Question

xyz corporation invests $13,000 into 91-day treasury bills with an interest rate of 1.8%. if the broker charges a $20 commission, what is the yield?
yield = ?%
$\text{yield} = \frac{\text{amount invested}(\text{interest rate})\left(\frac{\text{days invested}}{360\\ \text{days}}\
ight)}{\text{amount invested}\left(\frac{\text{days invested}}{360\\ \text{days}}\
ight) + \text{commission}}$
give your answer as a percent rounded to the nearest hundredth.

Explanation:

Step1: Calculate the numerator

The numerator is \( \text{amount invested} \times \text{interest rate} \times \frac{\text{days invested}}{360 \text{ days}} \).
Given \( \text{amount invested} = 13000 \), \( \text{interest rate} = 0.018 \), \( \text{days invested} = 91 \).
So numerator \( = 13000\times0.018\times\frac{91}{360} \)
\( 13000\times0.018 = 234 \)
\( 234\times\frac{91}{360}=\frac{234\times91}{360}=\frac{21294}{360} = 59.15 \)

Step2: Calculate the denominator

The denominator is \( \text{amount invested}\times\frac{\text{days invested}}{360 \text{ days}}+\text{commission} \).
\( \text{amount invested}\times\frac{\text{days invested}}{360 \text{ days}}=13000\times\frac{91}{360}=\frac{13000\times91}{360}=\frac{1183000}{360}\approx3286.11 \)
Commission is 20, so denominator \( = 3286.11 + 20=3306.11 \)

Step3: Calculate yield

Yield \(=\frac{\text{numerator}}{\text{denominator}}\times100\%=\frac{59.15}{3306.11}\times100\%\approx1.79\% \)

Answer:

\( 1.79\% \)