 = 1541.666\overline{6} \)

Step3: Calculate the yield

Yield = \( \frac{\text{numerator}}{\text{denominator}} \times 100\% \) (since we need to express as a percentage)
Yield = \( \frac{39.433\overline{3}}{1541.666\overline{6}} \times 100\% \)
\( \frac{39.433\overline{3}}{1541.666\overline{6}} \approx 0.025577 \)
Multiply by 100%: \( 0.025577\times 100\% = 2.5577\% \approx 2.56\% \) (rounded to the nearest hundredth)

Answer:

\( 2.56\% \)